On variable-order hybrid FracInt Covid-19 mathematical model: optimal control approach

Abstract

AbstractAn optimal control problem for the variable-order fractional-integer mathematical model of vaccination Covid 19 is presented in this research, where the order of the derivatives varies during the course of the time interval, becoming fractional or classical when it is more favourable. The variable-order derivatives are defined here using both the variable-order integral of Riemann–Liouville and the variable-order Caputo derivative. The existence, uniqueness, boundedness and positivity of the solutions are given. In order to test the rate for the detection of symptomatic infected people, two control variables are introduced. The optimality conditions are derived. The fractional-integer operator is approximated using Grünwald–Letnikov. Examples and comparative studies are presented to demonstrate the simplicity of the approximation approaches and the applicability of the utilized methods.

Keywords

• Coronavirus diseases
• Grünwald-Letnikov finite difference method
• Optimality conditions
• vaccination
• variable-order FracInt
• 37N25