Mathematical Model of Tuberculosis, Malaria, and HIV Coinfection with the Effect of Intervention

Abstract

Tuberculosis, malaria, and HIV are infectious diseases that have become major global health problems. Efforts to reduce the incidence and mortality of tuberculosis have undergone a long process, resulting in a significant annual decrease of up to 2%. In a single year, malaria cases can reach nearly 230,000,000, with up to 400,000 deaths worldwide. Meanwhile, approximately 37,000,000 people were living with HIV worldwide in 2020, with about 690,000 deaths due to AIDS reported in the same year. Within the framework of the Sustainable Development Goals (SDGs), particularly Goal 3 on good health and well-being, one of the key targets is to end the epidemics of tuberculosis, malaria, and HIV. This research examines the effects of various interventions on tuberculosis, malaria, and HIV coinfection. The interventions considered include preventive measures, mosquito nets, insecticides, contraception, tuberculosis treatment, malaria treatment, and antiretroviral (ARV) therapy for HIV. The mathematical model of tuberculosis, malaria, and HIV coinfection is well-defined, as it is proven to have non-negative solutions, to be bounded, and to remain within the positive invariant region. The tuberculosis, malaria, and HIV sub-models each have an asymptotically stable equilibrium when the basic reproduction number is less than one. Based on the results of numerical simulations of the sub-models, it can be observed that when the basic reproduction number exceeds one, the disease spreads throughout the population.