Dynamics of a prey-predator type ecological model in relevance to pest control

ABSTRACT

In this article, we propose and analyze a prey-predator-type ecological model in relevance to pest control. We consider that the system consists of two types of pests and their natural enemy as predator. The basic biological feasibility of the system is studied. Then, local stability analysis of all possible equilibria of the model is examined. Also, the global stability of the coexisting equilibrium point is studied using a suitable Lyapunov functional. Moreover, an optimal control problem is formulated and solved to find out the optimal pest control policy. Finally, we have illustrated some of the results through numerical simulations.

KEYWORDS:

• Prey-predator model
• pest control
• global stability
• optimal control policy

Acknowledgments

We are also very grateful to the anonymous reviewers and the Editor-in-Chief Prof. Jie Shen for their constructive comments and useful suggestions which have helped us to improve the manuscript significantly.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Research of A. Khatua is financially supported by Department of Science and Technology-INSPIRE, Government of India [No. DST/INSPIRE Fellowship/2016/IF160667, dated: 21 September 2016]. Research of T. K. Kar is partially supported by the Council of Scientific and Industrial Research (CSIR), India [File No. 25(0300)/19/EMR-II dated: 16 May 2019].

Notes on contributors

Soovoojeet Jana

Soovoojeet Jana received his MSc in Applied Mathematics from Vidyasagar University, WB, India in 2010 and PhD from IIEST, Shibpur, India in 2014. Currently, he is an Assistant Professor in Mathematics at Ramsaday College, Amta, Howrah, India.

Anupam Khatua

Anupam Khatua received his MSc in Applied Mathematics from the IIEST, Shibpur, WB, India in 2016. He received his PhD degree from IIEST, Shibpur, India in 2021. His research interests include mathematical epidemiology and ecology.

Manotosh Mandal

Manotosh Mandal received his MSc in Mathematics from the IIT, Kharagpur in 2012 and PhD from IIEST, Shibpur in 2021. He is currently working as an Assistant Professor in Mathematics at Tamralipta Mahavidyalaya, Tamluk, WB, India.

Tapan Kumar Kar

Tapan Kumar Kar received his MSc in Applied Mathematics from Calcutta University, WB, India in 1993 and PhD from Jadavpur University, India in 2004. At present, he is a Professor (HAG) in the Department of Mathematics, IIEST, Shibpur, India.