Olivia Prosper

Assessing the role of spatial heterogeneity and human movement in malaria dynamics and control.

Mathematical models developed for studying malaria dynamics often focus on a single, homogeneous population. However, human movement connects environments with potentially different malaria transmission characteristics. To address the role of human movement and spatial heterogeneity in malaria transmission and malaria control, we consider a simple malaria metapopulation model incorporating two regions, or patches, connected by human movement, with different degrees of malaria transmission in each patch. Using our two-patch model, we calculate and analyze the basic reproduction number, R(0), an epidemiologically important threshold quantity that indicates whether malaria will persist or go extinct in a population. Although R(0) depends on the rates of human movement, we show that R(0) is always bounded between the two quantities R(01) and R(02)-the reproduction numbers for the two patches if isolated. If without migration, the disease is endemic in one patch but not in the other, then the addition of human migration can cause the disease to persist in both patches. This result indicates that regions with low malaria transmission should have an interest in helping to control or eliminate malaria in regions with higher malaria endemicity if human movement connects them. Performing a sensitivity analysis of R(0) and the endemic equilibrium to various parameters in the two-patch model allowed us to determine, under different parameterizations of the model, which patch will be the better target for control measures, and within that patch, what type of control measure should be implemented. In the analysis of R(0), we found that if the extrinsic incubation period is shorter than the average mosquito lifespan, the control measures should be targeted towards reducing the mosquito biting rate. On the other hand, if the extrinsic incubation period is longer than the average mosquito lifespan, control measures targeting the mosquito death rate will be more effective. Intuitively, one might think that resources for malaria control should be allocated to the region with higher malaria transmission. However, our sensitivity analyses indicated that this is not always the case. In fact, if migration into the lower transmission patch is much faster than migration into the higher transmission patch, the lower transmission patch is potentially the better target for malaria control efforts. While human movement between regions poses challenges to malaria control and elimination, if estimates of relevant parameters in the model are known, including migration rates, our results can help inform which region to target and what type of control measure to implement for the greatest success.

Optimal vaccination and bednet maintenance for the control of malaria in a region with naturally acquired immunity.

Following over two decades of research, the malaria vaccine candidate RTS,S has reached the final stages of vaccine trials, demonstrating an efficacy of roughly 50% in young children. Regions with high malaria prevalence tend to have high levels of naturally acquired immunity (NAI) to severe malaria; NAI is caused by repeated exposure to infectious bites and results in large asymptomatic populations. To address concerns about how these vaccines will perform in regions with existing NAI, we developed a simple malaria model incorporating vaccination and NAI. Typically, if the basic reproduction number (R0) for malaria is greater than unity, the disease will persist; otherwise, the disease will become extinct. However, analysis of this model revealed that NAI, compounded by a subpopulation with only partial protection to malaria, may render vaccination efforts ineffective and potentially detrimental to malaria control, by increasing R0 and increasing the likelihood of malaria persistence even when R0<1. The likelihood of this scenario increases when non-immune infected individuals are treated disproportionately compared with partially immune individuals - a plausible scenario since partially immune individuals are more likely to be asymptomatically infected. Consequently, we argue that active case-detection of asymptomatic infections is a critical component of an effective malaria control program. We then investigated optimal vaccination and bednet control programs under two endemic settings with varying levels of naturally acquired immunity: a typical setting under which prevalence decays when R0<1, and a setting in which subthreshold endemic equilibria exist. A qualitative comparison of the optimal control results under the first setting revealed that the optimal policy differs depending on whether the goal is to reduce total morbidity, or to reduce clinical infections. Furthermore, this comparison dictates that control programs should place less effort in vaccination as the level of NAI in a population, and as disease prevalence, increases. In the second setting, we demonstrated that the optimal policy is able to confer long-term benefits with a 10-year control program by pushing the system into a new state where the disease-free equilibrium becomes the attracting equilibrium. While this result suggests that one can theoretically achieve long-term benefits with a short-term strategy, we illustrate that in this second setting, a small environmental change, or the introduction of new cases via immigration, places the population at high risk for a malaria epidemic.

