Effect of delay on the model of American cutaneous Leishmaniasis

This paper investigates the dynamics of transmission of a model of American cutaneous leishmaniasis (ACL). The model consists of infectious incidental hosts (humans), reservoir hosts (forest rodents, dogs, etc.) and vectors. A delay in the time between infection and infectiousness for the reservoir hosts is incorporated. In the absence of delay, it is observed that if R-0 > 1, then endemic equilibrium becomes stable and if R-0 < 1, then infection-free equilibrium becomes stable. The length of delay is estimated for preserving stability. Stability switching behavior of the system is also indicated. Lastly the results are verified through numerical simulations as far as possible.