The present paper deals with the problem of a ratio-dependent predator-prey model incorporating a prey refuge with disease in the prey-population. We assume the predator population will prefer only infected population for their diet as those are more vulnerable. Dynamical behaviours such as boundedness, local and global stability are addressed. We have also studied the effect of discrete time d...

We study a deterministic continuous-time predator-prey model with parasites, where the prey population is the intermediate host for the parasites. It is assumed that the parasites can affect the behavior of the predator-prey interaction due to infection. The asymptotic dynamics of the system are investigated. A stochastic version of the model is also presented and numerically simulated. We then...

In the current paper, we propose a two-prey-one-predator system with Holling type II predation functional response where prey species consumes the remains of the other prey species’ carcass given by their predator. Mathematical analysis of the proposed model equations with regard to non-negative invariance including stability and bifurcation are carried out. Next, we extend the deterministic sy...

We propose an optimal control framework to describe intra-seasonal predator-prey interactions, which are characterized by a continuous-time dynamical model comprising predator and prey density, as well as the energy budget of the prey over the length of a season. The model includes a time-dependent decision variable for the prey, representing the portion of the prey population in time that is a...

This paper aims to study the effect of Harvesting on predator species with time-delay on a Holling type-IV prey-predator model. Harvesting has a strong impact on the dynamic evolution of a population. Two delays are considered in the model of this paper to describe the time that juveniles of prey and predator take to mature. Dynamics of the system is studied in terms of local and Hopf bifurcati...

The stability of predator-prey system subject to the Allee effect is of considerable interest in recent times. The present investigation is an attempt to observe the stability nature of a discrete-time predator-prey system with Allee effect on predator, prey and on both the population. We have obtained the conditions for which the equilibrium points of each of the three cases are asymptotically...

This paper introduces a spatially heterogeneous diffusive predator–prey model unifying the classical Lotka–Volterra and Holling–Tanner ones through prey saturation coefficient, \begin{document}$ m(x) $\end{document} , which is heterogenous it allowed to 'degenerate'. Thus, in some patches of territory species can interact according kinetics, while others effects play significant role on dynamic...