Narrow Results

Our current research is based on the investigation of an eco-epidemiological model that solely includes illness in predators. Predators, both healthy and diseased, are thought to consume prey and breed; however, the offsprings are expected to be vulnerable. To achieve a more realistic and explicit outcome of the existing phenomena correlated with our model system, we consider that the process of disease transmission is mediated by some time lag and the intensity of disease prevalence is seasonally forced. Our simulation results show that the disease dies out for lower intensity of disease prevalence or higher rate of consumption of prey by susceptible predator. The system undergoes subcritical/supercritical Hopf bifurcation as the parameters representing the intensity of disease prevalence, consumption rate of prey by susceptible/infected predator vary. The system exhibits two types of bistabilities: the first one between stable coexistence and oscillating coexistence, and the second one between two oscillatory coexistence cycles. Moreover, we see that with gradual increase in the incubation delay, the system shows transitions from stable focus to limit cycle oscillations to period doubling oscillations to chaotic dynamics. Chaotic dynamics is also observed for the periodic changes in the intensity of disease prevalence if it takes much time for the pathogens to develop sufficiently inside body of the susceptible predators.

In the present paper, we investigate a prey–predator system with disease in both prey and predator populations and the predator population is cannibalistic in nature. The model is extended by introducing incubation delays in disease transmission terms. Local stability analysis of the system around the biologically feasible equilibria is studied. The bifurcation analysis of the system around the interior equilibrium is also studied. The sufficient conditions for the permanence of the system are derived in the presence of delays. We observe that incubation delays have the ability to destabilize the cannibalistic prey–predator system. Finally, we perform numerical experiments to substantiate our analytical findings.

Plant viral diseases have devastating effects on agricultural products worldwide. In this research, a delay differential equation model has been proposed for the transmission dynamics of plant viral disease using the vector-to-plant (primary) transmission and plant-to-plant (i.e. secondary) transmissions modeled via nonlinear (saturated) terms. Also, a time delay is considered in the model due to the incubation period of the plant. Feasibility and stability analyses of the equilibria of the model have been provided based on the basic reproduction numbers. Stability changes occur through Hopf bifurcation in both the delayed and non-delayed systems. Sensitivity analysis shows the impact of a parameter on the infection. The mathematical analysis of the model and numerical examples suggested that the disease will occur if the incubation period of the plant is small. Viral disease of a plant can be controlled by maintaining the distance between plants, removing the infected plants, and increasing crop resistance towards the disease.