Analytical and Numerical Solutions of a TB-HIV/AIDS Co-infection Model via Fractional Derivatives Without Singular Kernel

Dokuyucu, Mustafa Ali; Dutta, Hemen

Human beings, who have encountered a lot of diseases and viruses in the last century, conduct a lot of studies to defeat such diseases, particularly HIV, known as the human immunodeficiency virus, and AIDS disease known as advanced immunodeficiency syndrome. The said diseases can be quite dangerous for countries and even for the whole world as the mode of transmission and transmission rate of such diseases increase. The literature needs mathematical modeling and subsequent analysis of such diseases. In the light of this information, TB-HIV/AIDS coinfection model was analyzed. To this end, the model was firstly extended to the Caputo-Fabirizo fractional derivative obtained using the exponential function. Then, uniqueness solutions were investigated by the help of the fixed-point theorem. Thereafter, the uniqueness solution of the model was made by assuming certain parameters, and its stability analyzes were examined. Finally, numerical solutions of the mathematical model were made and its numerical simulations were shown.