A spatially stochastic epidemic model with partial immunization shows in mean field approximation the reinfection threshold

Reference:

Stollenwerk, N., van Noort, S., Martins, J., Aguiar, M., Hilker, F., Pinto, A. and Gomes, G., 2010. A spatially stochastic epidemic model with partial immunization shows in mean field approximation the reinfection threshold. Journal of Biological Dynamics, 4 (6), pp. 634-649.

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Official URL:

http://dx.doi.org/10.1080/17513758.2010.487159

Abstract

Recently, the notion of a reinfection threshold in epidemiological models of only partial immunity has been debated in the literature. We present a rigorous analysis of a model of reinfection which shows a clear threshold behaviour at the parameter point where the reinfection threshold was originally described. Furthermore, we demonstrate that this threshold is the mean field version of a transition in corresponding spatial models of immunization. The reinfection threshold corresponds to the transition between annular growth of an epidemics spreading into a susceptible area leaving recovered behind and compact growth of a susceptible-infected-susceptible region growing into a susceptible area. This transition between annular growth and compact growth was described in the physics literature long before the reinfection threshold debate broke out in the theoretical biology literature.

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