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

Abstract

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.

Evidence for carry-over effects of predator exposure on pathogen transmission potential

“…All adult mosquitoes can produce larvae (L m ) that can emerge as susceptible adults after their development period. We also assumed similar categories for the human population (the model is fully described in the electronic supplementary material) leading to a classic model for vector-borne pathogens [31]. In the presence or absence of predators, we simulated the expected outbreak size in a human population (number of individuals that have been infected at the end of the season) when one infectious human was introduced into a population of 100 individuals.…”

Modelling the effects of malaria infection on mosquito biting behaviour and attractiveness of humans

“…Most models developed since then have been similar deterministic population-based models [2,3,10,24,25] although recently stochastic individual-based simulation models have increased in prominence [17,28]. However, these models have rarely considered the impact of malaria infection in mosquitoes on their feeding frequency or the impact of malaria infection in humans on their attractiveness to mosquitoes.…”

Climate, environmental and socio-economic change: weighing up the balance in vector-borne disease transmission

“…Numerous mathematical models have been designed and used to quantitatively and qualitatively gain insights into the transmission dynamics and control of VBDs in human populations [145], with the earliest work dating back to the pioneering studies of Ross and Macdonald on malaria [146]; however, only a few of these models have incorporated the effects of climate and/or climate change [9,13,124,[147][148][149][150][151]. Recent models have included statistical and stochastic models [16,147,148,[152][153][154], approaches based on compartmental nonlinear ordinary and partial differential equations [9,149,155 -157] and nonlinear difference equation models [13,158].…”