title: Sensitivity Analysis and Optimal Control of Anthroponotic Cutaneous Leishmania.
abstract: This paper is focused on the transmission dynamics and optimal control of Anthroponotic Cutaneous Leishmania. The threshold condition R0 for initial transmission of infection is obtained by next generation method. Biological sense of the threshold condition is investigated and discussed in detail. The sensitivity analysis of the reproduction number is presented and the most sensitive parameters are high lighted. On the basis of sensitivity analysis, some control strategies are introduced in the model. These strategies positively reduce the effect of the parameters with high sensitivity indices, on the initial transmission. Finally, an optimal control strategy is presented by taking into account the cost associated with control strategies. It is also shown that an optimal control exists for the proposed control problem. The goal of optimal control problem is to minimize, the cost associated with control strategies and the chances of infectious humans, exposed humans and vector population to become infected. Numerical simulations are carried out with the help of Runge-Kutta fourth order procedure.
authors: Department of Mathematics, University of Science and Technology, Bannu, Khyber Pakhtunkhwa, Pakistan.|Department of Mathematics, University of Malakand Lower Dir, Khyber Pakhtunkhwa, Pakistan.
authors: Muhammad
authors: M
authors: Zamir
authors: Department of Mathematics, University of Malakand Lower Dir, Khyber Pakhtunkhwa, Pakistan.
authors: Gul
authors: G
authors: Zaman
authors: Department of Mathematics, Faculty of Science, King Abdul Aziz University, Jeddah, Saudi Arabia.
authors: Ali Saleh
authors: AS
authors: Alshomrani
mesh_terms: D000818:Animals; D003196:Computer Graphics; D004199:Disease Vectors; D006801:Humans; D007895:Leishmania tropica / Q000502:physiology; D016773:Leishmaniasis, Cutaneous / Q000517:prevention & control* / Q000635:transmission*; D008962:Models, Theoretical