https://doi.org/10.1140/epjp/s13360-023-04690-y
Regular Article
Dynamical study of lumpy skin disease model with optimal control analysis through pharmaceutical and non-pharmaceutical controls
1
Department of Mathematics and Statistics, College of Science, King Faisal University, 31982, Al-Ahsa, Saudi Arabia
2
Department of Mathematics, GC University, Lahore, Pakistan
3
Tandy School of Computer Science, The University of Tulsa, Tulsa, OK, USA
4
Department of Mathematics, Sahara Medical College Narowal, Narowal, Pakistan
5
Department of Mathematics, Division of Science and Technology, University of Education, 54770, Lahore, Pakistan
6
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan
a aikhan@kfu.edu.sa, azhar.butt@gcu.edu.pk
d
tariqismaeel@gcu.edu.pk
Received:
10
August
2023
Accepted:
14
November
2023
Published online:
28
November
2023
Lumpy skin disease (LSD) is an infectious disease that affects cattle population. The disease has disrupted economy of the affected countries due to decline in dairy products and sometimes due to death of the infected cattle. It is therefore necessary to develop a mathematical model that may help to eradicate the disease in an optimal way. For this, we propose a new mathematical model not only to understand the disease flow patterns but also to suggest strategies to control disease optimally. We examine the proposed model for existence of a unique solution and prove that the solutions are positive and bounded. We estimate the reproduction number 
to measure disease contagiousness and to test the proposed model for local and global stability at disease-free and endemic equilibrium points. We also present graphs to verify theoretical results of global stability at equilibrium points. We perform sensitivity analysis to determine the most influential parameters of the reproduction number and show their impact on graphically. The primary goal of this research is to test various possible disease prevention methods in order to find the best one. Therefore, we build an optimal control problem to explore the effects of treatment and precautionary measures on disease control in three different cases. In the first case, we analyze the impact of treatment strategy on the disease control and present the corresponding results graphically. In the second control methodology, we study the impact of adopting precautionary measures on sickness with possible end from society. In the third case, we implement treatment and adopting precautionary measure strategies together to observe their combined effect on disease control. Findings of all the three cases along with discussions and graphs will be presented and concluded at the end.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
