Dynamics of an SIR-Based COVID-19 Model With Linear Incidence Rate, Nonlinear Removal Rate, and Public Awareness

Abstract

The paper studies the dynamics of the classical susceptible-infectious-removed (SIR) model when applied to the transmission of COVID-19 disease. The model includes the classical linear incidence rate but considers a nonlinear removal rate that depends on the hospital-bed population ratio. The model also includes the effects of media on public awareness. We prove that when the basic reproduction number is less than unity the model can exhibit a number of nonlinear phenomena including saddle-node, backward, and Hopf bifurcations. The model is fitted to COVID-19 data pertinent to Saudi Arabia. Numerical simulations are provided to supplement the theoretical analysis and delineate the effects of hospital-bed population ratio and public awareness on the control of the disease.