A Model of Spatial Spread of an Infection with Applications to HIV/AIDS in Mali

DOI: 10.4236/am.2012.312256   PDF   HTML   XML   4,089 Downloads   6,057 Views   Citations

Abstract

In this paper we introduce a classical SI model to capture the spread of an infectious disease within a population. More precisely, the spatial diffusion of HIV/AIDS in a population is modeled. For that, we assume that the spread is due to the anarchical comportment of infected individuals along a road, especially, “lorry drivers”. The question which consists of the control of the infection is also addressed. Infected individuals moving from a town to another one, the diffusion is then anisotropic with a main direction of propagation, namely the road direction. Using a semi-group argument and a maximum principle, the uniqueness of a solution to the problem is established. This solution is also estimated. We end this paper by considering some numerical experiments in the case of HIV/AIDS spread in Mali along a road connecting two towns.

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O. Diallo, Y. Koné and J. Pousin, "A Model of Spatial Spread of an Infection with Applications to HIV/AIDS in Mali," Applied Mathematics, Vol. 3 No. 12, 2012, pp. 1877-1881. doi: 10.4236/am.2012.312256.

Conflicts of Interest

The authors declare no conflicts of interest.

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