Mathematical model of SIR epidemic system (COVID-19) with fractional derivative: stability and numerical analysis

In this paper, we study and analyze the susceptible-infectious-removed (SIR) dynamics considering the effect of health system. We consider a general incidence rate function and the recovery rate as functions of the number of hospital beds. We prove the existence, uniqueness, and boundedness of the model. We investigate all possible steady-state solutions of the model and their stability. The analysis shows that the free steady state is locally stable when the basic reproduction number R-0 is less than unity and unstable when R-0 > 1. The analysis shows that the phenomenon of backward bifurcation occurs when R-0 < 1. Then we investigate the model using the concept of fractional differential operator. Finally, we perform numerical simulations to illustrate the theoretical analysis and study the effect of the parameters on the model for various fractional orders.

Automated summary

The paper studies the SIR dynamics considering the effect of the health system and proves the existence, uniqueness, and boundedness of the model. It analyzes all possible steady-state solutions and their stability, showing that the free steady state is locally stable when the basic reproduction number is less than 1. The study also explores the model using fractional differential operators and performs numerical simulations to illustrate the theoretical analysis and the impact of parameters for various fractional orders.