An integer‑order SIS epidemic model having variable population and fear effect: comparing the stability with fractional order

This paper investigates the dynamics of an integer-order and fractional-order SIS
epidemic model with birth in both susceptible and infected populations, constant
recruitment, and the effect of fear levels due to infectious diseases. The existence,
uniqueness, non-negativity, and boundedness of the solutions for both proposed
models have been discussed. We have established the existence of various equilibrium
points and derived sufficient conditions that ensure the local stability under two cases
in both integer- and fractional-order models. Global stability has been vindicated using
Dulac–Bendixson criterion in the integer-order model. The forward transcritical bifurcation near the disease-free equilibrium has been investigated. The effect of fear level on infected density has also been observed. We have done numerical simulation by MATLAB to verify the theoretical results, found the impact of fear level on the dynamic behaviour of the infected population, and obtained a bifurcation diagram concerning the constant recruitment and fear level. Finally, we have compared the stability of the population in integer and fractional-order systems