The Rionero’s special type of Lyapunov function and its application to a diffusive epidemic model with information

We consider a SIR-like reaction-diffusion epidemic model which embeds opinion-driven human behavioural changes. We assume that the contagion rate is theoretically saturated with respect to the density of the disease prevalence. The model extends the general reaction-diffusion epidemic model proposed in 1993 by Capasso and Di Liddo. We study the nonlinear attractivity of the endemic steady state solution by employing a special Lyapunov function introduced in 2006 by S. Rionero. Sufficient conditions for the conditional nonlinear stability of the endemic equilibrium are derived.