CW-Department of Mathematics

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A Mathematical Model of HIV and Tb Co-Infection with Interventions, a Case of Siaya County in Kenya
(Kenyatta University, 2023) Vincent, Otieno Brian; Winfred Mutuku
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.