Peer-Reviewed Publications

* denotes equal contribution
$ denotes equal contribution
  1. L. F. Strube, S. Elgart and L. M. Childs (2024) Infection-induced increases to population size during cycles in a discrete-time epidemic model. Journal of Mathematical Biology, 88:60. doi:10.1007/s00285-024-02074-z
    Article at JOMB    Abstract
      [Hide]    One-dimensional discrete-time population models, such as those that involve Logistic or Ricker growth, can exhibit periodic and chaotic dynamics. Expanding the system by one dimension to incorporate epidemiological interactions causes an interesting complexity of new behaviors. Here, we examine a discrete-time two-dimensional susceptible-infectious (SI) model with Ricker growth and show that the introduction of infection can not only produce a distinctly different bifurcation structure than that of the underlying disease-free system but also lead to counter-intuitive increases in population size. We use numerical bifurcation analysis to determine the influence of infection on the location and types of bifurcations. In addition, we examine the appearance and extent of a phenomenon known as the ‘hydra effect,’ i.e., increases in total population size when factors, such as mortality, that act negatively on a population, are increased. Previous work, primarily focused on dynamics at fixed points, showed that the introduction of infection that reduces fecundity to the SI model can lead to a so-called ‘infection-induced hydra effect.’ Our work shows that even in such a simple two-dimensional SI model, the introduction of infection that alters fecundity or mortality can produce dynamics can lead to the appearance of a hydra effect, particularly when the disease-free population is at a cycle.
  2. L. F. Strube and L. M. Childs (2024) Multistability in a discrete-time SI epidemic model with Ricker growth: Infection-induced changes in population dynamics. In Mathematical and Computational Modeling of Phenomena Arising in Population Biology and Nonlinear Oscillations, AMS. doi:10.1090/conm/793/15902
    Book Chapter at AMS    Abstract
      [Hide]    One-dimensional discrete-time population models, such as those with logistic or Ricker growth, may exhibit periodic or chaotic dynamics depending on the parameter values. Adding epidemiological interactions into a population model increases its dimension and the resulting complexity of its dynamics. Previous work showed that a discrete susceptible-infectious-recovered (SIR) model with Ricker growth and density-dependent, non-fatal infection exhibits qualitatively similar total population dynamics in the presence and absence of disease. In contrast, a more complicated three-class susceptible-infectious-virus (SIV) system that includes disease-induced mortality does not. Instead, infection in the SIV system shifts the periodic behavior in a manner that distinguishes it from the corresponding disease-free system. Here, we examine a two-class susceptible-infectious (SI) model with Ricker population growth, density-dependent infection, and parameters that tune disease-induced mortality and the capacity of infected individuals to reproduce. We use numerical bifurcation analysis to determine the influence of infection on the qualitative structure of the long-time behavior. We show that when disease is allowed to alter reproduction or disease-induced mortality, infection produces distinctly different bifurcation structures than that of the underlying disease-free system. In particular, it shifts both the location of period-doubling bifurcations and the onset of chaos. Additionally, we show that disease-induced mortality introduces multistability into the system such that a given set of model parameters can produce multiple distinct qualitative behaviors depending upon initial conditions. This work demonstrates that the infection-induced changes in dynamics observed by previous authors do not require the presence of infecting virus particles in the environment. In doing so, our work also advances understanding of the conditions under which discrete epidemiological models exhibit multistability.
  3. T. Y. Lim, R. Xu, N. Ruktanonchai, O. Saucedo, L. M. Childs, M. S. Jalali, H. Rahmandad, and N. Ghaffarzadegan (2023) Why Similar Policies Resulted In Different COVID-19 Outcomes: How Responsiveness And Culture Influenced Mortality Rates. Health Affairs, doi:10.1377/hlthaff.2023.00713
    Article at Health Affairs    Abstract
      [Hide]    In the first two years of the COVID-19 pandemic, per capitamortality varied by more than a hundredfold across countries, despitemost implementing similar nonpharmaceutical interventions. Factorssuch as policy stringency, gross domestic product, and age distributionexplain only a small fraction of mortality variation. To address thispuzzle, we built on a previously validated pandemic model in whichperceived risk altered societal responses affecting SARS-CoV-2transmission. Using data from more than 100 countries, we found that akey factor explaining heterogeneous death rates was not the policyresponses themselves but rather variation in responsiveness.Responsiveness measures how sensitive communities are to evolvingmortality risks and how readily they adopt nonpharmaceuticalinterventions in response, to curb transmission. We further found thatresponsiveness correlated with two cultural constructs across countries:uncertainty avoidance and power distance. Our findings show that more responsive adoption of similar policies saves many lives, with important implications for the design and implementation of responses to future outbreaks.
  4. M. Walker, M. A. Robert, and L. M. Childs (2023) "Multiple Dimensions of Aedes aegypti Population Growth: Modeling the Impacts of Resource Dependence on Mass and Age at Emergence," In N. Tuncer, M. Martcheva, O. Prosper, L. M. Childs. Computational and Mathematical Population Dynamics. doi:10.1142/9789811263033_0006.
    Book Chapter at World Scientific    Abstract
      [Hide]    Mosquitoes are responsible for the transmission of many diseases which lead to a large burden on public health. The age and size of adult mosquitoes impacts their ability to transmit disease. Older mosquitoes are more likely to have acquired a pathogen, and larger mosquitoes typically have higher fitness. In this chapter, we examine how larval resources affect the age and mass distributions of adult mosquitoes. We develop a partial differential equation model of juvenile and adult mosquitoes across time, age, and mass, and we incorporate resource dependence in the juvenile growth and death functions to determine differential effects of these on mosquito population dynamics. We find that the resource-dependent growth shows much larger changes in population dynamics than resource-dependent death. Furthermore, we predict that longer oscillations in resource lead to more extreme swings in population size than shorter oscillations in resources or decaying resources. We discuss our results in the context of mitigation strategies for mosquito and mosquito-borne disease control.
  5. L. M. Childs and O. F. Prosper (2023) "Extending Analytical Solutions to Age–Mass Models of a Population," In N. Tuncer, M. Martcheva, O. Prosper, L. M. Childs. In Computational and Mathematical Population Dynamics. doi:10.1142/9789811263033_0008.
    Book chapter at World Scientific    Abstract
      [Hide]    There has been a long history of population models accounting for variations in physiological characteristics of individuals in the mathematical literature. Classically represented as the McKendrick partial differential equation (PDE) in time and age, there are multiple extensions that include, for example, mass and size. These extended equations rapidly become intractable analytically, without further simplifying assumptions, due to interconnections between the characteristics and fecundity. Here, we consider population dynamics using a three-dimensional PDE incorporating time, age, and an additional characteristic, which we consider to be mass, but without renewal. Such a scenario could represent pathogen development in a host prior to transmission. In advancement of previous work, our growth function remains a function of all three variables. Under conditions of separability, we obtain analytical results for the population dynamics. We confirm and extend these results with numerical simulations of our three-dimensional PDE. Our results can be used to understand age and characteristic, e.g., mass or size-dependent growth of populations.
  6. J. A. Tuazon, K. A. Read, B. K. Sreekumar, J. E. Roettger, M. J. Yaeger, S. Varikuti, S. Pokhrel, D. M. Jones, R. T. Warren, M. D. Powell, M. N. Rasheed, E. G. Duncan, L. M. Childs, K. M. Gowdy and K. J. Oestreich (2023) Eos Promotes TH2 Differentiation by Interacting with and Propagating the Activity of STAT5. Journal of Immunology. doi:10.4049/jimmunol.2200861.
    Article at Journal of Immunology    Abstract
      [Hide]    The Ikaros zinc-finger transcription factor Eos has largely been associated with sustaining the immunosuppressive functions of regulatory T cells. Paradoxically, Eos has more recently been implicated in promoting proinflammatory responses in the dysregulated setting of autoimmunity. However, the precise role of Eos in regulating the differentiation and function of effector CD4+ T cell subsets remains unclear. In this study, we find that Eos is a positive regulator of the differentiation of murine CD4+ TH2 cells, an effector population that has been implicated in both immunity against helminthic parasites and the induction of allergic asthma. Using murine in vitro TH2 polarization and an in vivo house dust mite asthma model, we find that EosKO T cells exhibit reduced expression of key TH2 transcription factors, effector cytokines, and cytokine receptors. Mechanistically, we find that the IL-2/STAT5 axis and its downstream TH2 gene targets are one of the most significantly downregulated pathways in Eos-deficient cells. Consistent with these observations, we find that Eos forms, to our knowledge, a novel complex with and supports the tyrosine phosphorylation of STAT5. Collectively, these data define a regulatory mechanism whereby Eos propagates STAT5 activity to facilitate TH2 cell differentiation.
  7. M. A. Greischar and L. M. Childs (2023) Extraordinary parasite multiplication rates in human malaria infections. Trends in Parasitology. doi:10.1016/
    Article at Trends in Parasitology    Abstract
      [Hide]    For pathogenic organisms, faster rates of multiplication promote transmission success, the potential to harm hosts, and the evolution of drug resistance. Parasite multiplication rates (PMRs) are often quantified in malaria infections, given the relative ease of sampling. Using modern and historical human infection data, we show that established methods return extraordinarily - and implausibly - large PMRs. We illustrate how inflated PMRs arise from two facets of malaria biology that are far from unique: (i) some developmental ages are easier to sample than others; (ii) the distribution of developmental ages changes over the course of infection. The difficulty of accurately quantifying PMRs demonstrates a need for robust methods and a subsequent re-evaluation of what is known even in the well-studied system of malaria.
  8. Z. Qu, D. Patterson, L. M. Childs, C. J. Edholm, J. Ponce, O. F. Prosper, and L. Zhao (2023) Modeling Immunity to Malaria with an Age-Structured PDE Framework. SIAP. doi:10.1137/21M1464427.
    Article at SIAM Applied Math    Abstract
      [Hide]    Malaria is one of the deadliest infectious diseases globally, causing hundreds of thousands of deaths each year. It disproportionately affects young children, with two-thirds of fatalities occurring in under-fives. Individuals acquire protection from disease through repeated exposure, and this immunity plays a crucial role in the dynamics of malaria spread. We develop a novel age-structured PDE malaria model, which couples vector-host epidemiological dynamics with immunity dynamics. Our model tracks the acquisition and loss of antidisease immunity during transmission and its corresponding nonlinear feedback onto the transmission parameters. We derive the basic reproduction number (R0) as the threshold condition for the stability of disease-free equilibrium; we also interpret R0 probabilistically as a weighted sum of cases generated by infected individuals at different infectious stages and different ages. We parametrize our model using demographic and immunological data from sub-Saharan regions. Numerical bifurcation analysis demonstrates the existence of an endemic equilibrium, and we observe a forward bifurcation in R0. Our numerical simulations reproduce the heterogeneity in the age distributions of immunity profiles and infection status created by frequent exposure. Motivated by the recently approved RTS,S vaccine, we also study the impact of vaccination; our results show a reduction in severe disease among young children but a small increase in severe malaria among older children due to lower acquired immunity from delayed exposure.
  9. K. Shea, R. K. Borchering, W. J. M. Probert, E. Howerton, T. L. Bogich, S.-L. Li, W. G. van Panhuis, C. Viboud, R. Aguás, A. A. Belov, S. H. Bhargava, S. M. Cavany, J. C. Chang, C. Chen, J. Chen, S. Chen, Y. Chen, L. M. Childs, C. C. Chow, I. Crooker, S. Y. Del Valle, G. España, G. Fairchild, R. C. Gerkin, T. C. Germann, Q. Gu, X. Guan, L. Guo, G. R. Hart, T. J. Hladish, N. Hupert, D. Janies, C. C. Kerr, D. J. Klein, E. Y. Klein, G. Lin, C. Manore, L. Ancel Meyers, J. E. Mittler, K. Mu, R. C. Núñez, R. J. Oidtman, R. Pasco, A. Pastore y Piontti, R. Paul, C. A. B. Pearson, D. R. Perdomo, T. A. Perkins, K. Piercei, A. N. Pillai, R. C. Rael, K. Rosenfeld, C. W. Ross, J. A. Spencer, A. B. Stoltzfus, K. B. Toh, S. Vattikuti, A. Vespignani, L. Wang, L. J. White, P. Xu, Y. Yang, O. N. Yogurtcu, W. Zhang, Y. Zhao, D. Zou, M. J. Ferrari, D. Pannell, M. J. Tildesley, J. Seifarth, E. Johnson, M. Biggerstaff, M. A. Johansson, R. B. Slayton, J. D. Levander, J. Stazer, J. Kerr, and M. C. Runge (2023) Multiple models for outbreak decision support in the face of uncertainty. PNAS. doi:10.1073/pnas.2207537120.
    Article at PNAS    Abstract
      [Hide]    Policymakers must make management decisions despite incomplete knowledge and conflicting model projections. Little guidance exists for the rapid, representative, and unbiased collection of policy-relevant scientific input from independent modeling teams. Integrating approaches from decision analysis, expert judgment, and model aggregation, we convened multiple modeling teams to evaluate COVID-19 reopening strategies for a mid-sized United States county early in the pandemic. Projections from seventeen distinct models were inconsistent in magnitude but highly consistent in ranking interventions. The 6-mo-ahead aggregate projections were well in line with observed outbreaks in mid-sized US counties. The aggregate results showed that up to half the population could be infected with full workplace reopening, while workplace restrictions reduced median cumulative infections by 82%. Rankings of interventions were consistent across public health objectives, but there was a strong trade-off between public health outcomes and duration of workplace closures, and no win-win intermediate reopening strategies were identified. Between-model variation was high; the aggregate results thus provide valuable risk quantification for decision making. This approach can be applied to the evaluation of management interventions in any setting where models are used to inform decision making. This case study demonstrated the utility of our approach and was one of several multimodel efforts that laid the groundwork for the COVID-19 Scenario Modeling Hub, which has provided multiple rounds of real-time scenario projections for situational awareness and decision making to the Centers for Disease Control and Prevention since December 2020.
