Comparative analysis on fractional optimal control of an SLBS model

Abstract

In this article, we examine the fractional optimal control strategy of computer virus propagation in a heterogeneous network. For this purpose, we first generalize an avail-able SLBS (Susceptible-Latent-Breaking-out) model in terms of the Caputo derivative an operator that models the relations of the computers in the network consistent with power-law. Herein, unit consistency is acquired for the fractional order model. Various control strategies are studied using antivirus programs installed in separate compartments of the fractional model. The goal of optimal control is to decrease the number of computers with malware and the expense of antivirus programs. To realize the desired aim, we initially analyze the stability of the virus-free and viral equilibrium points. We also calculate the basic reproduction number of the model including the control term. After that, we indicate the existence of the optimal control and achieve the necessary optimality conditions by utilizing Pontryagin's maximum principle. We numerically solve the arising nonlinear state and costate systems with the Adams-type predictor-corrector method. Eventually, we also study the relations of the computers in the network consistent with exponential-law modeled by Caputo-Fabrizio and Atangana-Baleanu operators, respectively. Thus all comparative results displaying the effects of singular and non-singular kernels on the model are plotted by MATLAB program.