We consider a SEAIR epidemic model with Atangana–Baleanu fractional-order derivative. We approximate the solution of the model using the numerical scheme developed by Toufic and Atangana. The numerical simulation corresponding to several fractional orders shows that, as the fractional order reduces from 1, the spread of the endemic grows slower. Optimal control analysis and simulation show that the control strategy designed is operative in reducing the number of cases in different compartments. Moreover, simulating the optimal profile revealed that reducing the fractional-order from 1 leads to the need for quick starting of the application of the designed control strategy at the maximum possible level and maintaining it for the majority of the period of the pandemic.

This paper deals with numerical treatment of singularly perturbed parabolic differential equations having large time delay. The highest order derivative term in the equation is multiplied by a perturbation parameter ε , taking arbitrary value in the interval 0 , 1 . For small values of ε , solution of the problem exhibits an exponential boundary layer on the right side of the spatial domain. The properties and bounds of the solution and its derivatives are discussed. The considered singularly perturbed time delay problem is solved using the Crank-Nicolson method in temporal discretization and exponentially fitted operator finite difference method in spatial discretization. The stability of the scheme is investigated and analysed using comparison principle and solution bound. The uniform convergence of the scheme is discussed and proven. The formulated scheme converges uniformly with linear order of convergence. The theoretical analysis of the scheme is validated by considering numerical test examples for different values of ε .

This paper deals with the numerical solution of singularly perturbed parabolic convection-diffusion problems with two small positive parameters multiplying the convection and diffusion terms. A parameter-uniform computational method is developed to solve these problems. The stability and consistency of the method are well established. Numerical experimentation is done and it is observed that the formulated method is stable, consistent and gives more accurate results than some methods exist in the literature.