Ratio-Dependent Vector-Host Model on Cutaneous Leishmaniasis—A Mathematical Study Based on Caputo-Fabrizio Fractional Derivative

Cutaneous Leishmaniasis (CL) is a neglected tropical complex vector-borne disease which is originated by the protozoa of the genus Leishmania. The disease is transmitted to human or animal through the bites of infected female Phlebotominae sand-fly (vector). This primarily affects the skin, mucous membranes and other internal organs. It is very noteworthy that the dynamic behavior of any living being not only depends on the conditions of its current state but also on those of its previous states . In this article we proposed and analyzed a four- dimensional ratio-dependent mathematical model that includes vector feeding preference of female sand flies for career hosts; additionally, we analyzed the Caputo-Fabrizio fractional version of the basic model to capture the effect of memory in the system. Based on different values of the fractional order $$\tau \in (0, 1)$$ , we compare the behaviour of the fractional-order model with the corresponding integer order model. All of the analytical results are validated through proper numerical simulations and are compared with some real clinical data.