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

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DOI: 10.4236/am.2012.312256    3,805 Downloads   5,690 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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

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