Disease Control via Indirect Z-Control Technique in a Discrete-Time Eco-Epidemiological System
摘要
An important aspect of population biology is the study of infectious diseases’ impact on ecological systems and how these diseases can be controlled or eradicated from the systems. In this article, we implement a control technique, the Z-type control for disease control purposes in a discrete-time eco-epidemiological system, where the preys are under the influence of an infectious disease and the predator species intake only diseased prey as their food by following the Holling type-I functional response. We first investigate the system dynamics without any control by varying two vital system parameters, and observe the appearance of a variety of complex dynamical scenarios like chaos, quasiperiodicity, periodic structures, and steady-state behavior in the parameter plane of the system. Then, after the implementation of the indirect Z-control mechanism by incorporating an exogenous measure for predator population, we notice that the system’s regular or irregular oscillations can be controlled. More fascinatingly, it comes to view that via this control strategy the infected prey population can be eradicated from the eco-epidemiological system. Using time series plots, we see that the value of the indirect controller is positive, which implies the inclusion of predators in the system in a specific amount (determined by the controller’s magnitude) for disease eradication. Also, we observe that initial densities of the populations play an essential role in the implementation of the Z-type control mechanism.