Chaotic dynamics in a novel COVID-19 pandemic model described by commensurate and incommensurate fractional-order derivatives

Mathematical models based on fractional-order differential equations have recently gained interesting insights into epidemiological phenomena, by virtue of their memory effect and nonlocal nature. This paper investigates the nonlinear dynamic behavior of a novel COVID-19 pandemic model described by commensurate and incommensurate fractional-order derivatives. The model is based on the Caputo operator and takes into account the daily new cases, the daily additional severe cases, and the daily deaths. By analyzing the stability of the equilibrium points and by continuously varying the values of the fractional order, the paper shows that the conceived COVID-19 pandemic model exhibits chaotic behaviors. The system dynamics are investigated via bifurcation diagrams, Lyapunov exponents, time series, and phase portraits. A comparison between integer-order and fractional-order COVID-19 pandemic models highlights that the latter is more accurate in predicting the daily new cases. Simulation results, besides to confirming that the novel fractional model well fit the real pandemic data, also indicate that the numbers of new cases, severe cases, and deaths undertake chaotic behaviors without any useful attempt to control the disease.

Automated summary

Mathematical models based on fractional-order differential equations have recently provided insights into epidemiological phenomena due to their memory effect and nonlocal nature. This paper investigates the nonlinear dynamic behavior of a novel COVID-19 pandemic model described by commensurate and incommensurate fractional-order derivatives. The study shows that the COVID-19 pandemic model exhibits chaotic behaviors by analyzing equilibrium points, varying fractional order values, and exploring system dynamics through various methods.