Numerical approach to solve Caputo‐Fabrizio‐fractional model of corona pandemic with optimal control design and analysis

• Published in: Mathematical methods in the applied sciences Vol. 46; no. 8; pp. 9751 - 9782
• Main Authors: Hanif, Asma, Kashif Butt, Azhar Iqbal, Ahmad, Waheed
• Format: Journal Article
• Language: English
• Published: Freiburg Wiley Subscription Services, Inc 30.05.2023
• Subjects: CF‐fractional derivative; COVID‐19; Design analysis; Mathematical models; numerical simulations; Optimal control; Optimization; Pandemics; stability; steady states; uniqueness
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.9085

In this manuscript, we have studied the dynamical behavior of a deadly COVID‐19 pandemic which has caused frustration in the human community. For this study, a new deterministic SEIHR fractional model is developed for the first time. The purpose is to perform a complete mathematical analysis and the design of an optimal control strategy for the proposed Caputo–Fabrizio fractional model. We have proved the existence and uniqueness of solutions by employing principle of mathematical induction. The positivity and the boundedness of solutions is proved using comprehensive mathematical techniques. Two main equilibrium points of the pandemic model are stated. The basic reproduction number for the model is computed using next generation technique to handle the future dynamics of the pandemic. We develop an optimal control problem to find the best controls for the quarantine and hospitalization strategies employed on exposed and infected humans, respectively. For numerical solution of the fractional model, we implemented the Adams–Bashforth method to prove the importance of order. A general fractional‐order optimal control problem and associated optimality conditions of Pontryagin type are discussed, with the goal to minimize the number of exposed and infected humans. The extremals are obtained numerically.