A Deterministic Model Of HIV Transmission Between Two Closed Patches Incorporating The Monod Equation

Abstract

Among other factors, migration has significantly contributed to the spread of HIV. Recent studies have revealed that new infections occur along major transport corridors and truck-drivers have overall higher prevalence rates of HIV and sexually transmitted infections than non-truck drivers’ counterparts. Therefore, there exist a link between population mobility and HIV infection, as populations along transport corridors remain substantial contributors of new infections. This research work documents a deterministic model of the dynamics of HIV transmission between two closed patches that incorporates the Monod equation in migration with truck drivers being the agents of HIV transmission. Migration is considered as a social determinant to health and have a significant impact on health‐ related vulnerabilities and access to services. We assumed that susceptible individuals become infected via sexual intercourse with HIV infected truck drivers and all the infected individuals ultimately developed AIDS exponentially. The model also assumed that the patches have different infection and susceptibility rates. The patches basic reproduction number, 𝑅0 was determined using the Next Generation Matrix. The results revealed that 𝑅0 should be kept below unity to eradicate the transmission of the virus. The Disease-Free Equilibrium Point was obtained based on the signs of the Eigen values of the Jacobian matrix. In the absence, the Disease-Free Equilibrium Point is both Locally Asymptotically and Globally Asymptotically Stable. It was further proved that the model did not display Endemic Equilibrium Point under a special property for epidemic models. The model findings are vital in guiding health practitioners, governmental and non-governmental health agencies in the development of effective mitigation strategies to reduce the spread of HIV.