Annals of Communications in Mathematics

AbstractThis paper provides a mathematical analysis of a host vectors disease model with the influence of available hospital resources. We derive the basic reproduction number Rh 0 of the model. We prove the existence of a unique disease-free equilibrium, which is stable when the basic reproduction number Rh 0 is less than 1, indicating that the disease can be eradicated under these conditions. However, when Rh 0 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 sensitivity analysis of the parameters is carried out to assess the most influential parameters in managing the epidemic.

ABSTRACT. In this paper, we analyze a vector-host epidemic model with a piecewise-smooth treatment rate. The use of piecewise-smooth treatment depicts the limited medical resource situation in the community. The treatment increases linearly with infective population until the treatment capacity is reached, after which constant treatment (i.e., maximum treatment) is applied. The analysis indicates that there exists a critical value \( I_{h0}^c = \frac{b_h}{\mu_h} \) for the infective human population level \( I_{h0} \) at which the health care system reaches its capacity. We derive that when \( I_{h0} \geq I_{h0}^c \), the dynamics of the model is completely determined by the basic reproduction number \( R_0 \). When \( I_{h0} < I_{h0}^c \), the model exhibits multiple endemic equilibria.