Theoretical Analysis of a COVID-19 CF-Fractional Model to Optimally Control the Spread of Pandemic

Abstract

In this manuscript, we formulate a mathematical model of the deadly COVID-19 pandemic to understand the dynamic behavior of COVID-19. For the dynamic study, a new SEIAPHR fractional model was purposed in which infectious individuals were divided into three sub-compartments. The purpose is to construct a more reliable and realistic model for a complete mathematical and computational analysis and design of different control strategies for the proposed Caputo–Fabrizio fractional model. We prove the existence and uniqueness of solutions by employing well-known theorems of fractional calculus and functional analyses. The positivity and boundedness of the solutions are proved using the fractional-order properties of the Laplace transformation. The basic reproduction number for the model is computed using a next-generation technique to handle the future dynamics of the pandemic. The local–global stability of the model was also investigated at each equilibrium point. We propose basic fixed controls through manipulation of quarantine rates and formulate an optimal control problem to find the best controls (quarantine rates) employed on infected, asymptomatic, and “superspreader” humans, respectively, to restrict the spread of the disease. For the numerical solution of the fractional model, a computationally efficient Adams–Bashforth method is presented. A fractional-order optimal control problem and the associated optimality conditions of Pontryagin maximum principle are discussed in order to optimally reduce the number of infected, asymptomatic, and superspreader humans. The obtained numerical results are discussed and shown through graphs.

Keywords

• COVID-19 epidemic model
• CF derivative
• existence and uniqueness
• Adams–Bashforth computational scheme
• optimal control