A Model of Spatial Spread of an Infection with Applications to HIV/AIDS in Mali
- 1 Faculté des Sciences et Techniques, USTTB, Bamako, Mali
- 2 Faculté des Sciences et Techniques, USTTB, Bamako, Mali
- 3 Institut Camille Jordan, INSA de Lyon, Lyon, France
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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