Mathematical modelling of Hantavirus: From the mean field to the individual level

GUILLERMO ABRAMSON

Progress in Mathematical Biology Research

Nova Science Publishers

Lugar: Hauppauge NY, USA; Año: 2008; p. 219 - 245

I review recent mathematical models of the epizootic of Hantavirus in mice populations. The models are mainly based on field observations of Peromyscus maniculatus populations in New Mexico, which hosts Sin Nombre virus. The sporadic disappearance of the infection during times of adverse conditions is explained as a phase transition controlled by the environment. Refinements of the model allow to include the effect of non-host competitors, as well as to assess the validity of the diffusion transport. A stochastic model, based on individual interactions, is also analyzed. We compare its macroscopic limit with the mean field model, and discuss some phenomena inherent to stochastic systems: the role of fluctuations, extinctions and stabilization of oscillations.