Stability analysis of a fractional SIR epidemic model with nonlinear incidence rate via modified Riemann-Liouville derivative

Abderrahim Mouaouine; Khalid Hattaf; Noura Yousfi; Academic Editor: Youssef EL FOUTAYENI

Research Communication | Open Access
Volume 2019 | Communication ID 232

Stability analysis of a fractional SIR epidemic model with nonlinear incidence rate via modified Riemann-Liouville derivative

Abderrahim Mouaouine, Khalid Hattaf, Noura Yousfi

Academic Editor: Youssef EL FOUTAYENI

Received	Accepted	Published
Jan 31, 2019	Feb 26, 2019	Mar 01, 2019

Abstract: In this work, we study the dynamics of a fractional SIR epidemic model with nonlinear incidence rate via the modified Riemann-Liouville derivative, which provide a framework for a fractional calculus which is quite parallel with the classical one, this modified fractional derivative applies to functions fractional differentiable but not necessarily differentiable. First, we prove the global existence of solutions, their positivity and boundedness. The disease-free equilibrium and the endemic equilibrium are calculated and their stability is investigated. Finally, numerical simulation are ...