Dynamics of a COVID-19 Model with a Nonlinear Incidence Rate, Quarantine, Media Effects, and Number of Hospital Beds

Abstract

In many countries the COVID-19 pandemic seems to witness second and third waves with dire consequences on human lives and economies. Given this situation the modeling of the transmission of the disease is still the subject of research with the ultimate goal of understanding the dynamics of the disease and assessing the efficacy of different mitigation strategies undertaken by the affected countries. We propose a mathematical model for COVID-19 transmission. The model is structured upon five classes: an individual can be susceptible, exposed, infectious, quarantined or removed. The model is based on a nonlinear incidence rate, takes into account the influence of media on public behavior, and assumes the recovery rate to be dependent on the hospital-beds to population ratio. A detailed analysis of the proposed model is carried out, including the existence and uniqueness of solutions, stability analysis of the disease-free equilibrium (symmetry) and sensitivity analysis. We found that if the basic reproduction number is less than unity the system can exhibit Hopf and backward bifurcations for some range of parameters. Numerical simulations using parameter values fitted to Saudi Arabia are carried out to support the theoretical proofs and to analyze the effects of hospital-beds to population ratio, quarantine, and media effects on the predicted nonlinear behavior.