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....
Autores principales: | , , |
---|---|
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 |