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, was determined using the Next Generation Matrix. The results revealed that 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. KEY WORDS : HIV/AIDS, Migration, Monod function, Basic reproduction number, Stability Analysis, Equilibria Points. DOI : 10.7176/MTM/9-6-03 Publication date : June 30 th 2019
Highlights
1.1 Background of the study Human immunodeficiency virus (HIV) is a retrovirus that mainly infects CD4+ T-cells
The analysis showed the existence of disease-free and Endemic Equilibrium points and that the stability existence was based on the value of the basic reproduction number
From the above sensitivity analysis, it is observed that the rate of migrations is inversely proportional to the basic reproduction number while the infection rates is directly proportional to the basic reproduction number. This implies that to reduce the spread of HIV infection more efforts and measures should be focused in reducing the infections and encouraging more migrations from Mombasa to Nairobi
Summary
1.1 Background of the study Human immunodeficiency virus (HIV) is a retrovirus that mainly infects CD4+ T-cells. Among the humans it’s transmitted as a result of sexual intercourse between the susceptible individual and infected person. 36.7 million people lived with HIV at the end of 2016 whereas 1.8 million people became infected in 2016 globally (WHO and UNAIDS 2017). The hosts move between the two patches at constant specific migration rate. The time frame for migration of truck drivers is considered to be short. The main feature of the model is that the transmission of HIV is contributed by migration and contact of infected individuals and individuals with AIDS with the susceptible sub-population. The individuals with HIV contribute more to the force of infection than those with AIDS. The infection rates for the two patches is considered to be varying
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