EFFECTS OF INVASION TIMING IN A ONE-DIMENSIONAL MODEL OF COMPETING SPECIES WITH AN INFECTIOUS DISEASE

In combining two classes of models, we are able to analyze the dynamics of two species that compete for the same resources while fighting a disease. The native species is the disease host and the invasive species enters their habitat and encounters the disease for the first time. Their natural response is to evolve resistance to the disease, and this can assist in their invasion of the natives\u27 habitat. We find conditions for coexistence of the two species, conditions under which an invasion would succeed and wipe out all native individuals, and conditions under which the invasion fails. We explore the timing of the invasion by causing the invasion to occur before the natives equilibrate with the disease

EFFECTS OF INVASION TIMING IN A ONE-DIMENSIONAL MODEL OF COMPETING SPECIES WITH AN INFECTIOUS DISEASE

In combining two classes of models, we are able to analyze the dynamics of two species that compete for the same resources while fighting a disease. The native species is the disease host and the invasive species enters their habitat and encounters the disease for the first time. Their natural response is to evolve resistance to the disease, and this can assist in their invasion of the natives\u27 habitat. We find conditions for coexistence of the two species, conditions under which an invasion would succeed and wipe out all native individuals, and conditions under which the invasion fails. We explore the timing of the invasion by causing the invasion to occur before the natives equilibrate with the disease

A predator-prey model with disease in prey

. The present investigation deals with the disease in the prey population having significant role in curbing the dynamical behaviour of the system of prey-predator interactions from both ecological and mathematical point of view. The predator-prey model introduced by Cosner et al. [1] has been wisely modified in the present work based on the biological point of considerations. Here one introduces the disease which may spread among the prey species only. Following the formulation of the model, all the equilibria are systematically analyzed and the existence of a Hopf bifurcation at the interior equilibrium has been duly carried out through their graphical representations with appropriate discussion in order to validate the applicability of the system under consideratio

A Mathematical Study on the Dynamics of an Eco-Epidemiological Model in the Presence of Delay

In the present work a mathematical model of the prey-predator system with disease in the prey is proposed. The basic model is then modified by the introduction of time delay. The stability of the boundary and endemic equilibria are discussed. The stability and bifurcation analysis of the resulting delay differential equation model is studied and ranges of the delay inducing stability as well as the instability for the system are found. Using the normal form theory and center manifold argument, we derive the methodical formulae for determining the bifurcation direction and the stability of the bifurcating periodic solution. Some numerical simulations are carried out to explain our theoretical analysis

Stability and Hopf bifurcation of a delay eco‐epidemiological model with nonlinear incidence rate

In this paper, a three‐dimensional eco‐epidemiological model with delay is considered. The stability of the two equilibria, the existence of Hopf bifurcation and the permanence are investigated. It is found that Hopf bifurcation occurs when the delay τ passes a sequence of critical values. Moreover, by applying Nyquist criterion, the length of delay is estimated for which the stability continues to hold. Numerical simulation with a hypothetical set of data has been done to support the analytical results. This work is supported by the National Natural Science Foundation of China (No. 10771104 and No.10471117), Program for Innovative Research Team (in Science and Technology) in University of Henan Province (No. 2010IRTSTHN006) and Program for Key Laboratory of Simulation and Control for Population Ecology in Xinyang Normal University (No. 201004) and Natural Science Foundation of the Education Department of Henan Province (No. 2009B1100200 and No. 2010A110017) First published online: 10 Feb 201

On invariant measures and the asymptotic behavior of a stochastic delayed SIRS epidemic model

This article is a total of 20 pages and contains 5 figures.In this paper, we consider a stochastic epidemic model with time delay and general incidence rate. We first prove the existence and uniqueness of the global positive solution. By using the Krylov-Bogoliubov method, we obtain the existence of invariant measures. Furthermore , we study a special case where the incidence rate is bilinear with distributed time delay. When the basic reproduction number R0 1, we prove that the invariant measure is unique and ergodic. The numerical simulations also validate our analytical results

Dynamical Behavior of an Eco-epidemiological Model Incorporating Prey Refuge and Prey Harvesting

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