New Caputo-Fabrizio fractional order ${\mathit{SEIAS}}_q{E}_q\mathit{HR}$ model for COVID-19 epidemic transmission with genetic algorithm based control strategy

Abstract

Fractional derivative has a memory and non-localization features that make it very useful in modelling epidemics’ transition. The kernel of Caputo-Fabrizio fractional derivative has many features such as non-singularity, non-locality and an exponential form. Therefore, it is preferred for modeling disease spreading systems. In this work, we suggest to formulate COVID-19 epidemic transmission via ${\mathit{SEIAS}}_q{E}_q\mathit{HR}$ paradigm using the Caputo-Fabrizio fractional derivation method. In the suggested fractional order COVID-19 ${\mathit{SEIAS}}_q{E}_q\mathit{HR}$ paradigm, the impact of changing quarantining and contact rates are examined. The stability of the proposed fractional order COVID-19 ${\mathit{SEIAS}}_q{E}_q\mathit{HR}$ paradigm is studied and a parametric rule for the fundamental reproduction number formula is given. The existence and uniqueness of stable solution of the proposed fractional order COVID-19 ${\mathit{SEIAS}}_q{E}_q\mathit{HR}$ paradigm are proved. Since the genetic algorithm is a common powerful optimization method, we propose an optimum control strategy based on the genetic algorithm. By this strategy, the peak values of the infected population classes are to be minimized. The results show that the proposed fractional model is epidemiologically well-posed and is a proper elect.