A Mathematical Model of HIV and Tb Co-Infection with Interventions, a Case of Siaya County in Kenya
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Date
2023
Authors
Vincent, Otieno Brian
Journal Title
Journal ISSN
Volume Title
Publisher
Kenyatta University
Abstract
In this research, we take into consideration a model of co-infection between HIV/AIDS
and TB with treatment of infectious and inactive forms of TB and HIV preventive and
therapeutic strategies. Speci cally we consider condom use, early ART and withdrawal
from sexual activities by individuals who are infected by HIV as controls. The model is
positively bounded. The spectral radius of the next generation matrix has been used to
determine the model's fundamental reproduction number. The model displays these
equilibria: a disease free and a co-infection equilibrium. By utilizing Routh-Hurwitz
standard and center manifold theory, the model has been qualitatively examined. When
R0 < 1,we discovered that the disease free equilibrium point was locally asymptotically
stable and not globally asymptotically stable. Sensitivity analysis of R0T and R0H
identi es $1 and $2, TB and HIV infection rates through e ective contact respectively,
as the main variables that if targeted, R0T and R0T are reduced. From numerical
simulation,we show that increasing HIV interventions reduces cases of latent TB
progressing to active TB and therefore is an additional strategy in the ght against
TB disease.
Description
A Project Presented to the School of Pure and Applied Sciences at Kenyatta University in Partial Completion of the Requirements for the Award of the Degree of Masters of Science in Applied Mathematics, November 2022
Keywords
A Mathematical Model, HIV and Tb Co-Infection, Interventions, a Case of Siaya County, Kenya