Open AccessSensitivity Analysis and Optimal Control of Anthroponotic Cutaneous Leishmania
Author(s) -
Muhammad Zamir,
Gul Zaman,
Ali Saleh Alshomrani
Publication year - 2016
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0160513
Subject(s) - sensitivity (control systems) , optimal control , transmission (telecommunications) , population , basic reproduction number , mathematical optimization , control (management) , control theory (sociology) , computer science , mathematics , medicine , artificial intelligence , engineering , telecommunications , environmental health , electronic engineering
This paper is focused on the transmission dynamics and optimal control of Anthroponotic Cutaneous Leishmania . The threshold condition R 0 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.