Construction and analysis of efficient numerical methods to solve Mathematical models of TB and HIV co-infection

• Main Author: Ahmed, Hasim Abdalla Obaid.
• Format: Others
• Language: English
• Published: 2011
• Subjects: Human Immunodeficiency Virus (HIV); Tuberculosis (TB); HIV-TB Co-infection; Dynamical System Theory; Distributed Delay; Bifurcation Analysis; Local Asymptotic Stability; Global Asymptotic Stability; Numerical Methods; Convergence Analysis.
• Online Access: http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_3704_1325661141

In this thesis, we study these models and design and analyze robust numerical methods to solve them. To proceed in this direction, first we study the sub-models and then the full model. The first sub-model describes the transmission dynamics of HIV that accounts for behavior change. The impact of HIV educational campaigns is also studied. Further, we explore the effects of behavior change and different responses of individuals to educational campaigns in a situation where individuals may not react immediately to these campaigns. This is done by considering a distributed time delay in the HIV sub-model. This leads to Hopf bifurcations around the endemic equilibria of the model. These bifurcations correspond to the existence of periodic solutions that oscillate around the equilibria at given thresholds. Further, we show how the delay can result in more HIV infections causing more increase in the HIV prevalence. Part of this study is then extended to study a co-infection model of HIV-TB. A thorough bifurcation analysis is carried out for this model. Robust numerical methods are then designed and analyzed for these models. Comparative numerical results are also provided for each model.