Control strategies and sensitivity analysis of anthroponotic visceral leishmaniasis model
This study proposes a mathematical model of Anthroponotic visceral leishmaniasis epidemic with saturated infection rate and recommends different control strategies to manage the spread of this disease in the community. To do this, first, a model formulation is presented to support these strategies,...
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Online Access: | http://dx.doi.org/10.1080/17513758.2017.1339835 |
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doaj-0b0e526edc7540d889e51d04773a1d672020-11-24T21:21:07ZengTaylor & Francis GroupJournal of Biological Dynamics1751-37581751-37662017-01-0111132333810.1080/17513758.2017.13398351339835Control strategies and sensitivity analysis of anthroponotic visceral leishmaniasis modelMuhammad Zamir0Gul Zaman1Ali Saleh Alshomrani2University of Science and TechnologyUniversity of MalakandKing Abdul Aziz UniversityThis study proposes a mathematical model of Anthroponotic visceral leishmaniasis epidemic with saturated infection rate and recommends different control strategies to manage the spread of this disease in the community. To do this, first, a model formulation is presented to support these strategies, with quantifications of transmission and intervention parameters. To understand the nature of the initial transmission of the disease, the reproduction number $ R_0 $ is obtained by using the next-generation method. On the basis of sensitivity analysis of the reproduction number $ R_0 $ , four different control strategies are proposed for managing disease transmission. For quantification of the prevalence period of the disease, a numerical simulation for each strategy is performed and a detailed summary is presented. Disease-free state is obtained with the help of control strategies. The threshold condition for globally asymptotic stability of the disease-free state is found, and it is ascertained that the state is globally stable. On the basis of sensitivity analysis of the reproduction number, it is shown that the disease can be eradicated by using the proposed strategies.http://dx.doi.org/10.1080/17513758.2017.1339835Leishmaniasisbasic reproductive numberstability of matricesmathematical modellinglocal and global stabilitysensitivity analysis |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Muhammad Zamir Gul Zaman Ali Saleh Alshomrani |
spellingShingle |
Muhammad Zamir Gul Zaman Ali Saleh Alshomrani Control strategies and sensitivity analysis of anthroponotic visceral leishmaniasis model Journal of Biological Dynamics Leishmaniasis basic reproductive number stability of matrices mathematical modelling local and global stability sensitivity analysis |
author_facet |
Muhammad Zamir Gul Zaman Ali Saleh Alshomrani |
author_sort |
Muhammad Zamir |
title |
Control strategies and sensitivity analysis of anthroponotic visceral leishmaniasis model |
title_short |
Control strategies and sensitivity analysis of anthroponotic visceral leishmaniasis model |
title_full |
Control strategies and sensitivity analysis of anthroponotic visceral leishmaniasis model |
title_fullStr |
Control strategies and sensitivity analysis of anthroponotic visceral leishmaniasis model |
title_full_unstemmed |
Control strategies and sensitivity analysis of anthroponotic visceral leishmaniasis model |
title_sort |
control strategies and sensitivity analysis of anthroponotic visceral leishmaniasis model |
publisher |
Taylor & Francis Group |
series |
Journal of Biological Dynamics |
issn |
1751-3758 1751-3766 |
publishDate |
2017-01-01 |
description |
This study proposes a mathematical model of Anthroponotic visceral leishmaniasis epidemic with saturated infection rate and recommends different control strategies to manage the spread of this disease in the community. To do this, first, a model formulation is presented to support these strategies, with quantifications of transmission and intervention parameters. To understand the nature of the initial transmission of the disease, the reproduction number $ R_0 $ is obtained by using the next-generation method. On the basis of sensitivity analysis of the reproduction number $ R_0 $ , four different control strategies are proposed for managing disease transmission. For quantification of the prevalence period of the disease, a numerical simulation for each strategy is performed and a detailed summary is presented. Disease-free state is obtained with the help of control strategies. The threshold condition for globally asymptotic stability of the disease-free state is found, and it is ascertained that the state is globally stable. On the basis of sensitivity analysis of the reproduction number, it is shown that the disease can be eradicated by using the proposed strategies. |
topic |
Leishmaniasis basic reproductive number stability of matrices mathematical modelling local and global stability sensitivity analysis |
url |
http://dx.doi.org/10.1080/17513758.2017.1339835 |
work_keys_str_mv |
AT muhammadzamir controlstrategiesandsensitivityanalysisofanthroponoticvisceralleishmaniasismodel AT gulzaman controlstrategiesandsensitivityanalysisofanthroponoticvisceralleishmaniasismodel AT alisalehalshomrani controlstrategiesandsensitivityanalysisofanthroponoticvisceralleishmaniasismodel |
_version_ |
1726000918201106432 |