Spatial Heterogeneity, Host Movement and Mosquito-Borne Disease Transmission

Mosquito-borne diseases are a global health priority disproportionately affecting low-income populations in tropical and sub-tropical countries. These pathogens live in mosquitoes and hosts that interact in spatially heterogeneous environments where hosts move between regions of varying transmission intensity. Although there is increasing interest in the implications of spatial processes for mosquito-borne disease dynamics, most of our understanding derives from models that assume spatially homogeneous transmission. Spatial variation in contact rates can influence transmission and the risk of epidemics, yet the interaction between spatial heterogeneity and movement of hosts remains relatively unexplored. Here we explore, analytically and through numerical simulations, how human mobility connects spatially heterogeneous mosquito populations, thereby influencing disease persistence (determined by the basic reproduction number R 0), prevalence and their relationship. We show that, when local transmission rates are highly heterogeneous, R 0 declines asymptotically as human mobility increases, but infection prevalence peaks at low to intermediate rates of movement and decreases asymptotically after this peak. Movement can reduce heterogeneity in exposure to mosquito biting. As a result, if biting intensity is high but uneven, infection prevalence increases with mobility despite reductions in R 0. This increase in prevalence decreases with further increase in mobility because individuals do not spend enough time in high transmission patches, hence decreasing the number of new infections and overall prevalence. These results provide a better basis for understanding the interplay between spatial transmission heterogeneity and human mobility, and their combined influence on prevalence and R 0.

Place-based attributes predict community membership in a mobile phone communication network.

Social networks can be organized into communities of closely connected nodes, a property known as modularity. Because diseases, information, and behaviors spread faster within communities than between communities, understanding modularity has broad implications for public policy, epidemiology and the social sciences. Explanations for community formation in social networks often incorporate the attributes of individual people, such as gender, ethnicity or shared activities. High modularity is also a property of large-scale social networks, where each node represents a population of individuals at a location, such as call flow between mobile phone towers. However, whether or not place-based attributes, including land cover and economic activity, can predict community membership for network nodes in large-scale networks remains unknown. We describe the pattern of modularity in a mobile phone communication network in the Dominican Republic, and use a linear discriminant analysis (LDA) to determine whether geographic context can explain community membership. Our results demonstrate that place-based attributes, including sugar cane production, urbanization, distance to the nearest airport, and wealth, correctly predicted community membership for over 70% of mobile phone towers. We observed a strongly positive correlation (r = 0.97) between the modularity score and the predictive ability of the LDA, suggesting that place-based attributes can accurately represent the processes driving modularity. In the absence of social network data, the methods we present can be used to predict community membership over large scales using solely place-based attributes.

Impact of enhanced malaria control on the competition between Plasmodium falciparum and Plasmodium vivax in India

The primary focus of malaria research and control has been on Plasmodium falciparum, the most severe of the four Plasmodium species causing human disease. However, the presence of both P. falciparum and Plasmodium vivax occurs in several countries, including India. We developed a mathematical model describing the dynamics of P. vivax and P. falciparum in the human and mosquito populations and fit this model to Indian clinical case data to understand how enhanced control measures affect the competition between the two Plasmodium species. Around 1997, funding for malaria control in India increased dramatically. Our model predicts that if India had not improved its control strategy, the two species of Plasmodium would continue to coexist. To determine which control measures contributed the most to the decline in the number of cases after 1997, we compared the fit of seven models to the 1997-2010 clinical case data. From this, we determined that increased use of bednets contributed the most to case reduction. During the enhanced control period, the best model predicts that P. vivax is out-competing P. falciparum. However, the reproduction numbers are extremely close to the invasion boundaries. Consequently, we cannot be confident that this outcome is the true future of malaria in India. We address this uncertainty by performing a parametric bootstrapping procedure for each of the seven models. This procedure, applied to the enhanced control period, revealed that the best model predicts that P. vivax outcompeting P. falciparum is the most likely outcome, whereas the remaining candidate models predict the opposite. Moreover, the predictions of the top model are counter to what one expects based on the case data alone. Although the proportion of cases due to falciparum has been increasing, the best fitting model reveals that this observation is insufficient to draw conclusions about the longterm competitive outcome of the two species.

