The Influence of Fear, Refuge, and Additional Food on the Dynamics of a Prey Interacting with a Predator Having an Infectious Disease

A mathematical model has been created and investigated that simulates the relationship between predator and prey with the appearance of an infectious disease in the predator population and additional food reservoirs for the predator.The prey declines its rate of growth due to it is enforced by the predator's rage to seek out a place where it will feel scared and safe.The bounds, existence, and uniqueness of the solution of the suggested model are examined.The local stability of the model at feasible equilibrium points was calculated.The Lyapunov function is utilized to identify the basin of attraction for each equilibrium point.The possibility of bifurcation when the parameters vary is also carefully discussed.Numerical simulations were then used to validate the analytical conclusions and provide insight into how parameter changes impacted the model's dynamics.Different attractors of the system are obtained, such as point, periodic, and nonlinear centers.