Optimized Fixed-Time Synergetic Controller via a modified Salp Swarm Algorithm for Acute and Chronic HBV Transmission System

Saadi Achour; Khalil Mokhtari; Abdelaziz Rahmoune; Fares Yazid

doi:10.13164/mendel.2023.2.191

Saadi Achour Laboratory of Pure and Applied Mathematics, University Amar Telidji of Laghouat, Algeria
Khalil Mokhtari Department of Industrial Engineering, University Abbes Laghrour of Khenchela, Algeria
Abdelaziz Rahmoune Laboratory of Pure and Applied Mathematics, University Amar Telidji of Laghouat, Algeria
Fares Yazid Laboratory of Pure and Applied Mathematics, University Amar Telidji of Laghouat, Algeria

DOI: https://doi.org/10.13164/mendel.2023.2.191

Keywords: Salp Swarm optimization Algorithm, Synergetic controller, Fixed-time control, Lyapunov stability, Hepatitis B Virus, Epidemic system

Abstract

In this paper, we propose a Salp Swarm Algorithm (SSA) Optimized Fixed-Time Synergetic Control (FTSC) strategy for the spread of hepatitis B infection. The utilization of the SSA optimization algorithm for optimizing the Synergetic Control (SC) fraction parameters presents a non-trivial challenge due to the restriction that only odd numbers can be used for the fractional power. Therefore, an enhanced and adapted version of the SSA algorithm is proposed to effectively address this specific scenario. Our strategic approach centers on the reduction of susceptible, acutely infected, and chronically infected individuals by employing control parameters like isolation, treatment, and vaccination. The objective is to drive these target state variables to their smallest values in a fixed-time, thereby effectively controlling the epidemic. We support our proposal with numerical simulations to demonstrate the feasibility and effectiveness of the control strategy. A comparison is conducted between FTSC and SC in scenarios with and without optimization. The results indicated that FTSC holds a distinct advantage, consistently demonstrating significant progress, with up to 30\% reduction in the total convergence time to zero, outperforming SC in each case.

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