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.

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 Macdonald's 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.

BackgroundMathematical models of parasite transmission can help integrate a large body of information into a consistent framework, which can then be used for gaining mechanistic insights and making predictions. However, uncertainty, spatial variability and complexity, can hamper the use of such models for decision making in parasite management programs.MethodsWe have adapted a Bayesian melding framework for calibrating simulation models to address the need for robust modelling tools that can effectively support management of lymphatic filariasis (LF) elimination in diverse endemic settings. We applied this methodology to LF infection and vector biting data from sites across the major LF endemic regions in order to quantify model parameters, and generate reliable predictions of infection dynamics along with credible intervals for modelled output variables. We used the locally calibrated models to estimate breakpoint values for various indicators of parasite transmission, and simulate timelines to parasite extinction as a function of local variations in infection dynamics and breakpoints, and effects of various currently applied and proposed LF intervention strategies.ResultsWe demonstrate that as a result of parameter constraining by local data, breakpoint values for all the major indicators of LF transmission varied significantly between the sites investigated. Intervention simulations using the fitted models showed that as a result of heterogeneity in local transmission and extinction dynamics, timelines to parasite elimination in response to the current Mass Drug Administration (MDA) and various proposed MDA with vector control strategies also varied significantly between the study sites. Including vector control, however, markedly reduced the duration of interventions required to achieve elimination as well as decreased the risk of recrudescence following stopping of MDA.ConclusionsWe have demonstrated how a Bayesian data-model assimilation framework can enhance the use of transmission models for supporting reliable decision making in the management of LF elimination. Extending this framework for delivering predictions in settings either lacking or with only sparse data to inform the modelling process, however, will require development of procedures to estimate and use spatio-temporal variations in model parameters and inputs directly, and forms the next stage of the work reported here.Electronic supplementary materialThe online version of this article (doi:10.1186/s13071-015-1132-7) contains supplementary material, which is available to authorized users.

Bill & Melinda Gates Foundation.

BackgroundLymphatic filariasis (LF) has been targeted by the WHO for global eradication leading to the implementation of large scale intervention programs based on annual mass drug administrations (MDA) worldwide. Recent work has indicated that locality-specific bio-ecological complexities affecting parasite transmission may complicate the prediction of LF extinction endpoints, casting uncertainty on the achievement of this initiative. One source of difficulty is the limited quantity and quality of data used to parameterize models of parasite transmission, implying the important need to update initially-derived parameter values. Sequential analysis of longitudinal data following annual MDAs will also be important to gaining new understanding of the persistence dynamics of LF. Here, we apply a Bayesian statistical-dynamical modelling framework that enables assimilation of information in human infection data recorded from communities in Papua New Guinea that underwent annual MDAs, into our previously developed model of parasite transmission, in order to examine these questions in LF ecology and control.ResultsBiological parameters underlying transmission obtained by fitting the model to longitudinal data remained stable throughout the study period. This enabled us to reliably reconstruct the observed baseline data in each community. Endpoint estimates also showed little variation. However, the updating procedure showed a shift towards higher and less variable values for worm kill but not for any other drug-related parameters. An intriguing finding is that the stability in key biological parameters could be disrupted by a significant reduction in the vector biting rate prevailing in a locality.ConclusionsTemporal invariance of biological parameters in the face of intervention perturbations indicates a robust adaptation of LF transmission to local ecological conditions. The results imply that understanding the mechanisms that underlie locally adapted transmission dynamics will be integral to identifying points of system fragility, and thus countermeasures to reliably facilitate LF extinction both locally and globally.