Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection

TL;DR

This paper develops a fractional order epidemic model for human respiratory syncytial virus, formulates an optimal control problem, and demonstrates improved cost-effectiveness of control measures over previous models.

Contribution

It introduces a non-local fractional order model and an optimal control framework, enhancing the accuracy and efficiency of epidemic intervention strategies.

Findings

Fractional model outperforms classical models in accuracy.

Optimal control reduces intervention costs significantly.

Cost-effectiveness analysis shows improved outcomes.

Abstract

A human respiratory syncytial virus surveillance system was implemented in Florida in 1999, to support clinical decision-making for prophylaxis of premature newborns. Recently, a local periodic SEIRS mathematical model was proposed in [Stat. Optim. Inf. Comput. 6 (2018), no.1, 139--149] to describe real data collected by Florida's system. In contrast, here we propose a non-local fractional (non-integer) order model. A fractional optimal control problem is then formulated and solved, having treatment as the control. Finally, a cost-effectiveness analysis is carried out to evaluate the cost and the effectiveness of proposed control measures during the intervention period, showing the superiority of obtained results with respect to previous ones.