Modelling and analysis of an epidemic model with awareness caused by deaths due to fear.

Abstract

In this paper, we establish a compartmental model in which the transmission rate is associated with the fear of being infected by COVID-19. We provide a detailed analysis of the epidemic model and established results for the existence of a positively invariant set. The expression of the basic reproduction number $R_0$ is characterized. It is shown that the disease-free equilibrium (DFE) is globally asymptotically stable if $R_0<1$, and the system exhibits a forward bifurcation if $R_0=1$. When $R_0>1$, the system is uniformly persistent, the DFE is unstable and there exists a unique and globally asymptotic stable endemic equilibrium (EE). We fit unknown parameters using the reported data in Canada from September 1 to October 10, 2021, and carry out sensitivity analysis. The quantitative analysis of the model with awareness demonstrates the significance of reducing the transmission rate and enhancing public protective awareness.