A seasonally forced eco-epidemic model with disease in predator and incubation delay

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.