This paper provides a mathematical analysis of a host vectors disease model with the influence of available hospital resources. We derive the basic reproduction number Rh0 of the model. We prove the existence of a unique disease-free equilibrium, which is stable when the basic reproduction number Rh0 is less than 1, indicating that the disease can be eradicated under these conditions. However, when Rh0 exceeds 1, the system exhibits multiple endemic equilibria, leading to the possible persistence of the disease into the population. The study also reveals the existence of bifurcations, indicating qualitative changes in the system’s dynamics depending on certain critical parameter values. A sensi- tivity analysis of the parameters is carried out to assess the most influential parameters in managing the epidemic.

Host-vector disease, Stability, Bifurcation