Delay-induced chaos and its possible control in a seasonally forced eco-epidemiological model with fear effect and predator switching

摘要

Fear of predation risk may assert privilege to prey animals by restricting their exposure to potential predators; meanwhile, it can also impose costs by constraining the exploration of optimal resources. In this article, we investigate the impact of fear on the dynamics of an eco-epidemiological switching model. We observe that both the force of infection and the fear factor affecting prey's reproduction carry out destabilizing role, while the system regains stability if the level of fear on disease transmission exceeds a certain threshold. We obtain an explicit expression for the basic reproduction number R-0 and show that R-0 < 1 leads to the total eradication of infection from the system. We extend our model by considering the fact that after sensing the predatory signals, prey takes some time for assessing the acute predation risk. The time lags involved in reducing the reproduction success as well as the intensity of disease transmission depend on prey's physiology and their individual reaction norms to the fear of predator. To capture a more realistic scenario, we construct the forced model by seasonally varying the costs of fear, disease transmission rate and the degree of preference of predator. Seasonal patterns in these intrinsic parameters add complexity to the ecosystem functioning by inducing higher periodic and chaotic oscillations. The chaotic behaviour is also observed in the forced system for the delay in the fear effect on prey's reproduction. However, time lag in the fear effect on the infection dynamics potentially suppresses the prevalence of such chaotic disorder. Thus, our findings may help to provide important ecological insights into the dynamics of predator-prey interactions involving parasites.