Nick W. Ruktanonchai

A systematic review of mathematical models of mosquito-borne pathogen transmission: 1970-2010

Mathematical models of mosquito-borne pathogen transmission originated in the early twentieth century to provide insights into how to most effectively combat malaria. The foundations of the Ross–Macdonald theory were established by 1970. Since then, there has been a growing interest in reducing the public health burden of mosquito-borne pathogens and an expanding use of models to guide their control. To assess how theory has changed to confront evolving public health challenges, we compiled a bibliography of 325 publications from 1970 through 2010 that included at least one mathematical model of mosquito-borne pathogen transmission and then used a 79-part questionnaire to classify each of 388 associated models according to its biological assumptions. As a composite measure to interpret the multidimensional results of our survey, we assigned a numerical value to each model that measured its similarity to 15 core assumptions of the Ross–Macdonald model. Although the analysis illustrated a growing acknowledgement of geographical, ecological and epidemiological complexities in modelling transmission, most models during the past 40 years closely resemble the Ross–Macdonald model. Modern theory would benefit from an expansion around the concepts of heterogeneous mosquito biting, poorly mixed mosquito-host encounters, spatial heterogeneity and temporal variation in the transmission process.

Recasting the theory of mosquito-borne pathogen transmission dynamics and control

Mosquito-borne diseases pose some of the greatest challenges in public health, especially in tropical and sub-tropical regions of the world. Efforts to control these diseases have been underpinned by a theoretical framework developed for malaria by Ross and Macdonald, including models, metrics for measuring transmission, and theory of control that identifies key vulnerabilities in the transmission cycle. That framework, especially Macdonalds formula for R0 and its entomological derivative, vectorial capacity, are now used to study dynamics and design interventions for many mosquito-borne diseases. A systematic review of 388 models published between 1970 and 2010 found that the vast majority adopted the Ross–Macdonald assumption of homogeneous transmission in a well-mixed population. Studies comparing models and data question these assumptions and point to the capacity to model heterogeneous, focal transmission as the most important but relatively unexplored component in current theory. Fine-scale heterogeneity causes transmission dynamics to be nonlinear, and poses problems for modeling, epidemiology and measurement. Novel mathematical approaches show how heterogeneity arises from the biology and the landscape on which the processes of mosquito biting and pathogen transmission unfold. Emerging theory focuses attention on the ecological and social context for mosquito blood feeding, the movement of both hosts and mosquitoes, and the relevant spatial scales for measuring transmission and for modeling dynamics and control.

Identifying Malaria Transmission Foci for Elimination Using Human Mobility Data

Humans move frequently and tend to carry parasites among areas with endemic malaria and into areas where local transmission is unsustainable. Human-mediated parasite mobility can thus sustain parasite populations in areas where they would otherwise be absent. Data describing human mobility and malaria epidemiology can help classify landscapes into parasite demographic sources and sinks, ecological concepts that have parallels in malaria control discussions of transmission foci. By linking transmission to parasite flow, it is possible to stratify landscapes for malaria control and elimination, as sources are disproportionately important to the regional persistence of malaria parasites. Here, we identify putative malaria sources and sinks for pre-elimination Namibia using malaria parasite rate (PR) maps and call data records from mobile phones, using a steady-state analysis of a malaria transmission model to infer where infections most likely occurred. We also examined how the landscape of transmission and burden changed from the pre-elimination setting by comparing the location and extent of predicted pre-elimination transmission foci with modeled incidence for 2009. This comparison suggests that while transmission was spatially focal pre-elimination, the spatial distribution of cases changed as burden declined. The changing spatial distribution of burden could be due to importation, with cases focused around importation hotspots, or due to heterogeneous application of elimination effort. While this framework is an important step towards understanding progressive changes in malaria distribution and the role of subnational transmission dynamics in a policy-relevant way, future work should account for international parasite movement, utilize real time surveillance data, and relax the steady state assumption required by the presented model.

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.

