Stability and Bifurcation Analysis in a Fractional-order Epidemic Model with Sub-optimal Immunity, Nonlinear Incidence and Saturated Recovery Rate

Recently, many deterministic mathematical model have been extended to fractional model, using some fractional differential equation. Numerous studies had shown that these fractional models are more realistic to represent the daily life phenomena. This paper focused on extending the model of a SIR epidemic to fractional model. More specifically, the study discussed the fractional SIR epidemic model with sub-optimal immunity, nonlinear incidence and saturated recovery rate. The fractional ordinary differential equations were defined in the sense of the Caputo derivative. Stability analysis of the equilibrium points of the models for the fractional models were presented. Furthermore, we investigated the Hopf bifurcation analysis. The result obtained showed that the model undergo Hopf bifurcation for some values, and further confirmed that choosing an appropriate figure of the fractional α ∈ (0,1] increase the stability region of the equilibrium points. © 2021. All Rights Reserved.