Journal of Applied Mathematics and Computing https://doi.org/10.1007/s12190-020-01379-8 ORIGINAL RESEARCH Dynamical response of an eco-epidemiological system with harvesting Harekrishna Das 1 · Absos Ali Shaikh 1 Received: 17 October 2019 © Korean Society for Informatics and Computational Applied Mathematics 2020 Abstract This article presents a study of Leslie–Gower predator–prey system to investigate the dynamics of disease transmission among predator species. The system includes the harvesting of infected predator. The positivity, boundedness of the solutions and permanence of the system are taken into consideration. The stability and Hopf bifurca- tion analyses around biologically feasible equilibria are scrutinized. The harvesting of infected predator plays a crucial role for the occurrence of limit cycle oscillations and stability around the interior equilibrium point. Our results disclose that infected preda- tor harvesting has a considerable consequence on the eco-epidemiological system. The optimal control theory has been applied to investigate optimal strategies for controlling the infection. Analytical findings are confirmed through numerical simulations. Keywords Eco-epidemiological system · Harvesting · Stability · Persistence · Hopf bifurcation Mathematics Subject Classification 92D30 · 92D40 · 65L07 · 49J15 · 34K18 1 Introduction Ecology is the part of biology that studies the interactions among organisms and their environment. Epidemiology deals with the incidence, distribution and possible con- trol of diseases and other factors relating to health. Eco-epidemic models deal with ecosystems of interacting populations among which a disease spreads [3,25,33,34]. A mathematical model describes a real-world phenomenon by means of mathematical language to understand the behaviour of a natural or physical system. Two impor- B Absos Ali Shaikh aask2003@yahoo.co.in Harekrishna Das hkdasm74@gmail.com 1 Department of Mathematics, The University of Burdwan, Burdwan 713104, West Bengal, India 123