  10. A. M. Early, F. Camponovo, S. Pelleau, G. C. Cerqueira, Y. Lazrek, B. Volney, M. Carrasquilla, B. Thoisy, C. O. Buckee, L. M. Childs, L. Musset, and D. E. Neafsey (2022) Declines in prevalence alter the optimal level of sexual investment for the malaria parasite Plasmodium falciparum. PNAS. doi:10.1073/pnas.2122165119.
    Article at PNAS    Abstract
      [Hide]    Successful infectious disease interventions can result in large reductions in parasite prevalence. Such demographic change has fitness implications for individual parasites and may shift the parasite’s optimal life history strategy. Here, we explore whether declining infection rates can alter Plasmodium falciparum’s investment in sexual versusasexual growth. Using a multiscale mathematical model, we demonstrate how the proportion of polyclonal infections, which decreases as parasite prevalence declines, affects the optimal sexual development strategy: Within-host competition in multiclone infections favors a greater investment in asexual growth whereas single-clone infections benefit from higher conversion to sexual forms. At the same time, drug treatment also imposes selection pressure on sexual development by shortening infection length and reducing within-host competition. We assess these models using 148 P. falciparum parasite genomes sampled in French Guiana over an 18-y period of intensive intervention (1998 to 2015). During this time frame, multiple public health measures, including the introduction of new drugs and expanded rapid diagnostic testing, were implemented, reducing P. falciparum malaria cases by an order of magnitude. Consistent with this prevalence decline, we see an increase in the relatedness among parasites, but no single clonal background grew to dominate the population. Analyzing individual allele frequency trajectories, we identify genes that likely experienced selective sweeps. Supporting our model predictions, genes showing the strongest signatures of selection include transcription factors involved in the development of P. falciparum’s sexual gametocyte form. These results highlight how public health interventions impose wide-ranging selection pressures that affect basic parasite life history traits.
  11. L. M. Childs, D. W. Dick, Z. Feng, J. M. Heffernan, J. Li, G. Rost (2022) Modeling waning and boosting of COVID-19 in Canada with vaccination. Epidemics. doi:10.1016/j.epidem.2022.100583.
    Article at Epidemics     Abstract
      [Hide]    SARS-CoV-2, the causative agent of COVID-19, has caused devastating health and economic impacts around the globe since its appearance in late 2019. The advent of effective vaccines leads to open questions on how best to vaccinate the population. To address such questions, we developed a model of COVID-19 infection by age that includes the waning and boosting of immunity against SARS-CoV-2 in the context of infection and vaccination. The model also accounts for changes to infectivity of the virus, such as public health mitigation protocols over time, increases in the transmissibility of variants of concern, changes in compliance to mask wearing and social distancing, and changes in testing rates. The model is employed to study public health mitigation and vaccination of the COVID-19 epidemic in Canada, including different vaccination programs (rollout by age), and delays between doses in a two-dose vaccine. We find that the decision to delay the second dose of vaccine is appropriate in the Canadian context. We also find that the benefits of a COVID-19 vaccination program in terms of reductions in infections is increased if vaccination of 15–19 year olds are included in the vaccine rollout.
  12. D. W. Dick, L. M. Childs, Z. Feng, J. Li, G. Rost, D. L. Buckeridge, N. H. Ogden, and J. M. Heffernan (2021) COVID-19 Seroprevalence in Canada ModellingWaning and Boosting COVID-19 Immunity in Canada a Canadian Immunization Research Network Study. Vaccines. doi:10.3390/vaccines10010017.
    Article at Vaccines     Abstract
      [Hide]    COVID-19 seroprevalence changes over time, with infection, vaccination, and waning immunity. Seroprevalence estimates are needed to determine when increased COVID-19 vaccination coverage is needed, and when booster doses should be considered, to reduce the spread and disease severity of COVID-19 infection. We use an age-structured model including infection, vaccination and waning immunity to estimate the distribution of immunity to COVID-19 in the Canadian population. This is the first mathematical model to do so. We estimate that 60–80% of the Canadian population has some immunity to COVID-19 by late Summer 2021, depending on specific characteristics of the vaccine and the waning rate of immunity. Models results indicate that increased vaccination uptake in age groups 12–29, and booster doses in age group 50+ are needed to reduce the severity COVID-19 Fall 2021 resurgence.
  13. R. I. Mukhamadiarov, S. Deng, S. R. Serrao, Priyanka, L. M. Childs, Uwe C. Tauber (2021) Requirements for the containment of COVID-19 disease outbreaks through periodic testing, isolation, and quarantine. Journal of Physics A: Mathematical and Theoretical. doi:10.1088/1751-8121/ac3fc3.
    Article at Journal of Physics A     Abstract
      [Hide]    We employ individual-based Monte Carlo computer simulations of a stochastic SEIR model variant on a two-dimensional Newman-Watts small-world network to investigate the control of epidemic outbreaks through periodic testing and isolation of infectious individuals, and subsequent quarantine of their immediate contacts. Using disease parameters informed by the COVID-19 pandemic, we investigate the effects of various crucial mitigation features on the epidemic spreading: fraction of the infectious population that is identifiable through the tests; testing frequency; time delay between testing and isolation of positively tested individuals; and the further time delay until quarantining their contacts as well as the quarantine duration. We thus determine the required ranges for these intervention parameters to yield effective control of the disease through both considerable delaying the epidemic peak and massively reducing the total number of sustained infections.
  14. M. Walker, K. Chandrasegaran, C. Vinauger, M. A. Robert, L. M. Childs (2021) Modeling the effect of Aedes aegypti's larval environment on adult body mass at emergence. PLOS Computational Biology. doi:10.1371/journal.pcbi.1009102.
    Article at PLOS Computational Biology     Abstract
      [Hide]    Mosquitoes vector harmful pathogens that infect millions of people every year, and developing approaches to effectively control mosquitoes is a topic of great interest. However, the success of many control measures is highly dependent upon ecological, physiological, and life history traits of mosquito species. The behavior of mosquitoes and their potential to vector pathogens can also be impacted by these traits. One trait of interest is mosquito body mass, which depends upon many factors associated with the environment in which juvenile mosquitoes develop. Our experiments examined the impact of larval density on the body mass of Aedes aegypti mosquitoes, which are important vectors of dengue, Zika, yellow fever, and other pathogens. To investigate the interactions between the larval environment and mosquito body mass, we built a discrete time mathematical model that incorporates body mass, larval density, and food availability and fit the model to our experimental data. We considered three categories of model complexity informed by data, and selected the best model within each category using Akaike’s Information Criterion. We found that the larval environment is an important determinant of the body mass of mosquitoes upon emergence. Furthermore, we found that larval density has greater impact on body mass of adults at emergence than on development time, and that inclusion of density dependence in the survival of female aquatic stages in models is important. We discuss the implications of our results for the control of Aedes mosquitoes and on their potential to spread disease.
  15. L. Strube, M. Walton, L. M. Childs (2021) Role of repeat infection in the dynamics of a simple model of waning and boosting immunity. Journal of Biological Systems. doi:10.1142/S021833902140012X.
    Article at JBS     Abstract
      [Hide]    Some infectious diseases produce lifelong immunity while others only produce temporary immunity. In the case of short-lived immunity, the level of protection wanes over time and may be boosted upon re-exposure, via infection or vaccination. Previous work developed a simple model capturing waning and boosting immunity, known as the Susceptible-Infectious-Recovered-Waned-Susceptible (SIRWS) model, which exhibits rich dynamical behavior including supercritical and subcritical Hopf bifurcations among other structures. Here, we extend the bifurcation analyses of the SIRWS model to examine the influence of all parameters on these bifurcation structures. We show that the bistable region, involving both a stable fixed point and a stable limit cycle, exists only for a small region of biologically realistic parameter space. Furthermore, we contrast the SIRWS model with a modified version, where immune boosting may involve the occurrence of a secondary infection. Analysis of this extended model shows that oscillations and bistability, as found in the SIRWS model, depend on strong assumptions about infectivity and recovery rate from secondary infection. Understanding the dynamics of models of waning and boosting immunity is important for accurately assessing epidemiological data.
  16. E. Stump, L. M. Childs, M. Walker, (2021) Parasitism of Aedes albopictus by Ascogregarina taiwanensis lowers its competitive ability against Aedes triseriatus. Parasites and Vectors. doi:10.1186/s13071-021-04581-0.
    Article at Parasites and Vectors     Abstract
      [Hide]    Background: Mosquitoes are vectors for diseases such as dengue, malaria and La Crosse virus that significantly impact the human population. When multiple mosquito species are present, the competition between species may alter population dynamics as well as disease spread. Two mosquito species, Aedes albopictus and Aedes triseriatus, both inhabit areas where La Crosse virus is found. Infection of Aedes albopictus by the parasite Ascogregarina taiwanensis and Aedes triseriatus by the parasite Ascogregarina barretti can decrease a mosquito’s fitness, respectively. In particular, the decrease in fitness of Aedes albopictus occurs through the impact of Ascogregarina taiwanensis on female fecundity, larval development rate, and larval mortality and may impact its initial competitive advantage over Aedes triseriatus during invasion. Methods: We examine the effects of parasitism of gregarine parasites on Aedes albopictus and triseriatus population dynamics and competition with a focus on when Aedes albopictus is new to an area. We build a compartmental model including competition between Aedes albopictus and triseriatus while under parasitism of the gregarine parasites. Using parameters based on the literature, we simulate the dynamics and analyze the equilibrium population proportion of the two species. We consider the presence of both parasites and potential dilution effects. Results: We show that increased levels of parasitism in Aedes albopictus will decrease the initial competitive advantage of the species over Aedes triseriatus and increase the survivorship of Aedes triseriatus. We find Aedes albopictus is better able to invade when there is more extreme parasitism of Aedes triseriatus. Furthermore, although the transient dynamics differ, dilution of the parasite density through uptake by both species does not alter the equilibrium population sizes of either species. Conclusions: Mosquito population dynamics are affected by many factors, such as abiotic factors (e.g. temperature and humidity) and competition between mosquito species. This is especially true when multiple mosquito species are vying to live in the same area. Knowledge of how population dynamics are affected by gregarine parasites among competing species can inform future mosquito control efforts and help prevent the spread of vector-borne disease.
  17. W. R. Shaw*, I. E. Holmdahl*, M. A. Itoe, K. Werling, M. Marquette, D. G. Paton, N. Singh, C. O. Buckee, L. M. Childs$, F. Catteruccia$, (2020) Multiple blood feeding in mosquitoes shortens the Plasmodium falciparum incubation period and increases malaria transmission potential. PLOS Pathogens. doi:10.1371/journal.ppat.1009131.
    Article at PLOS Pathogens     Abstract
      [Hide]    Many mosquito species, including the major malaria vector Anopheles gambiae, naturally undergo multiple reproductive cycles of blood feeding, egg development and egg laying in their lifespan. Such complex mosquito behavior is regularly overlooked when mosquitoes are experimentally infected with malaria parasites, limiting our ability to accurately describe potential effects on transmission. Here, we examine how Plasmodium falciparum development and transmission potential is impacted when infected mosquitoes feed an additional time. We measured P. falciparum oocyst size and performed sporozoite time course analyses to determine the parasite’s extrinsic incubation period (EIP), i.e. the time required by parasites to reach infectious sporozoite stages, in An. gambiae females blood fed either once or twice. An additional blood feed at 3 days post infection drastically accelerates oocyst growth rates, causing earlier sporozoite accumulation in the salivary glands, thereby shortening the EIP (reduction of 2.3 ± 0.4 days). Moreover, parasite growth is further accelerated in transgenic mosquitoes with reduced reproductive capacity, which mimic genetic modifications currently proposed in population suppression gene drives. We incorporate our shortened EIP values into a measure of transmission potential, the basic reproduction number R0, and find the average R0 is higher (range: 10.1%–12.1% increase) across sub-Saharan Africa than when using traditional EIP measurements. These data suggest that malaria elimination may be substantially more challenging and that younger mosquitoes or those with reduced reproductive ability may provide a larger contribution to infection than currently believed. Our findings have profound implications for current and future mosquito control interventions.
