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

• 作者: Jér?me Pousin Ouaténi Diallo Yaya Koné
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Spacial SPREAD of INFECTIONS Controlability MAXIMUM PRINCIPLE
• 年，卷（期）: 2012,（12）
• 页码范围: 1877-1881
• 页数: 5页
• 分类号: O1

摘要

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.