Narrow Results

It is generally, but not always, accepted that alternative food plays a stabilizing role in predator–prey interaction. Parasites, on the other hand, have the ability to change both the qualitative and quantitative dynamics of its host population. In recent times, researchers are showing growing interest in formulating models that integrate both the ecological and epidemiological aspects. The present paper deals with the effect of alternative food on a predator–prey system with disease in the predator population. We show that the system, in the absence of alternative food, exhibits different dynamics viz. stable coexistence, limit cycle oscillations, period-doubling bifurcation and chaos when infection rate is gradually increased. However, when predator consumes alternative food coupled with its focal prey, the system returns to regular oscillatory state from chaotic state through period-halving bifurcations. Our study shows that alternative food may have larger impact on the community structure and may increase population persistence.

In this paper, we have investigated women’s malignant disease, cervical cancer, by constructing the compartmental model. An extended fractal–fractional model is used to study the disease dynamics. The points of equilibria are computed analytically and verified by numerical simulations. The key role of $R_0$ in describing the stability of the model is presented. The sensitivity analysis of $R_0$ for deciding the role of certain parameters altering the disease dynamics is carried out. The numerical simulations of the proposed numerical technique are demonstrated to test the claimed facts.