Bifurcation from an Epidemic Model in the Presence of Memory Effects.

In this paper, we consider a fractional SIS epidemic system with logistic growth demographic and saturated incidence rate for susceptibles. First, we validate our model by proving the global existence, positivity as well as boundedness of solutions. Then, we give necessary and sufficient conditions for the extinction and persistence of the disease from the population. We also study the local asymptotic stability of the unique positive equilibrium point by analyzing the corresponding characteristic equation. We find that combining logistic growth and saturated incidence for susceptibles can lead the system dynamic behavior to exhibit stability switches. By choosing the growth rate and the carrying capacity of the population as the bifurcation parameters, the stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. Finally, numerical simulations are performed to verify the theoretical results, to fit real-time data from 10 June to 25 November of 2020 and also to predict the number of cumulative cases for COVID-19 in Morocco during 2021. [ABSTRACT FROM AUTHOR]