Deterministic Mathematical Modelling of Tuberculosis and HIV Diseases

Abstract

The main objective of mathematical modelling of infectious diseases is to identify and study the factors that influence the spread of disease and to predict the future dynamics of a particular disease or combination of diseases. Among all the prevailing infectious diseases in the world, the Acquired Immunodeficiency Syndrome (AIDS) is the most serious life threatening condition caused by infection with the Human Immunodeficiency Virus (HIV) for which there is no cure available at present. Tuberculosis (TB) is a common, and in many cases fatal, infectious disease caused by various strains of myco-bacteria, usually Mycobacterium Tuberculosis. The work done in this thesis focuses on the use of deterministic mathematical models and their analysis to gain qualitatively as well as quantitatively meaningful insight into the transmission dynamics of the Human Immunodeficiency Virus (HIV), Tuberculosis (TB) and HIV-TB co-infection. The potential role of various control measures (such as awareness, screening), reinfection and co-infection is addressed. The developed models are analyzed using the stability theory of differential equations.