Cargando…

Sensitivity Analysis and Optimal Control of Anthroponotic Cutaneous Leishmania

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....

Descripción completa

Detalles Bibliográficos
Autores principales: Zamir, Muhammad, Zaman, Gul, Alshomrani, Ali Saleh
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2016
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4978393/
https://www.ncbi.nlm.nih.gov/pubmed/27505634
http://dx.doi.org/10.1371/journal.pone.0160513
_version_ 1782447164672180224
author Zamir, Muhammad
Zaman, Gul
Alshomrani, Ali Saleh
author_facet Zamir, Muhammad
Zaman, Gul
Alshomrani, Ali Saleh
author_sort Zamir, Muhammad
collection PubMed
description 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.
format Online
Article
Text
id pubmed-4978393
institution National Center for Biotechnology Information
language English
publishDate 2016
publisher Public Library of Science
record_format MEDLINE/PubMed
spelling pubmed-49783932016-08-25 Sensitivity Analysis and Optimal Control of Anthroponotic Cutaneous Leishmania Zamir, Muhammad Zaman, Gul Alshomrani, Ali Saleh PLoS One Research Article 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. Public Library of Science 2016-08-09 /pmc/articles/PMC4978393/ /pubmed/27505634 http://dx.doi.org/10.1371/journal.pone.0160513 Text en © 2016 Zamir et al http://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Research Article
Zamir, Muhammad
Zaman, Gul
Alshomrani, Ali Saleh
Sensitivity Analysis and Optimal Control of Anthroponotic Cutaneous Leishmania
title Sensitivity Analysis and Optimal Control of Anthroponotic Cutaneous Leishmania
title_full Sensitivity Analysis and Optimal Control of Anthroponotic Cutaneous Leishmania
title_fullStr Sensitivity Analysis and Optimal Control of Anthroponotic Cutaneous Leishmania
title_full_unstemmed Sensitivity Analysis and Optimal Control of Anthroponotic Cutaneous Leishmania
title_short Sensitivity Analysis and Optimal Control of Anthroponotic Cutaneous Leishmania
title_sort sensitivity analysis and optimal control of anthroponotic cutaneous leishmania
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4978393/
https://www.ncbi.nlm.nih.gov/pubmed/27505634
http://dx.doi.org/10.1371/journal.pone.0160513
work_keys_str_mv AT zamirmuhammad sensitivityanalysisandoptimalcontrolofanthroponoticcutaneousleishmania
AT zamangul sensitivityanalysisandoptimalcontrolofanthroponoticcutaneousleishmania
AT alshomranialisaleh sensitivityanalysisandoptimalcontrolofanthroponoticcutaneousleishmania