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Sensitivity Analysis and Optimal Control of Anthroponotic Cutaneous Leishmania

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  • Muhammad Zamir
  • Gul Zaman
  • Ali Saleh Alshomrani

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.

Suggested Citation

  • Muhammad Zamir & Gul Zaman & Ali Saleh Alshomrani, 2016. "Sensitivity Analysis and Optimal Control of Anthroponotic Cutaneous Leishmania," PLOS ONE, Public Library of Science, vol. 11(8), pages 1-19, August.
    • Handle: RePEc:plo:pone00:0160513
    DOI: 10.1371/journal.pone.0160513
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    Cited by:

    1. Muntaser Safan & Alhanouf Altheyabi, 2023. "Mathematical Analysis of an Anthroponotic Cutaneous Leishmaniasis Model with Asymptomatic Infection," Mathematics, MDPI, vol. 11(10), pages 1-19, May.

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