Mathematical Analysis of a Fractional-order ”SIR” Epidemic Model with a General Nonlinear Saturated Incidence Rate in a Chemostat
Miled El Hajji *
ENIT-LAMSIN, BP. 37, 1002 Tunis-Belvedere, Tunis El Manar university, Tunis, Tunisia.
*Author to whom correspondence should be addressed.
Abstract
In the present work, a fractional-order differential equation based on the Susceptible-Infected- Recovered (SIR) model with nonlinear incidence rate in a continuous reactor is proposed. A profound qualitative analysis is given. The analysis of the local and global stability of equilibrium points is carried out. It is proved that if the basic reproduction number R > 1 then the disease-persistence (endemic) equilibrium is globally asymptotically stable. However, if R ≤ 1, then the disease-free equilibrium is globally asymptotically stable. Finally, some numerical tests are done in order to validate the obtained results.
Keywords: Fractional-Order ‘’SIR’’ model, Caputo fractional derivative, deterministic, nonlinearincidence rate, equilibrium points, local and global stability