Seasonal Variation of Carrying Capacity on Diseased Model Can Cause Species Extinction

Most natural populations experience fluctuations in biological and environmental factors which causes carrying capacity variation. In this paper, we have introduced a diseased prey-predator model with periodically varying carrying capacity. We have studied the effects of different amplitudes of oscillaton as well as different frequencies of oscillation on the dynamics of the model. We have done bifurcation analysis of the model with respect to the amplitude of oscillation and frequency of oscillation of the carrying capacity. We observe limit cycle, low periodic orbits, high periodic orbits and chaos in the model. We observe the existence of critical frequency and amplitude of oscillation of carrying capacity for which the prey population extinct. Through bifurcation analysis we observe oscillatory coexistence of species in the model. Our results confirm that amplitude and frequency of oscillation of carrying capacity are key parameters together with the force of infection and body size of intermediate predator in a diseased prey-predator model.