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.

Lymphatic filariasis is targeted for elimination as a public health problem by 2020. The principal approach used by current programmes is annual mass drug administration with two pairs of drugs with a good safety profile. However, one dose of a triple-drug regimen (ivermectin, diethylcarbamazine, and albendazole) has been shown to clear the transmissible stage of the helminth completely in treated individuals. The aim of this study was to use modelling to assess the potential value of mass drug administration with the triple-drug regimen for accelerating elimination of lymphatic filariasis in different epidemiological settings. We used three different transmission models to compare the number of rounds of mass drug administration needed to achieve a prevalence of microfilaraemia less than 1% with the triple-drug regimen and with current two-drug regimens. In settings with a low baseline prevalence of lymphatic filariasis (5%), the triple-drug regimen reduced the number of rounds of mass drug administration needed to reach the target prevalence by one or two rounds, compared with the two-drug regimen. For areas with higher baseline prevalence (10-40%), the triple-drug regimen strikingly reduced the number of rounds of mass drug administration needed, by about four or five, but only at moderate-to-high levels of population coverage (>65%) and if systematic non-adherence to mass drug administration was low. Simulation modelling suggests that the triple-drug regimen has potential to accelerate the elimination of lymphatic filariasis if high population coverage of mass drug administration can be achieved and if systematic non-adherence with mass drug administration is low. Future work will reassess these estimates in light of more clinical trial data and to understand the effect on an individual country's programme. Bill & Melinda Gates Foundation.

Quantitative analysis and mathematical models are useful tools in informing strategies to control or eliminate disease. Currently, there is an urgent need to develop these tools to inform policy to achieve the 2020 goals for neglected tropical diseases (NTDs). In this paper we give an overview of a collection of novel model-based analyses which aim to address key questions on the dynamics of transmission and control of nine NTDs: Chagas disease, visceral leishmaniasis, human African trypanosomiasis, leprosy, soil-transmitted helminths, schistosomiasis, lymphatic filariasis, onchocerciasis and trachoma. Several common themes resonate throughout these analyses, including: the importance of epidemiological setting on the success of interventions; targeting groups who are at highest risk of infection or re-infection; and reaching populations who are not accessing interventions and may act as a reservoir for infection,. The results also highlight the challenge of maintaining elimination ‘as a public health problem’ when true elimination is not reached. The models elucidate the factors that may be contributing most to persistence of disease and discuss the requirements for eventually achieving true elimination, if that is possible. Overall this collection presents new analyses to inform current control initiatives. These papers form a base from which further development of the models and more rigorous validation against a variety of datasets can help to give more detailed advice. At the moment, the models’ predictions are being considered as the world prepares for a final push towards control or elimination of neglected tropical diseases by 2020.

This paper develops a statistical framework for a retrospective analysis for well-observed livestock epidemics during which intervention policies may conceal cases, thus potentially biasing naively derived parameter and final size estimates. We apply the methods to the 2001 foot and mouth epidemic (FMD) in Great Britain, during which a large number of farms (about 7500) were pre-emptively culled as part of the control effort without ever being diagnosed as being infected. We infer farm-level infectivity and susceptibility parameters, a distribution for the delay from infection to report, together with a time varying farm infectivity profile for farms. Hidden infections among proactively culled farms were accounted for using a data augmentation approach utilising reversible jump MCMC methods. Simulated epidemics derived using the parameter estimates obtained reproduced the 2001 epidemic well. Our analysis demonstrates that time-varying infectivity profiles fit the 2001 data better than naive assumptions of constant infectiousness. We estimate that around 210 (or 2.8%) of the farms proactively culled in the 2001 epidemic were infected. However, for the parameter estimated obtained, preliminary simulation results indicate that had contiguous culling not been applied in 2001, the epidemic might have been substantially larger.