Changes in American Cutaneous Leishmaniasis transmission in response to human case detection

Abstract In this work, we investigate three mathematical models for the dynamics of American Cutaneous Leishmaniasis (ACL) transmission that are based on ordinary differential equations. The subpopulations of each model consists of infected incidental hosts, infected reservoir hosts, and infected vectors. The number of infected individual hosts is thought to influence the incidental host’s infection rate in the first model and the vectors’ death rate in the second whereas the third model integrates both of the impacts. There are two equilibrium points in each of the three models: the endemic equilibrium point and the disease-free equilibrium point. We noticed that the basic reproduction number is influenced by the overall populations of reservoir hosts and vectors, as well as the rates of infection and recovery of the reservoir hosts. For each model, the local and global stability of the two equilibrium points were investigated, and numerical simulations were carried out to support the analytical findings.