  18. M. Walker, M. Robert, L. M. Childs, (2020) he importance of density dependence in juvenile mosquito development and survival: A model-based investigation. Ecological Modelling. doi:10.1016/j.ecolmodel.2020.109357
    Article at Ecological Modelling     Abstract
      [Hide]    Mosquitoes are vectors of numerous pathogens that cause infectious diseases, and they pose a significant global health burden as a result. As such, more reliable field-relevant models to study mosquito population dynamics and life history traits such as development time and survival of mosquito larva would be of great value. In Aedes mosquitoes, progression through early life stages is known to be density-dependent. Despite its importance, density dependence is largely ignored or oversimplified in many existing simulation models, leading to less accurate predictions of development and survival during the early life stages. Furthermore, density dependence is frequently assumed to impact only larval survival and not development time in models, despite empirical evidence for density-dependent development. Here, we develop a discrete-time model of mosquito larval population dynamics which accounts for density impacts on both survival and development time. We demonstrate the validity of our model using publicly available semi-field data of larval density and pupation time across a six-month experiment. Using our model, we found that incorporating density dependence during larval development is important to the accurate prediction of mosquito pupation. This is especially true when considering density-dependent development time for mosquito larva as opposed to density-dependent larval survival. We determined that the incorporation of simple functional forms to describe density dependence in simulation models gives improved prediction results over models that ignore density dependence entirely. Such simple functional forms can easily be incorporated into existing models, and thus help improve field-relevant models of mosquito population dynamics, particularly in Aedes and other container-inhabiting mosquitoes that are known to experience density dependence during larval development.
  19. L. M. Childs*, O. F. Prosper*, (2020) The impact of within-vector parasite development on the extrinsic incubation period. Open Science. doi:10.1098/rsos.192173
    Article at Royal Society Open Science     Abstract
      [Hide]    Mosquito-borne diseases, in particular malaria, have a significant burden worldwide leading to nearly half a million deaths each year. The malaria parasite requires a vertebrate host, such as a human, and a vector host, the Anopheles mosquito, to complete its full life cycle. Here, we focus on the parasite dynamics within the vector to examine the first appearance of sporozoites in the salivary glands, which indicates a first time of infectiousness of mosquitoes. The timing of this period of pathogen development in the mosquito until transmissibility, known as the extrinsic incubation period, remains poorly understood. We develop compartmental models of within-mosquito parasite dynamics fitted with experimental data on oocyst and sporozoite counts. We find that only a fraction of oocysts burst to release sporozoites and bursting must be delayed either via a time-dependent function or a gamma-distributed set of compartments. We use Bayesian inference to estimate distributions of parameters and determine that bursting rate is a key epidemiological parameter. A better understanding of the factors impacting the extrinsic incubation period will aid in the development of interventions to slow or stop the spread of malaria.
  20. C. M. Peak, R. Kahn, Y. H. Grad, L. M. Childs, R. Li, M. Lipsitch, C. O. Buckee (2020) Modeling the comparative impact of individual quarantine vs. active monitoring of contacts for the mitigation of COVID-19. The Lancet Infectious Diseases. doi:10.1016/S1473-3099(20)30361-3.
    Article at The Lancet Infectious Diseases     Abstract
      [Hide]    Background: Voluntary individual quarantine and voluntary active monitoring of contacts are core disease control strategies for emerging infectious diseases such as COVID-19. Given the impact of quarantine on resources and individual liberty, it is vital to assess under what conditions individual quarantine can more effectively control COVID-19 than active monitoring. As an epidemic grows, it is also important to consider when these interventions are no longer feasible and broader mitigation measures must be implemented. Methods: To estimate the comparative efficacy of individual quarantine and active monitoring of contacts to control severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), we fit a stochastic branching model to reported parameters for the dynamics of the disease. Specifically, we fit a model to the incubation period distribution (mean 5·2 days) and to two estimates of the serial interval distribution: a shorter one with a mean serial interval of 4·8 days and a longer one with a mean of 7·5 days. To assess variable resource settings, we considered two feasibility settings: a high-feasibility setting with 90% of contacts traced, a half-day average delay in tracing and symptom recognition, and 90% effective isolation; and a low-feasibility setting with 50% of contacts traced, a 2-day average delay, and 50% effective isolation. Findings: Model fitting by sequential Monte Carlo resulted in a mean time of infectiousness onset before symptom onset of 0·77 days (95% CI −1·98 to 0·29) for the shorter serial interval, and for the longer serial interval it resulted in a mean time of infectiousness onset after symptom onset of 0·51 days (95% CI −0·77 to 1·50). Individual quarantine in high-feasibility settings, where at least 75% of infected contacts are individually quarantined, contains an outbreak of SARS-CoV-2 with a short serial interval (4·8 days) 84% of the time. However, in settings where the outbreak continues to grow (eg, low-feasibility settings), so too will the burden of the number of contacts traced for active monitoring or quarantine, particularly uninfected contacts (who never develop symptoms). When resources are prioritised for scalable interventions such as physical distancing, we show active monitoring or individual quarantine of high-risk contacts can contribute synergistically to mitigation efforts. Even under the shorter serial interval, if physical distancing reduces the reproductive number to 1·25, active monitoring of 50% of contacts can result in overall outbreak control (ie, effective reproductive number <1). Interpretation: Our model highlights the urgent need for more data on the serial interval and the extent of presymptomatic transmission to make data-driven policy decisions regarding the cost–benefit comparisons of individual quarantine versus active monitoring of contacts. To the extent that these interventions can be implemented, they can help mitigate the spread of SARS-CoV-2.
  21. R.-M. Carlsson, L. M. Childs, Z. Feng, J. W. Glasser, J. M. Heffernan, J. Li, G. Rost (2020) Modeling the waning and boosting of immunity from infection or vaccination. Journal of Theoretical Biology. doi:10.1016/j.jtbi.2020.110265.
    Article at JTB     Abstract
      [Hide]    Immunity following natural infection or immunization may wane, increasing susceptibility to infection with time since infection or vaccination. Symptoms, and concomitantly infectiousness, depend on residual immunity. We quantify these phenomena in a model population composed of individuals whose susceptibility, infectiousness, and symptoms all vary with immune status. We also model age, which affects contact, vaccination and possibly waning rates. The resurgences of pertussis that have been observed wherever effective vaccination programs have reduced typical disease among young children follow from these processes. As one example, we compare simulations with the experience of Sweden following resumption of pertussis vaccination after the hiatus from 1979 to 1996, reproducing the observations leading health authorities to introduce booster doses among school-aged children and adolescents in 2007 and 2014, respectively. Because pertussis comprises a spectrum of symptoms, only the most severe of which are medically attended, accurate models are needed to design optimal vaccination programs where surveillance is less effective.
  22. L. M. Childs, R. Hughes, J. C. Blackwood (2020) The role of increased gonotrophic cycles in the establishment of Wolbachia in Anopheles populations. Theoretical Ecology. doi:10.1007/s12080-020-00457-8
    Article at Theoretical Ecology     Abstract
      [Hide]    Wolbachia, a bacterium that infects insect populations, has been examined extensively in Drosophila populations and, in recent years, has garnered significant attention for its potential to reduce the spread of dengue in the Aedes mosquito population. Similar applications to Anopheles mosquitoes for the reduction of malaria have not been as thoroughly studied, as Anopheles were previously thought to be devoid of Wolbachia infection. The recent discovery, however, of Wolbachia in two separate wild Anopheles populations suggests further study is needed. We develop and analyze an ordinary differential equation model of Wolbachia infection in Anopheles mosquitoes, which demonstrate different reproductive phenotypes than Aedes mosquitoes when infected with Wolbachia. In particular, they do not show the hallmark cytoplasmic incompatibility phenotype - absence of viable offspring when infected males mate with uninfected females - or other standard sex-biasing phenotypes. Instead, evidence of increased speed of gonotrophic cycles by Wolbachia-infected females has been reported. We show that the ability for Wolbachia to invade for a basic reproductive number less than one (R_pop<1), found in other models, is significantly diminished here. However, the invasion threshold below R_pop<1 can be partially recovered with the increased speed of laying eggs, as incorporated through gonotrophic cycles. Our results highlight the need for further experimental and theoretical work if Wolbachia is to be considered as a form of malaria control.
  23. S. Erwin, L. M. Childs, S. M. Ciupe (2020) Mathematical model of broadly reactive plasma cell production. Scientific Reports. doi:10.1038/s41598-020-60316-8.
    Article at Scientific Reports     Abstract
      [Hide]    Strain-specifc plasma cells are capable of producing neutralizing antibodies that are essential for clearance of challenging pathogens. These neutralizing antibodies also function as a main defense against disease establishment in a host. However, when a rapidly mutating pathogen infects a host, successful control of the invasion requires shifting the production of plasma cells from strain-specifc to broadly reactive. In this study, we develop a mathematical model of germinal center dynamics and use it to predict the events that lead to improved breadth of the plasma cell response. We examine scenarios that lead to germinal centers that are composed of B-cells that come from a single strain-specifc clone, a single broadly reactive clone or both clones. We fnd that the initial B-cell clonal composition, T-follicular helper cell signaling, increased rounds of productive somatic hypermutation, and B-cell selection strength are among the mechanisms diferentiating between strain-specifc and broadly reactive plasma cell production during infections. Understanding the contribution of these factors to emergence of breadth may assist in boosting broadly reactive plasma cells production.
  24. L. M. Childs, D. B. Larremore (2020) Network Models for Malaria: Antigens, Dynamics, and Evolution Over Space and Time. In Reference Module in Biomedical Sciences, Elsevier. doi:10.1016/B978-0-12-801238-3.11512-0
    Book Chapter at Elsevier     Abstract
      [Hide]    Networks provide a flexible and powerful data structure for analysis of complex relationships, from genes and genomes, to geographical transmission regions. Recent advances in statistical inference, community detection, multilayer methods, and network visualization, now allow network analyses to be conducted rapidly, at large scale, and increasingly with statistical substantiation. In this Review Article, we summarize the various ways in which networks have been used to understand malaria parasites, primarily focused on genetics and genomics, but also touching on epidemiology and immunology. This review is written for the reader who does not have extensive experience with networks but is interested in learning about them and their applications for understanding and interpreting malaria antigenic diversity, evolution and transmission.
  25. M. A. Greischar, H. K. Alexander, F. Bashey, A. I. Bento, A. Bhattacharya, M. Bushman, L. M. Childs, D. R. Daversa, T. Day, C. L. Faust, M. E. Gallagher, S. Gandon, C. K. Glidden, F. W. Halliday, K. A. Hanley, T. Kamiya, A. F. Read, P. Schwabl, A. R. Sweeny, A. T. Tate, R. N. Thompson, N. Wale, H. J. Wearing, P. J. Yeh, N. Mideo (2020) Evolutionary consequences of feedbacks between within-host competition and disease control. Evolution, Medicine and Public Health. doi:10.1093/emph/eoaa004
    Article at Evol, Med & Public Health     Abstract
      [Hide]    Competition often occurs among diverse parasites within a single host, but control efforts could change its strength. We examined how the interplay between competition and control could shape the evolution of parasite traits like drug resistance and disease severity.
  26. L. M. Childs, F. El Moustaid, Z. Gajewski, S. Kadelka, R. Nikin-Beers, J. W. Smith, Jr., M. Walker, L. R. Johnson (2019) Linked within-host and between-host models and data for infectious diseases: a systematic review. PeerJ. doi:10.7717/peerj.7057
    Article at PeerJ     Abstract
      [Hide]    The observed dynamics of infectious diseases are driven by processes across multiple scales. Here we focus on two: within-host, that is, how an infection progresses inside a single individual (for instance viral and immune dynamics), and between-host, that is, how the infection is transmitted between multiple individuals of a host population. The dynamics of each of these may be influenced by the other, particularly across evolutionary time. Thus understanding each of these scales, and the links between them, is necessary for a holistic understanding of the spread of infectious diseases. One approach to combining these scales is through mathematical modeling. We conducted a systematic review of the published literature on multi-scale mathematical models of disease transmission (as defined by combining within-host and between-host scales) to determine the extent to which mathematical models are being used to understand across-scale transmission, and the extent to which these models are being confronted with data. Following the PRISMA guidelines for systematic reviews, we identified 24 of 197 qualifying papers across 30 years that include both linked models at the within and between host scales and that used data to parameterize/calibrate models. We find that the approach that incorporates both modeling with data is under-utilized, if increasing. This highlights the need for better communication and collaboration between modelers and empiricists to build well-calibrated models that both improve understanding and may be used for prediction.
