Study of an eco-epidemiological model with Z-type control. (August 2018) - Alzahrani, Abdullah K.; Alshomrani, Ali Saleh; Pal, Nikhil; Samanta, Sudip
Highlights: We study an eco-epidemic model with Z-type control mechanism. In the absence of Z-controller, disease destabilizes the system and produces chaos. Z-control scheme helps to achieve a desired infected prey density. Applying Z-controller, we can control disease as well as population oscillation. Abstract: In the present paper, an eco-epidemic model with Z-type control mechanism has been proposed and analyzed. We consider a predator-prey model with Holling type-II functional response, where prey is subjected to disease infection. We observe that disease may destabilize the system by producing chaotic oscillations. To confirm the occurrence of chaos, we draw the Poincare map and also compute the Lyapunov exponents. We further observe that if the indirect Z-controller is applied in the predator population, then the chaos as well as the disease can be eliminated from the system. To explore the global dynamics of the system and the possible applications of Z-type control mechanism, we perform extensive numerical experiments.