Nonlinear Dyn DOI 10.1007/s11071-015-2040-2 ORIGINAL PAPER Effect of harvesting and infection on predator in a prey–predator system Soovoojeet Jana · Srabani Guria · Uttam Das · T. K. Kar · Abhijit Ghorai Received: 26 September 2014 / Accepted: 17 March 2015 © Springer Science+Business Media Dordrecht 2015 Abstract In this article, we propose and analyze a mathematical model of a prey–predator system where infection spreads among the predators and predator is subject to harvesting. Dynamical behavior of the sys- tem is studied, and the consequences of harvesting on the long-run equilibrium fish biomass are evaluated. Optimal control theory has been used to determine the optimal harvesting policy for fish stocks to max- imize the discounted utility of harvesting over time, employing a constant time discount rate. Some simu- lation works are given to verify our analytic results. S. Jana (B ) Department of Applied Science, Haldia Institute of Technology, Haldia 721657, West Bengal, India e-mail: soovoojeet@gmail.com S. Guria · T. K. Kar Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, West Bengal, India e-mail: srabaniguria@gmail.com T. K. Kar e-mail: tkar1117@gmail.com U. Das Department of Mathematics, Sree Chaitanya College, Habra, 24PGS (N.) 743268, India e-mail: uttam_das76@yahoo.in A. Ghorai Department of Mathematics, Shibpur Sikshalaya Shibpur, Howrah 711102, West Bengal, India e-mail: ssgabhijit@gmail.com Keywords Prey–predator · Eco-epidemic · Harvesting · Optimal control · Bifurcation · Stability Mathematics Subject Classification 92D25 · 49J15 · 91B76 · 37N25 1 Introduction Mathematical models have recently been heavily used to describe different ecological systems and their dynamical behaviors. Interaction between prey and their predators is one of the ecological problems in which not only theoretical ecologists but also applied mathematicians have shown their interests. Also rapid development of computing techniques enables the sim- ulation works and model predictions in a quite better way than the earlier stages. Ecological models are char- acterized by interactions among all the species present in the environment. In ecology, predation is one of the most important interactions among different popula- tion species. Throughout their works, the researchers like Das et al. [6], Gao et al. [7], Jana et al. [16], Jana and Kar [15, 17], Kar [18], Kuang and Takeuchi [24], Song and Guo [29], Venturino [30], Xu and Ma [36], Yongzhen et al. [37], Zhang et al. [38], and references therein have obtained many new and interesting results on the dynamics of prey–predator systems. Mathematical modeling is a good and important tool for the study of epidemiological problems. Classical predator–prey models formed with the help of the sys- 123