The Dynamics of an Eco‐Epidemiological Model with Nonlinear Incidence Rate

Abstract

This paper treats the dynamical behavior of eco-epidemiological model with nonlinear incidence rate. A Holling type II prey-predator model withSI-type of disease in prey has been proposed and analyzed. The existence, uniqueness, and boundedness of the solution of the system are studied. The local and global dynamical behaviors are investigated. The conditions, which guarantee the occurring of Hopf bifurcation of the system, are established. Finally, further investigations for the global dynamics of the proposed system are carried out with the help of numerical simulations.

Mathematical Analysis of a Prey–Predator System: An Adaptive Back-Stepping Control and Stochastic Approach

“…They proved that prey refuge had a stabilizing effect on the prey-predator interaction. Numerous examples of the prey-predator relationship with infection in the prey population have been found in various studies [12][13][14][15][16][17].…”

Sis Model With Harvesting in Food Chain Model

“…Mathematical models have become critical tools in understanding and analyzing the spread and control of infectious diseases by studying different types of disease such as SI, SIS. Some infectious diseases in the ecosystem are transmitted through direct contact [6]. In addition to disease, harvesting can in turn greatly affect the dynamics of the prey-predator system, and harvesting can reduce the numbers of prey or predators [7].…”

Sis Model With Harvesting in Food Chain Model

“…Mathematical models have become critical tools in understanding and analyzing the spread and control of infectious diseases by studying different types of disease such as SI, SIS. Some infectious diseases in the ecosystem are transmitted through direct contact [6]. In addition to disease, harvesting can in turn greatly affect the dynamics of the prey-predator system, and harvesting can reduce the numbers of prey or predators [7].…”