The Application of Saturated Incidence Rate with Delay and Awareness in Modelling the Spread of Infectious Diseases

Abstract

The current state as regards the spread of the coronavirus disease 2019 indicates that the major preventive measure is minimizing individual contact with the virus. Consequently, this paper derived a mathematical model using saturated incidence rate with the disease incubating period as a delay parameter along other parameters measuring the inhibitory effects of awareness dissemination from the media, general campaign and individual interactions. The analytical evaluation of the model indicates that the stability of the disease-free and the endemic steady states of the model are determined by the basic reproduction number. In addition, the disease-free steady state is independent of the incubating period, whereas the endemic steady state is initially stable but undergoes Hopf bifurcation as the incubating period exceeds the critical value by exhibiting periodic oscillation and become unstable. The outcome of the numerical simulation of the model via MATLAB application affirmed the results obtained analytically.

Keywords: Infectious Diseases, Model, Incidence rate, Basic reproduction number, Hopf bifurcation