  27. D. G. Paton, L. M. Childs, M. A. Itoe, I. E. Holmdahl, C. O. Buckee, F. Catteruccia (2019) Exposing Anopheles mosquitoes to antimalarials blocks Plasmodium parasite transmission. Nature. doi:10.1038/s41586-019-0973-1
    Article at Nature     Abstract
      [Hide]    Bites of Anopheles mosquitoes transmit Plasmodium falciparum parasites that cause malaria, which kills hundreds of thousands of people every year. Since the turn of this century, efforts to prevent the transmission of these parasites via the mass distribution of insecticide-treated bed nets have been extremely successful, and have led to an unprecedented reduction in deaths from malaria. However, resistance to insecticides has become widespread in Anopheles populations, which has led to the threat of a global resurgence of malaria and makes the generation of effective tools for controlling this disease an urgent public health priority. Here we show that the development of P. falciparum can be rapidly and completely blocked when female Anopheles gambiae mosquitoes take up low concentrations of specific antimalarials from treated surfaces—conditions that simulate contact with a bed net. Mosquito exposure to atovaquone before, or shortly after, P. falciparum infection causes full parasite arrest in the midgut, and prevents transmission of infection. Similar transmission-blocking effects are achieved using other cytochrome b inhibitors, which demonstrates that parasite mitochondrial function is a suitable target for killing parasites. Incorporating these effects into a model of malaria transmission dynamics predicts that impregnating mosquito nets with Plasmodium inhibitors would substantially mitigate the global health effects of insecticide resistance. This study identifies a powerful strategy for blocking Plasmodium transmission by female Anopheles mosquitoes, which has promising implications for efforts to eradicate malaria.
  28. J. C. Blackwood, L. M. Childs (2018) An introduction to compartmental modeling for the budding infectious disease modeler. Letters in Biomathematics. doi:10.1080/23737867.2018.1509026
    Article at Letters in Biomath     Abstract
      [Hide]    Mathematical models are ubiquitous in the study of the transmission dynamics of infectious diseases, In particular, the classic ‘susceptible-infectious-recovered’ (SIR) paradigm provides a modeling framework that can be adapted to describe the core transmission dynamics of a range of human and wildlife diseases. These models provide an important tool for uncovering the mechanisms generating observed disease dynamics, evaluating potential control strategies, and predicting future outbreaks. With ongoing advances in computational tools as well as access to disease incidence data, the use of such models continues to increase. Here, we provide a basic introduction to disease modeling that is primarily intended for individuals who are new to developing SIR-type models. In particular, we highlight several common issues encountered when structuring and analyzing these models.
  29. N. M. Archer, N. Petersen, M. A. Clark, C. O. Buckee, L. M. Childs, M. T. Duraisingh (2018) Resistance to Plasmodium falciparum in sickle cell trait erythrocytes is driven by oxygen-dependent growth inhibition. PNAS. doi:10.1073/pnas.1804388115
    Article at PNAS     Abstract
      [Hide]    Sickle cell trait (AS) confers partial protection against lethal Plasmodium falciparum malaria. Multiple mechanisms for this have been proposed, with a recent focus on aberrant cytoadherence of parasite-infected red blood cells (RBCs). Here we investigate the mechanistic basis of AS protection through detailed temporal mapping. We find that parasites in AS RBCs maintained at low oxygen concentrations stall at a specific stage in the middle of intracellular growth before DNA replication. We demonstrate that polymerization of sickle hemoglobin (HbS) is responsible for this growth arrest of intraerythrocytic P. falciparum parasites, with normal hemoglobin digestion and growth restored in the presence of carbon monoxide, a gaseous antisickling agent. Modeling of growth inhibition and sequestration revealed that HbS polymerization-induced growth inhibition following cytoadherence is the critical driver of the reduced parasite densities observed in malaria infections of individuals with AS. We conclude that the protective effect of AS derives largely from effective sequestration of infected RBCs into the hypoxic microcirculation.
  30. M. Walker, J. C. Blackwood, V. Brown, L. M. Childs (2018) Modelling Allee effects in a transgenic mosquito population during range expansion. Journal of Biological Dynamics. doi:10.1080/17513758.2018.1464219
    Article at JBD     Abstract
      [Hide]    Mosquitoes are vectors for many diseases that cause significant mortality and morbidity. As mosquito populations expand their range, they may undergo mate-finding Allee effects such that their ability to successfully reproduce becomes difficult at low population density. With new technology, creating target specific gene modification may be a viable method for mosquito population control. We develop a mathematical model to investigate the effects of releasing transgenic mosquitoes into newly established, low-density mosquito populations. Our model consists of two life stages (aquatic and adults), which are divided into three genetically distinct groups: heterogeneous and homogeneous transgenic that cause female infertility and a homogeneous wild type. We perform analytical and numerical analyses on the equilibria to determine the level of saturation needed to eliminate mosquitoes in a given area. This model demonstrates the potential for a gene drive system to reduce the spread of invading mosquito populations.
  31. R. Nikin-Beers, J. C. Blackwood, L. M. Childs, S. M. Ciupe, (2018) Unraveling within-host signatures of dengue infection at the population level. Journal of Theoretical Biology. doi:10.1016/j.jtbi.2018.03.004
    Article via PubMed     Abstract
      [Hide]    Dengue virus causes worldwide concern with nearly 100 million infected cases reported annually. The within-host dynamics differ between primary and secondary infections, where secondary infections with a different virus serotype typically last longer, produce higher viral loads, and induce more severe disease. We build upon the variable within-host virus dynamics during infections resulting in mild dengue fever and severe dengue hemorrhagic fever. We couple these within-host virus dynamics to a population-level model through a system of partial differential equations creating an immuno-epidemiological model. The resulting multiscale model examines the dynamics of between-host infections in the presence of two circulating virus strains that involves feedback from the within-host and between-hosts interactions, encompassing multiple scales. We analytically determine the relationship between the model parameters and the characteristics of the model’s solutions, and find an analytical threshold under which infections persist in the population. Furthermore, we develop and implement a full numerical scheme for our immuno-epidemiological model, allowing the simulation of population dynamics under variable parameter conditions.
  32. O. Maxian*, A. Neufeld*, E. J. Talis*, L. M. Childs$, J. C. Blackwood$, (2017) Zika virus dynamics: When does sexual transmission matter? Epidemics. doi:10.1016/j.epidem.2017.06.003
    Article via Science Direct     Abstract
      [Hide]    The Zika virus (ZIKV) has captured worldwide attention with the ongoing epidemic in South America and its link to severe birth defects, most notably microcephaly. ZIKV is spread to humans through a combination of vector and sexual transmission, but the relative contribution of these transmission routes to the overall epidemic remains largely unknown. Furthermore, a disparity in the reported number of infections between males and females has been observed. We develop a mathematical model that describes the transmission dynamics of ZIKV to determine the processes driving the observed epidemic patterns. Our model reveals a 4.8% contribution of sexual transmission to the basic reproductive number, R0. This contribution is too minor to independently sustain an outbreak but suggests that vector transmission is the main driver of the ongoing epidemic. We also find a minor, yet statistically significant, difference in the mean number of cases in males and females, both at the peak of the epidemic and at equilibrium. While this suggests an intrinsic disparity between males and females, the differences do not account for the vastly greater number of reported cases for females, indicative of a large reporting bias. In addition, we identify conditions under which sexual transmission may play a key role in sparking an epidemic, including temperate areas where ZIKV mosquito vectors are less prevalent.
  33. L. M. Childs*, O. F. Prosper*, (2017) Simulating within-vector generation of the malaria parasite diversity. PLoS One. doi:10.1371/journal.pone.0177941
    Article at PLOS One     Abstract
      [Hide]    Plasmodium falciparum, the most virulent human malaria parasite, undergoes asexual reproduction within the human host, but reproduces sexually within its vector host, the Anopheles mosquito. Consequently, the mosquito stage of the parasite life cycle provides an opportunity to create genetically novel parasites in multiply-infected mosquitoes, potentially increasing parasite population diversity. Despite the important implications for disease transmission and malaria control, a quantitative mapping of how parasite diversity entering a mosquito relates to diversity of the parasite exiting, has not been undertaken. To examine the role that vector biology plays in modulating parasite diversity, we develop a two-part model framework that estimates the diversity as a consequence of different bottlenecks and expansion events occurring during the vector-stage of the parasite life cycle. For the underlying framework, we develop the first stochastic model of within-vector P. falciparum parasite dynamics and go on to simulate the dynamics of two parasite subpopulations, emulating multiply infected mosquitoes. We show that incorporating stochasticity is essential to capture the extensive variation in parasite dynamics, particularly in the presence of multiple parasites. In particular, unlike deterministic models, which always predict the most fit parasites to produce the most sporozoites, we find that occasionally only parasites with lower fitness survive to the sporozoite stage. This has important implications for onward transmission. The second part of our framework includes a model of sequence diversity generation resulting from recombination and reassortment between parasites within a mosquito. Our two-part model framework shows that bottlenecks entering the oocyst stage decrease parasite diversity from what is present in the initial gametocyte population in a mosquito’s blood meal. However, diversity increases with the possibility for recombination and proliferation in the formation of sporozoites. Furthermore, when we begin with two parasite subpopulations in the initial gametocyte population, the probability of transmitting more than two unique parasites from mosquito to human is over 50% for a wide range of initial gametocyte densities.
  34. C. Peak, L. M. Childs, Y. H. Grad, C. O. Buckee, (2017) Comparing nonpharmaceutical interventions for containing emerging epidemics. PNAS. doi:10.1073/pnas.1616438114
    Article at PNAS     Abstract
      [Hide]    Strategies for containing an emerging infectious disease outbreak must be nonpharmaceutical when drugs or vaccines for the pathogen do not yet exist or are unavailable. The success of these nonpharmaceutical strategies will depend on not only the effectiveness of isolation measures but also the epidemiological characteristics of the infection. However, there is currently no systematic framework to assess the relationship between different containment strategies and the natural history and epidemiological dynamics of the pathogen. Here, we compare the effectiveness of quarantine and symptom monitoring, implemented via contact tracing, in controlling epidemics using an agent-based branching model. We examine the relationship between epidemic containment and the disease dynamics of symptoms and infectiousness for seven case-study diseases with diverse natural histories, including Ebola, influenza A, and severe acute respiratory syndrome (SARS). We show that the comparative effectiveness of symptom monitoring and quarantine depends critically on the natural history of the infectious disease, its inherent transmissibility, and the intervention feasibility in the particular healthcare setting. The benefit of quarantine over symptom monitoring is generally maximized for fast-course diseases, but we show the conditions under which symptom monitoring alone can control certain outbreaks. This quantitative framework can guide policymakers on how best to use nonpharmaceutical interventions and prioritize research during an outbreak of an emerging pathogen.
  35. L. M. Childs*, F. Y. Cai*, E. G. Kakani*, S. N. Mitchell, D. Paton, P. Gabrieli, C. O. Buckee$, F. Catteruccia$, (2016) Disrupting Mosquito Reproduction and Parasite Development for Malaria Control. PLoS Pathogens. doi:10.1371/journal.ppat.1006060
    Article at PLOS Pathogens    Abstract
      [Hide]    The control of mosquito populations with insecticide treated bed nets and indoor residual sprays remains the cornerstone of malaria reduction and elimination programs. In light of widespread insecticide resistance in mosquitoes, however, alternative strategies for reducing transmission by the mosquito vector are urgently needed, including the identification of safe compounds that affect vectorial capacity via mechanisms that differ from fast-acting insecticides. Here, we show that compounds targeting steroid hormone signaling disrupt multiple biological processes that are key to the ability of mosquitoes to transmit malaria. When an agonist of the steroid hormone 20-hydroxyecdysone (20E) is applied to Anopheles gambiae females, which are the dominant malaria mosquito vector in Sub Saharan Africa, it substantially shortens lifespan, prevents insemination and egg production, and significantly blocks Plasmodium falciparum development, three components that are crucial to malaria transmission. Modeling the impact of these effects on Anopheles population dynamics and Plasmodium transmission predicts that disrupting steroid hormone signaling using 20E agonists would affect malaria transmission to a similar extent as insecticides. Manipulating 20E pathways therefore provides a powerful new approach to tackle malaria transmission by the mosquito vector, particularly in areas affected by the spread of insecticide resistance.

