Sensitivity analysis and optimal countermeasures control of model of the spread of COVID-19 co-infection with HIV/AIDS

This paper analyzes and examines the optimal control in the co-infection of COVID-19 with HIV/AIDS by providing preventive and treatment control measures. The population is divided into eight subpopulations. The preventive control of COVID-19 is denoted by u1. The preventive control of HIV/AIDS is denoted by u2. The treatment control of COVID-19 is denoted by u3, and the treatment control of COVID-19 for the subpopulation co-infected with HIV/AIDS is denoted by u4. Based on the model analysis, non-endemic and endemic equilibrium points are obtained, along with the basic reproduction number of the COVID-19, HIV/AIDS, and COVID-19-HIV/AIDS sub-models. Numerical simulations reveal that using preventive control u1 is more effective in reducing the spread of COVID-19 compared to u3 or u4, both individually and together. Preventive control u2 is more effective in controlling the spread of HIV/AIDS compared to the absence of control. The sensitivity analysis of parameter identifies parameters that significantly affect the reduction or increase in the spread of COVID-19-HIV/AIDS co-infection. We found that in order to reduce the co-infection’s spread, we should pay attention to the reducing the contact rate of HIV/AIDS patients or increasing their treatment rate.