Analysis of novel fractional COVID-19 model with real-life data application

Abstract

The current work is of interest to introduce a detailed analysis of the novel fractional COVID-19 model. Non-local fractional operators are one of the most efficient tools in order to understand the dynamics of the disease spread. For this purpose, we intend as an attempt at investigating the fractional COVID-19 model through Caputo operator with order $\chi \in (0,1)$ . Employing the fixed point theorem, it is shown that the solutions of the proposed fractional model are determined to satisfy the existence and uniqueness conditions under the Caputo derivative. On the other hand, its iterative solutions are indicated by making use of the Laplace transform of the Caputo fractional operator. Also, we establish the stability criteria for the fractional COVID-19 model via the fixed point theorem. The invariant region in which all solutions of the fractional model under investigation are positive is determined as the non-negative hyperoctant $R_{+}^7$ . Moreover, we perform the parameter estimation of the COVID-19 model by utilizing the non-linear least squares curve fitting method. The sensitivity analysis of the basic reproduction number $R_0^c$ is carried out to determine the effects of the proposed fractional model's parameters on the spread of the disease. Numerical simulations show that all results are in good agreement with real data and all theoretical calculations about the disease.

Keywords: COVID-19; Caputo derivative; Epidemiology; Fractional operators; Numerical scheme.