Dynamics of a Fractional-Order COVID-19 Epidemic Model with Quarantine and Standard Incidence Rate

Abstract

In this paper, we propose a fractional-order COVID-19 epidemic model with a quarantine and standard incidence rate using the Caputo fractional-order derivative. The model consists of six classes: susceptible (S), exposed (E), infected (I), quarantined (Q), recovered (R), and deceased (M). In our proposed model, we simultaneously consider the recovery rate and quarantine rate of infected individuals, which has not been considered in other fractional-order COVID-19 epidemic models. Furthermore, we consider the standard incidence rate in the model. For our proposed model, we prove the existence, uniqueness, non-negativity, and boundedness of the solution. The model has two equilibrium points: disease-free equilibrium and endemic equilibrium. Implementing the spectral radius of the next-generation matrix, we obtain the basic reproduction number ((Formula presented.)). The disease-free equilibrium always exists and is locally and globally asymptotically stable only if (Formula presented.). On the other hand, endemic equilibrium exists and is globally asymptotically stable if (Formula presented.). Our numerical simulation confirms the stability properties of the equilibrium. The smaller the order of the derivative, the slower the convergence of the solution of the model. Both the recovery rate and quarantine rate of the infected class are important parameters determining the stability of the equilibrium point. Based on parameter estimation from COVID-19 data in Indonesia, the fractional-order model has better performance than the first-order model for both the calibration and 20-day forecasting of confirmed daily active cases of COVID-19.