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.

Figure 1.

Temporal trend in the publication of models included in the bibliography, grouped by pathogen and binned by (a) year and (b) 5-year period.

Figure 2.

Themes and trends. (a) Number by pathogen (bars) and relative per cent (points) of models that explicitly modelled aquatic mosquito populations by year (question 25). (b) Number by pathogen and relative per cent of models that modelled pathogen latency in mosquitoes by year (question 53). (c) Number by pathogen and relative per cent of models that incorporated potential co-infections or superinfection by year (question 68). (d) Number by pathogen and relative per cent of models that used a simulation-based approach by year (questions 51 and 63).

Figure 3.

Selected results. (a) Assumptions about pathogen latency in mosquitoes, grouped by pathogen and in total (numbers of each in parentheses). The range of assumptions includes: pathogen latency was not modelled at all (yellow); it was either implicitly or explicitly modelled (blue, red); and it was modelled with or without temperature dependence (dark, light). (b) Assumptions about the mixing of mosquito–host encounters (well-mixed or not well-mixed, top versus bottom rectangles) and the distribution of blood meals on hosts (homogeneous or heterogeneous, left versus right rectangles). The area of each square corresponds to the proportion of models that make each combination of assumptions, and colour denotes difference from the Ross–Macdonald model. (c) Number of models that included individual control measures and combinations thereof. Each bar represents a unique combination of control measures included in at least one model. Bars are grouped according to how many control measures appeared in a single model, and multicoloured bars indicate which control measures comprised each combination.

Figure 4.

Analysis of RM-index values, which quantify in how many ways models differ from core assumptions of the Ross–Macdonald theory and range from 0 to 15. (a) Distribution of RM-index values across all models. (b) Number of models in which a particular pair of core assumptions differed from Ross–Macdonald simultaneously. (c) Correlation coefficients for each pair of core assumptions. Pairs with positive correlations frequently appeared together or were frequently omitted together, whereas pairs with negative correlations tended not to appear together in the same models. (d) Number of models, grouped by pathogen, in which each of the 15 core assumptions differed from those of the Ross–Macdonald model. Core assumptions are specified by the questions from the questionnaire presented in table 2.