  36. W. R. Shaw, P. Marcenac, L. M. Childs, C. O. Buckee, F. Baldini, S. P. Sawadogo, R. K. Dabire, A. Diabate, F. Catteruccia, (2016) Wolbachia infection in natural Anopheles populations affect egg laying and negatively correlate with Plasmodium development. Nature Communications, 7:11772. doi:10.1038/ncomms11772
    Article via PubMed     Abstract
      [Hide]    The maternally inherited alpha-proteobacterium Wolbachia has been proposed as a tool to block transmission of devastating mosquito-borne infectious diseases like dengue and malaria. Here we study the reproductive manipulations induced by a recently identified Wolbachia strain that stably infects natural mosquito populations of a major malaria vector, Anopheles coluzzii, in Burkina Faso. We determine that these infections significantly accelerate egg laying but do not induce cytoplasmic incompatibility or sex-ratio distortion, two parasitic reproductive phenotypes that facilitate the spread of other Wolbachia strains within insect hosts. Analysis of 221 blood-fed A. coluzzii females collected from houses shows a negative correlation between the presence of Plasmodium parasites and Wolbachia infection. A mathematical model incorporating these results predicts that infection with these endosymbionts may reduce malaria prevalence in human populations. These data suggest that Wolbachia may be an important player in malaria transmission dynamics in Sub-Saharan Africa.

