From puddles to planet: modeling approaches to vector-borne diseases at varying resolution and scale
Modeling mosquito transmission of pathogens has a long history starting with the foundational work of Ross and Macdonald, who established the mathematical formalisms for modeling the transmission of malaria between a vector and a host population. The Ross–Macdonald model identifies five key quantities: mosquito population density, mosquito survival probabilities, mosquito blood feeding frequency, mosquito host preferences, and parasite development in mosquitoes. This basic model was extended first for modeling the Garki project and later in the cyclical feeding models. From 1970 through 2010, there was a rapid proliferation of mathematical models of vector-borne disease, but most of these models retained the basic Ross–Macdonald structures and assumptions, as cataloged and analyzed in the comprehensive review by Reiner et al.
Filling in the intermediate spatial scales
Between the scales of the very short spatial-scale aquatic habitats modeled in mechanistic detail and the global patterns of mosquito species habitat lie many spatial scales containing important dynamics. Two generalized model concepts that facilitate questions at scales between puddles and the planet are patch models and continuous space models (figure 1). Patch models function as metapopulations dividing landscapes into smaller subareas, or ‘patches.’ Hosts and vectors within the same single patch can interact strongly, and connectivity on the landscape is determined by weaker interactions among patches occurring through time spent at risk by hosts, or migration of hosts, vectors, or both. Other frameworks utilize a continuous space in which feeding and oviposition locations are single points. The relationship between continuous space and patch models can be seen in figure2.
Conclusions: The explosion in models of vector-borne diseases has recently begun to include a broader set of frameworks for modeling spatial effects and dynamics that include spatially heterogeneous landscapes knit together by host and vector movement. Moving beyond models of a single population of vectors mixing with a single population of hosts to capture spatial dynamics and variability requires data on human and mosquito movement, human population patterns, and pathogen distribution at broad geographic scales or within-city microscales.