Journal of Applied Nonlinear Dynamics
Optimal Control and Stability Analysis of Malaria Disease: A Model Based Approach
Journal of Applied Nonlinear Dynamics 10(4) (2021) 775790  DOI:10.5890/JAND.2021.12.014
Manotosh Mandal$^{1,2}$, Soovoojeet Jana$^{3}$ , U. K. Pahari$^{4}$, T. K. Kar$^{2}$
$^{1}$ Dept. of Mathematics, Tamralipta Mahavidyalaya, Tamluk, Purba Medinipur, West Bengal, India
$^{2}$ Dept. of Mathematics, IIEST, Shibpur, Howrah, West Bengal, India
$^{3}$ Dept. of Mathematics, Ramsaday College, Amt7111401, Howrah, West Bengal, India
$^{4}$ Department of Mathematics, Netaji Nagar Day College, Kolkata  700092
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Abstract
In this paper we have proposed a three dimensional mathematical model on malaria disease by considering two distinct classes namely susceptible and infected human population and infected mosquito population. Basic reproductive number of the system has been obtained and its relation regarding the behavior of the system has been established. Two control parameters, namely treatment control on infected human population and insecticide control on mosquito populations are applied in the present system. We formulate and solve the optimal control problem considering treatment and insecticide as the control variables. All the theoretical results are verified by some computer simulation works.
Acknowledgments
The research work of Dr. Soovoojeet Jana is
financially supported by Department of Science \& Technology and Biotechnology, Government of West Bengal (Memo no. 201 (Sanc)/S&T/P/S
T/16G12/2018 dated 19/02/2019). Further, the authors are very much grateful to
the anonymous reviewers and Dr. Shanmuganathan Rajasekar, Associate Editor
of Journal of Applied Nonlinear Dynamics, for their constructive comments
and helpful suggestions, which have helped us significant improvement of the
article.
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