A fractional-order compartmental model for predicting the spread of the Covid-19 pandemic

TL;DR

This paper introduces a fractional-order compartmental model for Covid-19 that incorporates multiple population groups and analyzes its stability, sensitivity, and parameter estimation using data from various US states to inform mitigation strategies.

Contribution

It presents a novel fractional-order Covid-19 model with stability analysis and parameter estimation based on real data, enhancing understanding of disease dynamics and control measures.

Findings

Basic reproduction number slightly above one, indicating need for stricter measures.

Model parameters estimated from data across multiple states.

Increased cases observed when stay-at-home orders are lifted.

Abstract

We propose a time-fractional compartmental model (SEI$_A$I$_S$HRD) comprising of the susceptible, exposed, infected (asymptomatic and symptomatic), hospitalized, recovered and dead population for the Covid-19 pandemic. We study the properties and dynamics of the proposed model. The conditions under which the disease-free and endemic equilibrium points are asymptotically stable are discussed. Furthermore, we study the sensitivity of the parameters and use the data from Tennessee state (as a case study) to discuss identifiability of the parameters of the model. The non-negative parameters in the model are obtained by solving inverse problems with empirical data from California, Florida, Georgia, Maryland, Tennessee, Texas, Washington and Wisconsin. The basic reproduction number is seen to be slightly above the critical value of one suggesting that stricter measures such as the use of face-masks, social distancing, contact tracing, and even longer stay-at-home orders need to be enforced in order to mitigate the spread of the virus. As stay-at-home orders are rescinded in some of these states, we see that the number of cases began to increase almost immediately and may continue to rise until the end of the year 2020 unless stricter measures are taken.