Narrow Results

In the present paper, an eco-epidemiological model consisting of susceptible prey, infected prey and predator has been proposed and analyzed. We have obtained conditions for the existence and persistence of all the three populations. To study the global dynamics of the system, numerical simulations have been performed. Our simulation results show that the system enters into quasi-periodic solutions or chaotic depending upon the choice of system parameters. To confirm the chaotic behavior of the system, we have calculated Lyapunov exponent and constructed Poincare section. Our analysis reveals that the infection and predation rates specially on the infected prey population are the key parameters that play crucial roles for controlling the chaotic dynamics of the system.

The present paper deals with the problem of a predator-prey system with disease in the prey population. We observe the dynamics of such a system under the influence of severe as well as unnoticeable parasite attack and also alternative food sources for predator population. We assume the predator population will prefer only infected population for their diet as those are more vulnerable. Local and global stability of the system around the biological feasible equilibria are studied. The conditions for which all three species will persist are worked out. Our results indicate that in the case of severe parasite attack, the predator population will prefer the alternative food source and not the infected one. But the strategy is reversed in the case of unnoticeable parasite attack.

In this paper, we have proposed and analyzed an agricultural pest control system. For this purpose, an eco-epidemiological type predator–prey model has been proposed with the consideration of a sound predator population and two classes of pest populations namely susceptible pest and infected pest. Further to consider uncertainty, we modify our model and transform it into a fuzzy system with incorporation of imprecise parameters. The dynamical behavior of the proposed model has been investigated by examining the existence and stability criteria of all feasible equilibria. An optimal control problem is formed by considering the pesticide control as the control parameter and then the problem is solved both theoretically and numerically with the help of some computer simulation works.

This paper studies the dynamics of interacting Tilapia fish and Pelican bird population in the Salton Sea. We assume that the diseases spread in Tilapia fish follows the Holling type II response function, and the interaction between Tilapia and Pelican follows the Beddington–DeAngelis response function. The dynamics of diffusive and delayed system are discussed separately. Analytically, all the feasible equilibria and their stability are discussed. The criterion for Turing instability is derived. Based on the normal form theory and center manifold arguments, the existence of stability criterion and the direction of Hopf bifurcation are obtained. Numerical simulation shows the occurrence Hopf bifurcation, double Hopf bifurcation and transcritical bifurcation scenarios. The snap shot shows the spot, spot-strip mix patterns in the whole domain. Further, the stability switching phenomena is observed in the delayed system. Our comprehensive study highlights the effect of different parameters, multiple time delay and extinction in Pelican populations.