Modelling and control of a fractional-order epidemic model with fear effect

Abstract

In this paper, we formulate and study a new fractional-order SIS epidemic model with fear effect of an infectious disease and treatment control. The existence and uniqueness, nonnegativity and finiteness of the system solutions for the proposed model have been analysed. All equilibria of the model system are found, and their local and also global stability analyses are examined. Conditions for fractional backward and fractional Hopf bifurcation are also analysed. We study how the disease control parameter, level of fear and fractional order play a role in the stability of equilibria and Hopf bifurcation. Further, we have established our analytical results through several numerical simulations.

Keywords

Fractional derivative / Fractional SIS epidemic model / Fractional stability conditions / Fractional Hopf bifurcation / Fear effect / Fractional backward bifurcation

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Funding

Department of Science and Technology, Government of West Bengal(201 (Sanc.)/ST/P/S&T/16G- 12/2018 dt 19-02-2019)

RIGHTS & PERMISSIONS

The Joint Center on Global Change and Earth System Science of the University of Maryland and Beijing Normal University