Computational investigation of tuberculosis and HIV/AIDS co-infection in fuzzy environment

Abstract Tuberculosis (TB) and human immunodeficiency virus (HIV)/acquired immunodeficiency virus (AIDS) have a fatal bidirectional connection with a significant global epidemic overlap. People living with HIV-positive are over 30 times more likely than HIV-negative people to develop TB and active TB causes the chronic immunological activation, which accelerates HIV/AIDS disease development. This gives computational investigation of a TB and HIV/AIDS co-infection in fuzzy environment. The application of fuzzy theory aids in addressing the difficulties associated with measuring uncertainty in mathematical representations of the diseases. Here, the fuzzy reproduction number and fuzzy equilibrium points are obtained by using a model relevant to a specific group described by the triangular membership function. Two numerical techniques, namely, forward Euler’s method and Runge–Kutta method, are developed within a fuzzy framework to address the model. We have also employed the non-standard finite difference scheme, which ensures the preservation of the essential properties such as positivity, convergence, and consistency. Numerical simulations are also conducted to illustrate the applicability of the developed technique.