Analysis and robust simulation of mathematical models of HIV and Leishmaniasis co-infection

Abstract

The purpose of this thesis is the theoretical and numerical study of epidemiological models of Visceral Leishmaniasis (VL) and human immunode ciency virus (HIV) coinfection. We study these models theoretically and design and analyze robust numerical methods to solve them. The rst sub-model describes the transmission dynamics of VL and incorporates three populations: the human, the reservoir, and the vector host populations. Then we study the Anthroponotic Visceral Leishmaniasis (AVL) between the human and the vector host population. The second sub-model describes a deterministic SIAT (Susceptible-Infected-AIDS-Treated) HIV/AIDS model that incorporates the treatments of HIV-infected and AIDS-infected individuals.