Stability Analysis for Co-Dynamics of COVID-19 and HIV-AIDS with Public Sensitization and Education as Controls

Abstract

Infectious diseases have denied humanity joy and resources over the centuries. Major diseases such as rabies (1885), whooping cough (1914), flu influenza (1945), and COVID-19 changed the course of life. Hence, a need for alternative methods of combating infections with optimal cost. The coronavirus has shocked the world and it was devastating. The human immunodeficiency virus (HIV) epidemic has caused individuals to rethink their sexual lives, especially in Africa, where the disease has plagued several souls. The authors developed a compartmental model for co-infection of COVID-19 and HIV infection with optimal control. The following controls were incorporated into the model: education/sensitization of susceptible populations, use of anti-retroviral therapy, treatment of co-infected populations, and treatment of the COVID-19-infected population are essential in the fight against HIV and COVID-19 infections. Qualitative and quantitative solutions to the model were determined and analyzed. The HIV-COVID-19-free equilibrium of the co-dynamics model was found to be locally asymptotically stable whenever the reproductive rate was less than one and unstable otherwise. The co-dynamic model was extended to include some controls. This was to establish which strategy is suitable for combating the spread of the COVID-19-infected population. The results of our numerical simulations revealed that in combating COVID-19 and HIV spread, education of susceptible populations and treatment of COVID-19-infected populations are the best options. There has been a reduction in COVID-19 infection, an increase in the COVID-19 recovery population, and a substantial reduction in COVID-19 populations due to this control strategy. The findings of this study are an important step in the fight against HIV and COVID-19. Hence, policymakers should place priority on public education on HIV/COVID-19 infections and treatment of the COVID-infected population when combating these diseases.