Study of a Diseased Volterra Type Population Model featuring Prey Refuge and Fear Influence

Abstract

In order to study the local stability characteristics of a predator-prey dynamical model, this work proposes a Volterra-type model that takes into account the fear influence of prey resulting from predator domination. Because of an outbreak of disease in the prey species, the prey gets classified as either healthy or diseased. Both predator and prey species compete for their resources. In addition, the prey sought refuge against the predator. All these factors are addressed when setting up the mathematical model. The biological validity of the model is ensured by testing its boundedness. The equilibrium points have been identified. The short-term behavior of the system is analyzed at all equilibrium points. Routh Hurwitz conditions are employed to examine the local stability property.