Exploring the complex dynamics of a diffusive epidemic model: stability and bifurcation analysis (Q6545611)

Arguing that individuals often change their behaviour during the periods when the infection spreads through the population, the authors suggest exploring the impact of the behavioural trends in a population on the rate of infection spread. This leads to a diffusive SIR model with the Holling type II functional response where a non-monotone incidence rate accounts for the impact of psychological effects. The model demonstrates rich behaviour experiencing both forward and backward bifurcations when two endemic equilibria coexist with the infection-free equilibrium, as well as various local and global codimension two bifurcations including saddle-node, Hopf and Bogdanov-Takens bifurcations. The authors study stability properties of the equilibria and address the impact of the variation of parameters on the dynamics of the model. Numerical simulations are performed and epidemiologic implications of theoretical results are discussed.