A Mathematical Model for HIV- COVID-19 Co-Infection Dynamics in Kenya

Authors : Kimulu Ancent Makau; Oke Abayomi Samuel; Muli Charles Ndambuki

Volume/Issue : Volume 8 - 2023, Issue 8 - August

Google Scholar : https://bit.ly/3TmGbDi

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Abstract : The COVID-19 virus has been one of the deadly virus since it was first reported in December 2019 in Wahun, China. However vaccines have been developed for COVID-19 which were approved to be safe and reduced the infections, none such vaccine has been discovered for HIV. These two diseases are viral and this model is designed to study the co-infection dynamics in Kenya. Several models have been done on the HIV-COVID -19 co-infections in the world and our model focused on dynamics of Kenyan co-infected population. This study focused on the effect of COVID – 19 infection on HIV infected population. The equilibrium points were determined and their stability was determined using the Jacobian method. The reproduction number was obtained using the Next Generation Method. The DFE was asymptotically stable when Ro < 1 and unstable when Ro > 1. The model was solved numerically using MATLAB ode45 solver and the results shows that increase in the COVID-19 infection rate leads to increase in the co-infected population, the treated and the viral suppressed populations in the system. This implies that the co-infected population responds better to treatment to reduce their viral load in their bodies and hence reducing thedanger of death due to the co-infection.

Keywords : HIV, COVID-19, Co – Infection, Dynamics, Coronavirus, Next Generation Matrix.

The COVID-19 virus has been one of the deadly virus since it was first reported in December 2019 in Wahun, China. However vaccines have been developed for COVID-19 which were approved to be safe and reduced the infections, none such vaccine has been discovered for HIV. These two diseases are viral and this model is designed to study the co-infection dynamics in Kenya. Several models have been done on the HIV-COVID -19 co-infections in the world and our model focused on dynamics of Kenyan co-infected population. This study focused on the effect of COVID – 19 infection on HIV infected population. The equilibrium points were determined and their stability was determined using the Jacobian method. The reproduction number was obtained using the Next Generation Method. The DFE was asymptotically stable when Ro < 1 and unstable when Ro > 1. The model was solved numerically using MATLAB ode45 solver and the results shows that increase in the COVID-19 infection rate leads to increase in the co-infected population, the treated and the viral suppressed populations in the system. This implies that the co-infected population responds better to treatment to reduce their viral load in their bodies and hence reducing thedanger of death due to the co-infection.

Keywords : HIV, COVID-19, Co – Infection, Dynamics, Coronavirus, Next Generation Matrix.