Mathematical Model of HIV and Cholera Co-Infection in the Presence of Treatment

Subject Areas : International Journal of Mathematical Modelling & Computations

Kumama Cheneke ¹ , Geremew Edessa ² , Purnachandra Koya ³

1 - Department of Mathematics, Wollega University, Nekemte, Ethiopia
2 - Department of Mathematics, Wollega University, Nekemte, Ethiopia
3 - Department of Mathematics, Wollega University, Nekemte, Ethiopia

Received: 2020-02-05 Accepted : 2020-12-20 Published : 2020-12-25

Keywords: Stability, Sensitivity, HIV- Cholera coinfection, Well-posed,

Abstract :

In the current study, a deterministic mathematical model of HIV and Cholera co-infection is developed to analyze the impact of treatments in the presence of diseases in the population. The model consists of nine classes of the human population and one class of bacteria population. The formulated model is mathematically well-posed and biologically meaningful. The reproduction number is employed to analyze the extinction or spreading of the disease in the population. it is observed that cholera has a positive impact on HIV patients and HIV also has a positive impact on cholera patients. A separate analysis of each infection model and co-infection model is presented. Further, the stability analysis of equilibrium points is included. Finally, numerical simulations are performed using Matlab software. The result of numerical simulations shows that early treatment is very powerful for clearing or controlling cholera within a specified period of time and supports HIV/AIDS patients to live more years.