HIV and COVID-19 co-infection: A mathematical model and optimal control

A new mathematical model for COVID-19 and HIV/AIDS is considered to assess the impact of COVID-19 on HIV dynamics and vice-versa. Investigating the epidemiologic synergy between COVID-19 and HIV is important. The dynamics of the full model is driven by that of its sub-models; therefore, basic analysis of the two sub-models; HIV-only and COVID-19 only is carried out. The basic reproduction number is computed and used to prove local and global asymptotic stability of the sub-models' disease-free and endemic equilibria. Using the <i>fmincon</i> function in the Optimization Toolbox of MATLAB, the model is fitted to real COVID-19 data set from South Africa. The impact of intervention measures, namely, COVID-19 and HIV prevention interventions and COVID-19 treatment are incorporated into the model using time-dependent controls. It is observed that HIV prevention measures can significantly reduce the burden of co-infections with COVID-19, while effective treatment of COVID-19 could reduce co-infections with opportunistic infections such as HIV/AIDS. In particular, the COVID-19 only prevention strategy averted about 10,500 new co-infection cases, with similar number also averted by the HIV-only prevention control.