An analysis of time-delay epidemic model for TB, HIV, and AIDS co-infections

Abstract

This paper presents a time-delay epidemic model for Tuberculosis(TB), Human Immunodeficiency Virus(HIV), and Acquired Immunodeficiency Syndrome(AIDS) co-infection. Our study examines how delay impacts mathematical models of TB, HIV, and AIDS. There are four classes in the proposed system — Susceptibles, TB infectives, HIV infectives (with or without TB), and AIDS patients. A model shows four states of equilibrium: disease-free, HIV-free, TB-free, and endemic. If the reproduction number R0 is less than one, the disease-free equilibrium is locally asymptotically stable. If R0 greater than one, at least one infection will be present in the population Positive endemic equilibrium is always locally stable, but it can become globally stable under certain circumstances, indicating the disease has become endemic. TB and HIV infections drop as a result of recovery, and endemic equilibrium leads to TB free conditions. The number of people living with AIDS declines when TB is not associated with HIV infection. The model is also numerically analyzed to see how some important parameters affect the disease’s progression. Mathematical and numerical methods are employed to study the impact of delay.