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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Main Authors: Muhammad Zamir, Gul Zaman, Ali Saleh Alshomrani
Format: Article
Language:English
Published: Taylor & Francis Group 2017-01-01
Series:Journal of Biological Dynamics
Subjects:
Online Access:http://dx.doi.org/10.1080/17513758.2017.1339835
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spelling 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
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AT gulzaman controlstrategiesandsensitivityanalysisofanthroponoticvisceralleishmaniasismodel
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