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

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 variable recovery rate that depends on the hospital-bed population ratio. The model also includes the effects of media on public awareness that may lead to a decrease in the disease transmission. 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. Numerical simulations, based on some parameters' values associated with Saudi Arabia, are also provided to supplement the theoretical analysis and to delineate the effects of hospital-bed population ratio and media coverage on the disease control.