Qualitative analysis of an epidemic model with nonlinear incidence rate in the time of COVID-19

Abstract

In this paper we propose and study an epidemic model with nonlinear incidence rate, describing some factors effect (protection, exposure, immigration, social distancing, vaccination) on the spread of certain diseases on the community like the novel coronavirus COVID-19. The dynamical behavior of the proposed model is examined. We investigate the existence and stability of the disease-free equilibrium and the endemic equilibrium. The existence of a limit cycle is studied. Simulations of the model are performed to illustrate and support the theoretical results.

Subject Classification:

• 34A34
• 34C23
• 34C25
• 92C60
• 92D25

Keywords:

• Epidemic model
• Covid-19
• Nonlinear incidence
• Stability
• Psychological effect
• Cure rate