Modeling Co-Dynamics of COVID-19, HIV and TB: Optimal Control, Cost-Effectiveness, and the Role of Vaccination Behavior

Abstract

Despite the availability of numerous treatments and preventive measures for Coronavirus Disease 2019 (COVID-19), Human Immunodeficiency Virus (HIV) and tuberculosis (TB), these diseases continue to pose significant public health concerns with far-reaching socioeconomic implications. This dissertation aims to identify effective and efficient control strategies to mit igate coinfections of COVID-19 and HIV, as well as the concurrent infections of COVID-19, HIV, and TB, using mathematical models. It provides models that govern the transmission dy namics of COVID-19, HIV/AIDS and TB. For the formulated models, we establish the invari ant region, positivity, and boundedness of the solutions; determine the reproduction numbers of the sub-models and the co-infection model; and examine the existence and stability of the equi libria. Parametric estimation and curve fitting were performed using data from Ethiopia, and numerical simulations were employed to support and clarify the analytical findings, demonstrat ing the effects of various parameters on COVID-19, HIV and TB co-infection and illustrating how preventive efforts impact the co-infected population. The first model examines the trans mission of COVID-19 and HIV, taking into account individuals with advanced HIV/AIDS and those at risk of death from both diseases. Numerical simulations highlight that factors such as increased infectiousness among HIV patients and low vaccination rates lead to higher co- infec tion rates, while increased COVID-19 vaccination and treatment reduce mortality. The second model evaluates four intervention strategies—HIV prevention, HIV treatment, COVID-19 vac cination, and COVID-19 treatment— with simulations showing reductions in co-infections. A cost-effectiveness analysis identifies the combined approach of vaccination and treatment as the most viable strategy. The third model addresses the broader co-infection scenario involving TB. The model emphasizes the importance of vaccination, though challenges like vaccine ineffi cacy, waning immunity, and low information coverage persist. Numerical simulations show that waning immunity and high reinfection rates can exacerbate co-infection peaks, but information driven vaccination strategies significantly mitigate these effects. Collectively, these three models underscore the need for coordinated efforts in vaccination, treatment, and public health commu nication to address the challenges posed by COVID-19, HIV and TB co-infection. The models provide essential guidance for developing targeted interventions and public health strategies aimed at reducing co-infection cases and associated mortality while accounting for complex behavioral and epidemiological factors such as waning immunity and the role of information dissemination.