TITLE:
A Model of Spatial Spread of an Infection with Applications to HIV/AIDS in Mali
AUTHORS:
Ouaténi Diallo, Yaya Koné, Jérôme Pousin
KEYWORDS:
Spacial Spread of Infections; Controlability; Maximum Principle
JOURNAL NAME:
Applied Mathematics,
Vol.3 No.12,
December
14,
2012
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.