  37. J.C. Blackwood* and L. M. Childs*, (2016) The role of interconnectivity in control of an Ebola epidemic. Scientific Reports, 6:29262. doi:10.1038/srep29262
    Article via PubMed    Abstract
      [Hide]    Several West African countries - Liberia, Sierra Leone and Guinea - experienced significant morbidity and mortality during the largest Ebola epidemic to date, from late 2013 through 2015. The extent of the epidemic was fueled by outbreaks in large urban population centers as well as movement of the pathogen between populations. During the epidemic there was no known vaccine or drug, so effective disease control required coordinated efforts that include both standard medical and community practices such as hospitalization, quarantine and safe burials. Due to the high connectivity of the region, control of the epidemic not only depended on internal strategies but also was impacted by neighboring countries. In this paper, we use a deterministic framework to examine the role of movement between two populations in the overall success of practices designed to minimize the extent of Ebola epidemics. We find that it is possible for even small amounts of intermixing between populations to positively impact the control of an epidemic on a more global scale.

  38. H. H. Chang, L. M. Childs, and C. O. Buckee, (2016) Variation in infection length and superinfection enhance selection efficiency in the human malaria parasite. Scientific Reports, 6:26370. doi:10.1038/srep26370
    Article via PubMed    Abstract
      [Hide]    The capacity for adaptation is central to the evolutionary success of the human malaria parasite Plasmodium falciparum. Malaria epidemiology is characterized by the circulation of multiple, genetically diverse parasite clones, frequent superinfection, and highly variable infection lengths, a large number of which are chronic and asymptomatic. The impact of these characteristics on the evolution of the parasite is largely unknown, however, hampering our understanding of the impact of interventions and the emergence of drug resistance. In particular, standard population genetic frameworks do not accommodate variation in infection length or superinfection. Here, we develop a population genetic model of malaria including these variations, and show that these aspects of malaria infection dynamics enhance both the probability and speed of fixation for beneficial alleles in complex and non-intuitive ways. We find that populations containing a mixture of short- and long-lived infections promote selection efficiency. Interestingly, this increase in selection efficiency occurs even when only a small fraction of the infections are chronic, suggesting that selection can occur efficiently in areas of low transmission intensity, providing a hypothesis for the repeated emergence of drug resistance in the low transmission setting of Southeast Asia.

