Mathematical modeling and stability analysis of Pine Wilt Disease with optimal control

Mathematical modeling and stability analysis of Pine Wilt Disease with optimal control

Abstract This paper presents and examine a mathematical system of equations which describes the dynamics of pine wilt disease (PWD). Firstly, we examine the model with constant controls. Here, we investigate the disease equilibria and calculate the basic reproduction number of the disease. Secondly,...

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Main Authors: M. A. Khan, K. Ali, E. Bonyah, K. O. Okosun, S. Islam, A. Khan
Format: Article
Language:English
Published: Nature Publishing Group 2017-06-01
Series:Scientific Reports
Online Access:https://doi.org/10.1038/s41598-017-03179-w
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spelling doaj-c34112cf49424709a46683b71882a7712020-12-07T23:58:52ZengNature Publishing GroupScientific Reports2045-23222017-06-017111910.1038/s41598-017-03179-wMathematical modeling and stability analysis of Pine Wilt Disease with optimal controlM. A. Khan0K. Ali1E. Bonyah2K. O. Okosun3S. Islam4A. Khan5Department of Mathematics, Abdul Wali Khan UniversityDepartment of Mathematics, Abdul Wali Khan, University MardanDepartment of Mathematics and Statistics, Kumasi Technical UniversityDepartment of Mathematics, Vaal University of TechnologyDepartment of Mathematics, Abdul Wali Khan, University MardanDepartment of Physics, Abdul Wali Khan University MardanAbstract This paper presents and examine a mathematical system of equations which describes the dynamics of pine wilt disease (PWD). Firstly, we examine the model with constant controls. Here, we investigate the disease equilibria and calculate the basic reproduction number of the disease. Secondly, we incorporate time dependent controls into the model and then analyze the conditions that are necessary for the disease to be controlled optimally. Finally, the numerical results for the model are presented.https://doi.org/10.1038/s41598-017-03179-w
collection DOAJ
language English
format Article
sources DOAJ
author M. A. Khan
K. Ali
E. Bonyah
K. O. Okosun
S. Islam
A. Khan
spellingShingle M. A. Khan
K. Ali
E. Bonyah
K. O. Okosun
S. Islam
A. Khan
Mathematical modeling and stability analysis of Pine Wilt Disease with optimal control
Scientific Reports
author_facet M. A. Khan
K. Ali
E. Bonyah
K. O. Okosun
S. Islam
A. Khan
author_sort M. A. Khan
title Mathematical modeling and stability analysis of Pine Wilt Disease with optimal control
title_short Mathematical modeling and stability analysis of Pine Wilt Disease with optimal control
title_full Mathematical modeling and stability analysis of Pine Wilt Disease with optimal control
title_fullStr Mathematical modeling and stability analysis of Pine Wilt Disease with optimal control
title_full_unstemmed Mathematical modeling and stability analysis of Pine Wilt Disease with optimal control
title_sort mathematical modeling and stability analysis of pine wilt disease with optimal control
publisher Nature Publishing Group
series Scientific Reports
issn 2045-2322
publishDate 2017-06-01
description Abstract This paper presents and examine a mathematical system of equations which describes the dynamics of pine wilt disease (PWD). Firstly, we examine the model with constant controls. Here, we investigate the disease equilibria and calculate the basic reproduction number of the disease. Secondly, we incorporate time dependent controls into the model and then analyze the conditions that are necessary for the disease to be controlled optimally. Finally, the numerical results for the model are presented.
url https://doi.org/10.1038/s41598-017-03179-w
work_keys_str_mv AT makhan mathematicalmodelingandstabilityanalysisofpinewiltdiseasewithoptimalcontrol
AT kali mathematicalmodelingandstabilityanalysisofpinewiltdiseasewithoptimalcontrol
AT ebonyah mathematicalmodelingandstabilityanalysisofpinewiltdiseasewithoptimalcontrol
AT kookosun mathematicalmodelingandstabilityanalysisofpinewiltdiseasewithoptimalcontrol
AT sislam mathematicalmodelingandstabilityanalysisofpinewiltdiseasewithoptimalcontrol
AT akhan mathematicalmodelingandstabilityanalysisofpinewiltdiseasewithoptimalcontrol
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