A new fractional HRSV model and its optimal control: A non-singular operator approach

Abstract

In the current work, a fractional version of SIRS model is extensively investigated for the HRSV disease involving a new derivative operator with Mittag-Leffler kernel in the Caputo sense (ABC). The fixed-point theory is employed to show the existence and uniqueness of the solution for the model under consideration. In order to see the performance of this model, simulation and comparative analyses are carried out according to the real experimental data from the state of Florida. To believe upon the results obtained, the fractional order is allowed to vary between (0,1) whereupon the physical observations show that the fractional dynamical character depends on the order of derivative operator and approaches an integer solution as α tends to 1. These features make the model more applicable when presented in the structure of fractional-order with ABC derivative. The effect of treatment by an optimal control strategy is also examined on the evolution of susceptible, infectious, and recovered individuals. Simulation results indicate that our fractional modeling and optimal control scheme are less costly and more effective than the proposed approach in the classical version of the model to diminish the HRSV infected individuals.