Simulating Within-Vector Generation of the Malaria Parasite Diversity

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.

A Model for Spheroid versus Monolayer Response of SK-N-SH Neuroblastoma Cells to Treatment with 15-Deoxy-PGJ2

Researchers have observed that response of tumor cells to treatment varies depending on whether the cells are grown in monolayer, as in vitro spheroids or in vivo. This study uses data from the literature on monolayer treatment of SK-N-SH neuroblastoma cells with 15-deoxy-PGJ 2 and couples it with data on growth rates for untreated SK-N-SH neuroblastoma cells grown as multicellular spheroids. A linear model is constructed for untreated and treated monolayer data sets, which is tuned to growth, death, and cell cycle data for the monolayer case for both control and treatment with 15-deoxy-PGJ 2. The monolayer model is extended to a five-dimensional nonlinear model of in vitro tumor spheroid growth and treatment that includes compartments of the cell cycle (G 1, S, G 2/M) as well as quiescent (Q) and necrotic (N) cells. Monolayer treatment data for 15-deoxy-PGJ 2 is used to derive a prediction of spheroid response under similar treatments. For short periods of treatment, spheroid response is less pronounced than monolayer response. The simulations suggest that the difference in response to treatment of monolayer versus spheroid cultures observed in laboratory studies is a natural consequence of tumor spheroid physiology rather than any special resistance to treatment.

Modeling the Response ofAnopheles gambiae(Diptera: Culicidae) Populations in the Kenya Highlands to a Rise in Mean Annual Temperature

Abstract A dynamical model of Anopheles gambiae larval and adult populations is constructed that matches temperature-dependent maturation times and mortality measured experimentally as well as larval instar and adult mosquito emergence data from field studies in the Kenya Highlands. Spectral classification of high-resolution satellite imagery is used to estimate household density. Indoor resting densities collected over a period of one year combined with predictions of the dynamical model give estimates of both aquatic habitat and total adult mosquito densities. Temperature and precipitation patterns are derived from monthly records. Precipitation patterns are compared with average and extreme habitat estimates to estimate available aquatic habitat in an annual cycle. These estimates are coupled with the original model to produce estimates of adult and larval populations dependent on changing aquatic carrying capacity for larvae and changing maturation and mortality dependent on temperature. This paper offers a general method for estimating the total area of aquatic habitat in a given region, based on larval counts, emergence rates, indoor resting density data, and number of households. Altering the average daily temperature and the average daily rainfall simulates the effect of climate change on annual cycles of prevalence of An. gambiae adults. We show that small increases in average annual temperature have a large impact on adult mosquito density, whether measured at model equilibrium values for a single square meter of habitat or tracked over the course of a year of varying habitat availability and temperature.

Intermittent Preventive Treatment (IPT) and the Spread of Drug Resistant Malaria

Intermittent Preventive Treatment (IPT) is a malaria control strategy in which vulnerable asymptomatic individuals are given a full curative dose of an antimalarial medication at specified intervals, regardless of whether they are infected with malaria or not. A mathematical model is developed to explore the effect of IPT use on the malaria prevalence and control under different scenarios. The model includes both drug-sensitive and drug-resistant strains of the parasite as well as interactions between human hosts and mosquitoes. The basic reproduction numbers for both strains and the invasion reproduction numbers are computed and used to examine the role of IPT on the development of resistant infections. Numerical simulations are performed to examine the effect of treatment of symptomatic infections and IPT on the prevalence levels of both strains. The model results suggest that the schedule of IPT may have an important influence on the prevalence of resistant infections as well as the total infections of both strains. Moreover, the extent to which IPT may influence the development of resistant strains depends also on the half-life of the drug used. A sensitivity and uncertainty analysis indicates the model outcomes are most sensitive to several model parameters including the reduction factor of transmission for the resistant strain, rate of immunity loss, and the clearance rate of sensitive infections.