Diseased prey predator model with general Holling type interactions

Bifurcation and hybrid control of a discrete eco-epidemiological model with Holling type-III

In this paper, a three dimensional discrete eco-epidemiological model with Holling type-III functional response is proposed. Boundedness of the solutions of the system is analyzed. Existence condition and stability of all fixed points are discussed for the proposed model. Furthermore, we obtained the transcritical bifurcation surfaces of the system by bifurcation theory. Based on the explicit criteria for the Neimark Sacker bifurcation and flip bifurcation, we obtained that the system undergoes these two types of bifurcations at the positive fixed point. Then we apply a hybrid control strategy that based on both parameter perturbation and a state feedback strategy to control the Neimark-Sacker bifurcation. Finally, some numerical simulations are carried out to support the analytical results.

Backward bifurcation, oscillations and chaos in an eco-epidemiological model with fear effect

This paper considers an eco-epidemiological model with disease in the prey population. The disease in the prey divides the total prey population into two subclasses, susceptible prey and infected prey. The model also incorporates fear of predator that reduces the growth rate of the prey population. Furthermore, fear of predator lowers the activity of the prey population, which reduces the disease transmission. The model is well-posed with bounded solutions. It has an extinction equilibrium, susceptible prey equilibrium, susceptible prey-predator equilibrium, and coexistence equilibria. Conditions for local stability of equilibria are established. The model exhibits fear- induced backward bifurcation and bistability. Extensive numerical simulations show the presence of oscillations and occurrence of chaos due to fear induced lower disease transmission in the prey population.

Study of the interactive effect of prey toxin and optimal foraging strategy on a predator–prey model

The optimal foraging theory predicts that predators choose prey with more net rate of energy intake and less energy costs if there are multiple food sources available. Toxins are found in many species in nature. Those toxins may be produced by prey as self-protection from predatory animals, or come from other sources such as pesticide residue. Therefore, it requires a balance between energy intake and toxicity damage. In order to study the interactive effect of prey toxin and optimal foraging strategy, we construct a predator–prey model with toxin-induced functional response and optimal foraging property. Dynamical analysis shows that the optimal strategy system presents more complex dynamical behavior than the fixed preference system. We conclude that optimal foraging strategy might play a key role in stabilizing or destabilizing the coexistence states of the species in the system, depending on the level of prey toxins.

Effects of allochthonous inputs in the control of infectious disease of prey

Allochthonous inputs are important sources of productivity in many food webs and their influences on food chain model demand further investigations. In this paper, assuming the existence of allochthonous inputs for intermediate predator, a food chain model is formulated with disease in the prey. The stability and persistence conditions of the equilibrium points are determined. Extinction criterion for infected prey population is obtained. It is shown that suitable amount of allochthonous inputs to intermediate predator can control infectious disease of prey population, provided initial intermediate predator population is above a critical value. This critical intermediate population size increases monotonically with the increase of infection rate. It is also shown that control of infectious disease of prey is possible in some cases of seasonally varying contact rate. Dynamical behaviours of the model are investigated numerically through one and two parameter bifurcation analysis using MATCONT 2.5.1 package. The occurrence of Hopf and its continuation curves are noted with the variation of infection rate and allochthonous food availability. The continuation curves of limit point cycle and Neimark Sacker bifurcation are drawn by varying the rate of infection and allochthonous inputs. This study introduces a novel natural non-toxic method for controlling infectious disease of prey in a food chain model.