Integrated Dynamics of Eco-Epidemic Systems: Nonlinear Prey Refuge, Predator Exploitation, Fear Impact, and Infection Control

The article investigates an eco-epidemic predator-prey model, where only the prey population becomes infected. Both the prey populations take nonlinear prey refuge with different coefficients to protect themselves from their predator. Fear of predators reduces the growth rate and activity of the prey population, which in turn reduces the rate of disease transmission. The model system incorporates treatment for infected individuals. After formulation of the model system, some preliminary results of the system are executed and followed by system’s points of equilibrium. We have calculated the basic reproduction number that holds a crucial role in determining the eradication of disease from the system. Analysis of the system’s bifurcation with respect to different crucial parameters is executed. By increasing the value of treatment parameters to a certain extent, it is found that the disease can be eradicated from the system. Further, Pontryagin’s maximum principal is used to optimize the disease control. Some numerical simulations illustrate and validate the obtained results.