Fractional-Order SEIQRDP Model for Simulating the Dynamics of COVID-19 Epidemic

Abstract

Goal: Coronavirus disease (COVID-19) is a contagious disease caused by a newly discovered coronavirus, initially identified in the mainland of China, late December 2019. COVID-19 has been confirmed as a higher infectious disease that can spread quickly in a community population depending on the number of susceptible and infected cases and also depending on their movement in the community. Since January 2020, COVID-19 has reached out to many countries worldwide, and the number of daily cases remains to increase rapidly. Method: Several mathematical and statistical models have been developed to understand, track, and forecast the trend of the virus spread. Susceptible-Exposed-Infected-Quarantined-Recovered-Death-Insusceptible (SEIQRDP) model is one of the most promising epidemiological models that has been suggested for estimating the transmissibility of the COVID-19. In the present study, we propose a fractional-order SEIQRDP model to analyze the COVID-19 pandemic. In the recent decade, it has proven that many aspects in many domains can be described very successfully using fractional order differential equations. Accordingly, the Fractional-order paradigm offers a flexible, appropriate, and reliable framework for pandemic growth characterization. In fact, due to its non-locality properties, a fractional-order operator takes into consideration the variables' memory effect, and hence, it takes into account the sub-diffusion process of confirmed and recovered cases. Results-The validation of the studied fractional-order model using real COVID-19 data for different regions in China, Italy, and France show the potential of the proposed paradigm in predicting and understanding the pandemic dynamic. Conclusions: Fractional-order epidemiological models might play an important role in understanding and predicting the spread of the COVID-19, also providing relevant guidelines for controlling the pandemic.

Keywords: COVID-19; Coronavirus; SEIR models; fractional-order derivative; pandemic.

Fig. 1.

SEIQRDP compartment epidemic model showing the protection rate, , the infection rate, , the inverse of the average latent time, , the rate at which infectious people enter in quarantine, , the time dependent cure rate, , and the time dependent mortality rate .

Fig. 2.

Predictions of the proposed fractional model using data from China.

Fig. 3.

Predictions of the proposed fractional model using data from Italy.

Fig. 4.

Predictions of the proposed fractional model using data from France.