Exploring the high-resolution mapping of gender-disaggregated development indicators

Improved understanding of geographical variation and inequity in health status, wealth and access to resources within countries is increasingly being recognized as central to meeting development goals. Development and health indicators assessed at national or subnational scale can often conceal important inequities, with the rural poor often least well represented. The ability to target limited resources is fundamental, especially in an international context where funding for health and development comes under pressure. This has recently prompted the exploration of the potential of spatial interpolation methods based on geolocated clusters from national household survey data for the high-resolution mapping of features such as population age structures, vaccination coverage and access to sanitation. It remains unclear, however, how predictable these different factors are across different settings, variables and between demographic groups. Here we test the accuracy of spatial interpolation methods in producing gender-disaggregated high-resolution maps of the rates of literacy, stunting and the use of modern contraceptive methods from a combination of geolocated demographic and health surveys cluster data and geospatial covariates. Bayesian geostatistical and machine learning modelling methods were tested across four low-income countries and varying gridded environmental and socio-economic covariate datasets to build 1×1 km spatial resolution maps with uncertainty estimates. Results show the potential of the approach in producing high-resolution maps of key gender-disaggregated socio-economic indicators, with explained variance through cross-validation being as high as 74–75% for female literacy in Nigeria and Kenya, and in the 50–70% range for many other variables. However, substantial variations by both country and variable were seen, with many variables showing poor mapping accuracies in the range of 2–30% explained variance using both geostatistical and machine learning approaches. The analyses offer a robust basis for the construction of timely maps with levels of detail that support geographically stratified decision-making and the monitoring of progress towards development goals. However, the great variability in results between countries and variables highlights the challenges in applying these interpolation methods universally across multiple countries, and the importance of validation and quantifying uncertainty if this is undertaken.

Advances in mapping malaria for elimination: fine resolution modelling of Plasmodium falciparum incidence

The long-term goal of the global effort to tackle malaria is national and regional elimination and eventually eradication. Fine scale multi-temporal mapping in low malaria transmission settings remains a challenge and the World Health Organisation propose use of surveillance in elimination settings. Here, we show how malaria incidence can be modelled at a fine spatial and temporal resolution from health facility data to help focus surveillance and control to population not attending health facilities. Using Namibia as a case study, we predicted the incidence of malaria, via a Bayesian spatio-temporal model, at a fine spatial resolution from parasitologically confirmed malaria cases and incorporated metrics on healthcare use as well as measures of uncertainty associated with incidence predictions. We then combined the incidence estimates with population maps to estimate clinical burdens and show the benefits of such mapping to identifying areas and seasons that can be targeted for improved surveillance and interventions. Fine spatial resolution maps produced using this approach were then used to target resources to specific local populations, and to specific months of the season. This remote targeting can be especially effective where the population distribution is sparse and further surveillance can be limited to specific local areas.

Mapping internal connectivity through human migration in malaria endemic countries.

Human mobility continues to increase in terms of volumes and reach, producing growing global connectivity. This connectivity hampers efforts to eliminate infectious diseases such as malaria through reintroductions of pathogens, and thus accounting for it becomes important in designing global, continental, regional, and national strategies. Recent works have shown that census-derived migration data provides a good proxy for internal connectivity, in terms of relative strengths of movement between administrative units, across temporal scales. To support global malaria eradication strategy efforts, here we describe the construction of an open access archive of estimated internal migration flows in endemic countries built through pooling of census microdata. These connectivity datasets, described here along with the approaches and methods used to create and validate them, are available both through the WorldPop website and the WorldPop Dataverse Repository.

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.

Census-derived migration data as a tool for informing malaria elimination policy

BackgroundNumerous countries around the world are approaching malaria elimination. Until global eradication is achieved, countries that successfully eliminate the disease will contend with parasite reintroduction through international movement of infected people. Human-mediated parasite mobility is also important within countries near elimination, as it drives parasite flows that affect disease transmission on a subnational scale.MethodsMovement patterns exhibited in census-based migration data are compared with patterns exhibited in a mobile phone data set from Haiti to quantify how well migration data predict short-term movement patterns. Because short-term movement data were unavailable for Mesoamerica, a logistic regression model fit to migration data from three countries in Mesoamerica is used to predict flows of infected people between subnational administrative units throughout the region.ResultsPopulation flows predicted using census-based migration data correlated strongly with mobile phone-derived movements when used as a measure of relative connectivity. Relative population flows are therefore predicted using census data across Mesoamerica, informing the areas that are likely exporters and importers of infected people. Relative population flows are used to identify community structure, useful for coordinating interventions and elimination efforts to minimize importation risk. Finally, the ability of census microdata inform future intervention planning is discussed in a country-specific setting using Costa Rica as an example.ConclusionsThese results show long-term migration data can effectively predict the relative flows of infected people to direct malaria elimination policy, a particularly relevant result because migration data are generally easier to obtain than short-term movement data such as mobile phone records. Further, predicted relative flows highlight policy-relevant population dynamics, such as major exporters across the region, and Nicaragua and Costa Rica’s strong connection by movement of infected people, suggesting close coordination of their elimination efforts. Country-specific applications are discussed as well, such as predicting areas at relatively high risk of importation, which could inform surveillance and treatment strategies.