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.
A systematic review of mathematical models of mosquito-borne pathogen transmission
Reiner, R. C., Perkins, T. A., Barker, C. M., Niu, T., Chaves, L. F., Ellis, A. M., George, D. B., Le Menach, A., Pulliam, J. R. C., Bisanzio, D., Buckee, C., Chiyaka, C., Cummings, D. A. T., Garcia, A. J., Gatton, M. L., Gething, P. W., Hartley, D. M., Johnston, G., Klein, E. Y., ... Smith, D. L. (2013). A systematic review of mathematical models of mosquito-borne pathogen transmission: 1970-2010. Journal of the Royal Society Interface, 10(81), . https://doi.org/10.1098/rsif.2012.0921