Mathematical Analysis of a Fractional-order ”SIR” Epidemic Model with a General Nonlinear Saturated Incidence Rate in a Chemostat

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Miled El Hajji

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

Article Details

How to Cite
El Hajji, M. (2019). Mathematical Analysis of a Fractional-order ”SIR” Epidemic Model with a General Nonlinear Saturated Incidence Rate in a Chemostat. Asian Research Journal of Mathematics, 12(2), 1-12. https://doi.org/10.9734/arjom/2019/v12i230082
Section
Original Research Article