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In this paper an eco-epidemiological model incorporating a prey refuge and prey harvesting with disease in the prey-population is considered. Predators are assumed to consume both the susceptible and infected prey at different rates. The positivity and boundedness of the solution of the system are discussed. The existence and stability of the biologically feasible equilibrium points are investigated. Numerical simulations are performed to support our analytical findings. [ABSTRACT FROM AUTHOR]

In this paper, a Holling-Tanner predator-prey model with ratio-dependent functional response and non-linear prey harvesting is analyzed. The mathematical analysis of the model includes existence, uniqueness and boundedness of positive solutions. It also includes the permanence, local stability and bifurcation analysis of the model. The ratio-dependent model always has complex dynamics in the vicinity of the origin; the dynamical behaviors of the system in the vicinity of the origin have been studied by means of blow up transformation. The parametric conditions under which bionomic equilibrium point exist have been derived. Further, an optimal harvesting policy has been discussed by using Pontryagin maximum principle. The numerical simulations have been presented in support of the analytical findings. [ABSTRACT FROM AUTHOR]

In this paper we discuss the harvesting of the prey species making a fraction of them to be accessed by the predator while both the prey and predator are being subjected to Beddington-DeAngelis functional response. It is observed that a Hopf-bifurcation may occur around the interior equilibrium taking the environmental carrying capacity of the prey species as the parameter. Some numerical examples and the corresponding curves are studied using Maple to explain the results of the proposed model. [ABSTRACT FROM AUTHOR]

This paper deals with the qualitative analysis of a disease transmission delay induced prey predator system in which disease spreads among the predator species only. The growth of the predators' susceptible and infected subpopulations is assumed as modified Leslie--Gower type. Sufficient conditions for the persistence, permanence, existence and stability of equilibrium points are obtained. Global asymptotic stability of the system is investigated around the coexisting equilibrium using a geometric approach. The existence of Hopf bifurcation phenomenon is also examined with respect to some important parameters of the system. The criterion for disease a transmission delay the induced Hopf bifurcation phenomenon is obtained and subsequently, we use a normal form method and the center manifold theorem to examine the nature of the Hopf bifurcation. It is clearly observed that competition among predators can drive the system to a stable from an unstable state. Also the infection and competition among predator population enhance the availability of prey for harvesting when their values are high. Finally, some numerical simulations are carried out to illustrate the analytical results. [ABSTRACT FROM AUTHOR]