Parameters and order identification of fractional-order epidemiological systems by Levy-PSO and its application for the spread of COVID-19

To identify the knowledge about parameters and order is very important for the modeling of fractional-order epidemiological systems. In this paper, such an identification problem is formulated as a nonlinear optimization problem. For solving this, the Levy-PSO algorithm, which is obtained by applying Levy flight to generalize the classical particle swarm optimization (PSO), is used. More precisely, we first utilize Levy-PSO to identify the constant parameters and the order of fractional-order SIR, SEIR systems with simulated data to show the effectiveness of our proposed identification strategy. Then, we continue employing Levy-PSO to solve the parameter estimation problem of fractional-order SEAIR model under the real data of COVID-19 in Shanghai from 2/26/2022 to 4/27/2022. Numerical examples and associated comparisons with other existing methods allow us to achieve that our proposed identification strategy can generate a good performance with high accuracy and rapid convergence.