  39. N. Obaldia III, G. S. Dow, L. Gerena, D. Kyle, W. Otero, P. Y. Mantel, N. Baro, R. Daniels, A. Mukherjee, L. M. Childs, C. O. Buckee, M. T. Duraisingh, S. K. Volkman, D. F. Wirth, and M. Marti, (2016) Altered drug susceptibility during host adaptation of a Plasmodium falciparum strain in a non-human primate model. Scientific Reports. doi:10.1038/srep21216
    Article via PubMed    Abstract
      [Hide]    Infections with Plasmodium falciparum, the most pathogenic of the Plasmodium species affecting man, have been reduced in part due to artemisinin-based combination therapies. However, artemisinin resistant parasites have recently emerged in South-East Asia. Novel intervention strategies are therefore urgently needed to maintain the current momentum for control and elimination of this disease. In the present study we characterize the phenotypic and genetic properties of the multi drug resistant (MDR) P. falciparum Thai C2A parasite strain in the non-human Aotus primate model, and across multiple passages. Aotus infections with C2A failed to clear upon oral artesunate and mefloquine treatment alone or in combination, and ex vivo drug assays demonstrated reduction in drug susceptibility profiles in later Aotus passages. Further analysis revealed mutations in the pfcrt and pfdhfr loci and increased parasite multiplication rate (PMR) across passages, despite elevated pfmdr1 copy number. Altogether our experiments suggest alterations in parasite population structure and increased fitness during Aotus adaptation. We also present data of early treatment failures with an oral artemisinin combination therapy in a pre-artemisinin resistant P. falciparum Thai isolate in this animal model.

  40. L. M. Childs, E. B. Baskerville, and S. Cobey, (2015) Trade-offs in antibody repertoires to complex antigens. Philosophical Transactions of the Royal Society of London B: Biological Sciences, 370(1676). doi:10.1098/rstb.2014.0245
    Article via PubMed     Abstract
      [Hide]    Pathogens vary in their antigenic complexity. While some pathogens such as measles present a few relatively invariant targets to the immune system, others such as malaria display considerable antigenic diversity. How the immune response copes in the presence of multiple antigens, and whether a trade-off exists between the breadth and efficacy of antibody (Ab)-mediated immune responses, are unsolved problems. We present a theoretical model of affinity maturation of B-cell receptors (BCRs) during a primary infection and examine how variation in the number of accessible antigenic sites alters the Ab repertoire. Naive B cells with randomly generated receptor sequences initiate the germinal centre (GC) reaction. The binding affinity of a BCR to an antigen is quantified via a genotype-phenotype map, based on a random energy landscape, that combines local and distant interactions between residues. In the presence of numerous antigens or epitopes, B-cell clones with different specificities compete for stimulation during rounds of mutation within GCs. We find that the availability of many epitopes reduces the affinity and relative breadth of the Ab repertoire. Despite the stochasticity of somatic hypermutation, patterns of immunodominance are strongly shaped by chance selection of naive B cells with specificities for particular epitopes. Our model provides a mechanistic basis for the diversity of Ab repertoires and the evolutionary advantage of antigenically complex pathogens.

  41. S. K. Nilsson*, L. M. Childs*, C. O. Buckee, and M. Marti, (2015) Targeting human transmission biology for malaria elimination. PLoS Pathogens, 11(6):e1004871. doi:10.1371/journal.ppat.1004871
    Article via PubMed     Abstract
      [Hide]    Malaria remains one of the leading causes of death worldwide, despite decades of public health efforts. The recent commitment by many endemic countries to eliminate malaria marks a shift away from programs aimed at controlling disease burden towards one that emphasizes reducing transmission of the most virulent human malaria parasite, Plasmodium falciparum. Gametocytes, the only developmental stage of malaria parasites able to infect mosquitoes, have remained understudied, as they occur in low numbers, do not cause disease, and are difficult to detect in vivo by conventional methods. Here, we review the transmission biology of P. falciparum gametocytes, featuring important recent discoveries of genes affecting parasite commitment to gametocyte formation, microvesicles enabling parasites to communicate with each other, and the anatomical site where immature gametocytes develop. We propose potential parasite targets for future intervention and highlight remaining knowledge gaps.

  42. L. M. Childs and C. O. Buckee, (2015) Dissecting the determinants of malaria chronicity: why within-host models struggle to reproduce infection dynamics. Journal of the Royal Society Interface, 12(104):20142379. doi:10.1098/rsif.2014.1379
    Article via PubMed    Abstract
      [Hide]    The duration of infection is fundamental to the epidemiological behaviour of any infectious disease, but remains one of the most poorly understood aspects of malaria. In endemic areas, the malaria parasite Plasmodium falciparum can cause both acute, severe infections and asymptomatic, chronic infections through its interaction with the host immune system. Frequent superinfection and massive parasite genetic diversity make it extremely difficult to accurately measure the distribution of infection lengths, complicating the estimation of basic epidemiological parameters and the prediction of the impact of interventions. Mathematical models have qualitatively reproduced parasite dynamics early during infection, but reproducing long-lived chronic infections remains much more challenging. Here, we construct a model of infection dynamics to examine the consequences of common biological assumptions for the generation of chronicity and the impact of co-infection. We find that although a combination of host and parasite heterogeneities are capable of generating chronic infections, they do so only under restricted parameter choices. Furthermore, under biologically plausible assumptions, co-infection of parasite genotypes can alter the course of infection of both the resident and co-infecting strain in complex non-intuitive ways. We outline the most important puzzles for within-host models of malaria arising from our analysis, and their implications for malaria epidemiology and control.

