Spatial heterogeneity in simple deterministic SIR models assessed ecologically

Edward Kyle Waters, Harvinder Sidhu, Geoff Mercer


Patchy or divided populations can be important to infectious disease transmission. We first show that Lloyd’s mean crowding index, an index of patchiness from ecology, appears as a term in simple deterministic epidemic models of the SIR type. Using these models, we demonstrate that the rate of movement between patches is crucial for epidemic dynamics. In particular, there is a relationship between epidemic final size and epidemic duration in patchy habitats: controlling inter-patch movement will reduce epidemic duration, but also final size. This suggests that a strategy of quarantining infected areas during the initial phases of a virulent epidemic might reduce epidemic duration, but leave the population vulnerable to future epidemics by inhibiting the development of herd immunity.



SIR model, ecology, infectious diseases, spatial dynamics


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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.