In this article, we propose and analyze a compartmental model for HIV-Cholera co-infection. We establish the existence, uniqueness, and positivity of the solution. The disease-free equilibrium (DFE) point is then identified and its local stability and global stability is analyzed to better understand the dynamics of this co-infection. A sensitivity analysis is conducted to explore potential strategies for limiting secondary infections.
Finally, numerical simulations illustrate our theoretical results, showing that when the contact rate between susceptible and infected individuals is significantly reduced, the infected population will decline, with cholera disappearing after four hundred (400) days and HIV after Five hundred (500) days.
This study highlights that the most influential parameters for controlling the disease are the contact rates $\beta_H$, $\beta_C$, and $\beta_{HC}$. Numerical results show that both diseases will disappear when the basic reproduction number $\mathcal{R}_0$ remains below one, but the diseases remain endemic in the population when $\mathcal{R}_0$ is greater than one.