Optimal Control Problem of Hybrid FracInt Variable-Order Mathematical Model for Covid-19 with Time Delay

Document Type : Original Article

Authors

1 Cairo university, faculty of science, Cairo, Egypt

2 Department of Mathematics, Faculty of science , Suez University, Egypt

3 Mathematics Department, Faculty of Education, Sana’a University, Yemen

4 The Higher Institute for Computer Science and Information System, Fifth Settlement, Egypt

Abstract

This paper investigates the variable-order FracInt derivative with time delay to examine the corona-virus disease. In the present research, an issue with optimal control is presented for the combined variable-order Coronavirus FracInt Model with time delay. The Caputo derivative and the Riemann-Liouville integral are combined linearly to yield the derivative of hybrid fractional order. The definition of the variable-order derivatives is fracInt order derivatives. We provide the solutions’ existence, boundedness, positivity, and reproductive number R_0. Two control factors, v_1 and v_2 are thought to lessen the risk of infection spreading to healthy people. The new hybrid variable-order operator can be approximated using the Grünwald-Letnikov approximation. The optimality system is solved using a hybrid variable-order operator combined with the non-standard finite difference approach. Lastly, the theoretical analysis of the proposed model has been supported by numerical simulations. Finally, the illness can be effectively controlled by the suggested FracInt system, as illustrated by the numerical results. In the future, we will use the FracInt variable-order operator for solving numerically epidemic model diseases such as Lumpy-Skin and Monkey-pox diseases.

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