  43. L. M. Childs, N. N. Abuelezam, C. Dye, S. Gupta, M. B. Murray, B. Williams, and C. O. Buckee, (2015) Modelling challenges in context: Lessons from malaria, HIV and tuberculosis. Epidemics, 10:102-107. doi:10.1016/j.epidem.2015.02.002
    Article via PubMed     Abstract
      [Hide]    Malaria, HIV, and tuberculosis (TB) collectively account for several million deaths each year, with all three ranking among the top ten killers in low-income countries. Despite being caused by very different organisms, malaria, HIV, and TB present a suite of challenges for mathematical modellers that are particularly pronounced in these infections, but represent general problems in infectious disease modelling, and highlight many of the challenges described throughout this issue. Here, we describe some of the unifying challenges that arise in modelling malaria, HIV, and TB, including variation in dynamics within the host, diversity in the pathogen, and heterogeneity in human contact networks and behaviour. Through the lens of these three pathogens, we provide specific examples of the other challenges in this issue and discuss their implications for informing public health efforts.

  44. B. I. Coleman, K. M. Skillman, R. H. Y. Jiang, L. M. Childs, L. M. Altenhofen, M. Ganter, Y. Leung, I. Goldowitz, B. F. C. Kafsack, M. Marti, M. Llinas, C. O. Buckee, and M. T. Duraisingh, (2014) A Plasmodium falciparum histone deacetylase links parasite persistence and sexual conversion. Cell Host Microbe, 16(2):177-86. doi:10.1016/j.chom.2014.06.014
    Article via PubMed    Abstract
      [Hide]    The asexual forms of the malaria parasite Plasmodium falciparum are adapted for chronic persistence in human red blood cells, continuously evading host immunity using epigenetically regulated antigenic variation of virulence-associated genes. Parasite survival on a population level also requires differentiation into sexual forms, an obligatory step for further human transmission. We reveal that the essential nuclear gene, P. falciparum histone deacetylase 2 (PfHda2), is a global silencer of virulence gene expression and controls the frequency of switching from the asexual cycle to sexual development. PfHda2 depletion leads to dysregulated expression of both virulence-associated var genes and PfAP2-g, a transcription factor controlling sexual conversion, and is accompanied by increases in gametocytogenesis. Mathematical modeling further indicates that PfHda2 has likely evolved to optimize the parasite's infectious period by achieving low frequencies of virulence gene expression switching and sexual conversion. This common regulation of cellular transcriptional programs mechanistically links parasite transmissibility and virulence.

  45. L. M. Childs*, W. E. England*, M. J. Young, J. S. Weitz, and R. J. Whitaker, (2014) CRISPR-induced distributed immunity in microbial populations. PLoS One, 9(7):e0101710. doi:10.1371/journal.pone.0101710
    Article via PubMed     Abstract
      [Hide]    In bacteria and archaea, viruses are the primary infectious agents, acting as virulent, often deadly pathogens. A form of adaptive immune defense known as CRISPR-Cas enables microbial cells to acquire immunity to viral pathogens by recognizing specific sequences encoded in viral genomes. The unique biology of this system results in evolutionary dynamics of host and viral diversity that cannot be fully explained by the traditional models used to describe microbe-virus coevolutionary dynamics. Here, we show how the CRISPR-mediated adaptive immune response of hosts to invading viruses facilitates the emergence of an evolutionary mode we call distributed immunity - the coexistence of multiple, equally-fit immune alleles among individuals in a microbial population. We use an eco-evolutionary modeling framework to quantify distributed immunity and demonstrate how it emerges and fluctuates in multi-strain communities of hosts and viruses as a consequence of CRISPR-induced coevolution under conditions of low viral mutation and high relative numbers of viral protospacers. We demonstrate that distributed immunity promotes sustained diversity and stability in host communities and decreased viral population density that can lead to viral extinction. We analyze sequence diversity of experimentally coevolving populations of Streptococcus thermophilus and their viruses where CRISPR-Cas is active, and find the rapid emergence of distributed immunity in the host population, demonstrating the importance of this emergent phenomenon in evolving microbial communities.

  46. N. L. Held, L. M. Childs, M. Davison, J. S. Weitz, R. J. Whitaker, and D. Bhaya, (2013) CRISPR-Cas systems to probe ecological diversity and host-viral interactions. In CRISPR-Cas Systems, Springer-Verlag Berlin Heidelberg. doi:10.1007/978-3-642-34657-6-9
    Book Chapter at Springer
  47. L. M. Childs, N. Held, M. Young, R. Whittaker, and J. Weitz, (2012) Multi-scale Model of CRISPR-induced Coevolutionary dynamics: Diversification at the interface of Lamarck and Darwin. Evolution, 66(7):2015--2029. doi:10.1111/j.1558-5646.2012.01595.x
    Article via PubMed    Abstract
      [Hide]    The CRISPR (Clustered Regularly Interspaced Short Palindromic Repeats) system is a recently discovered type of adaptive immune defense in bacteria and archaea that functions via directed incorporation of viral and plasmid DNA into host genomes. Here, we introduce a multiscale model of dynamic coevolution between hosts and viruses in an ecological context that incorporates CRISPR immunity principles. We analyze the model to test whether and how CRISPR immunity induces host and viral diversification and the maintenance of many coexisting strains. We show that hosts and viruses coevolve to form highly diverse communities. We observe the punctuated replacement of existent strains, such that populations have very low similarity compared over the long term. However, in the short term, we observe evolutionary dynamics consistent with both incomplete selective sweeps of novel strains (as single strains and coalitions) and the recurrence of previously rare strains. Coalitions of multiple dominant host strains are predicted to arise because host strains can have nearly identical immune phenotypes mediated by CRISPR defense albeit with different genotypes. We close by discussing how our explicit eco-evolutionary model of CRISPR immunity can help guide efforts to understand the drivers of diversity seen in microbial communities where CRISPR systems are active.

  48. L. M. Childs, M. Paskow, S. Morris, M. Hesse and S. Strogatz, (2011) From inflammation to wound healing: using a simple model to understand the functional versatility of murine macrophages. Bulletin of Mathematical Biology. doi:10.1007/s11538-011-9637-5
    Article via PubMed     Abstract
      [Hide]    Macrophages are fundamental cells of the innate immune system. Their activation is essential for such distinct immune functions as inflammation (pathogen-killing) and tissue repair (wound healing). An open question has been the functional stability of an individual macrophage cell: whether it can change its functional profile between different immune responses such as between the repair pathway and the inflammatory pathway. We studied this question theoretically by constructing a rate equation model for the key substrate, enzymes and products of the pathways; we then tested the model experimentally. Both our model and experiments show that individual macrophages can switch from the repair pathway to the inflammation pathway but that the reverse switch does not occur.

  49. L. M. Childs and S. Strogatz, (2008) Stability diagram for the Forced Kuramoto model. CHAOS, 18: 043128. doi 10.1063/1.3049136
    Articel at ArXiv    Abstract
      [Hide]    We analyze the periodically forced Kuramoto model. This system consists of an infinite population of phase oscillators with random intrinsic frequencies, global sinusoidal coupling, and external sinusoidal forcing. It represents an idealization of many phenomena in physics, chemistry and biology in which mutual synchronization competes with forced synchronization. In other words, the oscillators in the population try to synchronize with one another while also trying to lock onto an external drive. Previous work on the forced Kuramoto model uncovered two main types of attractors, called forced entrainment and mutual entrainment, but the details of the bifurcations between them were unclear. Here we present a complete bifurcation analysis of the model for a special case in which the infinite-dimensional dynamics collapse to a two-dimensional system. Exact results are obtained for the locations of Hopf, saddle-node, and Takens-Bogdanov bifurcations. The resulting stability diagram bears a striking resemblance to that for the weakly nonlinear forced van der Pol oscillator.

Other Publications

  1. N. Tuncer, M. Martcheva, O. Prosper, and L. M. Childs (2023) "Preface," In N. Tuncer, M. Martcheva, O. Prosper, L. M. Childs. In Computational and Mathematical Population Dynamics, World Scientific. doi:10.1142/9789811263033_fmatter.
    Book chapter at World Scientific
  2. L. M. Childs (2021) "Spruce Budworm and the Forest,"" In P. Kraikivski, editor, Case Studies in Systems Biology. Springer, New York. doi:10.1007/978-3-030-67742-8
    Book Chapter at Springer
  3. N. Ghaffarzadegan, L. M. Childs, and U. C. Tauber (2020) Diverse Computer Simulation Models Provide Unified Lessons on University Operation during a Pandemic. BioScience. doi:10.1093/biosci/biaa122
    Article at BioScience
  4. L. M. Childs (2020) Choosing Intervention Strategies During an Emerging Epidemic. SIAM News, Article at SIAM News

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