Mathematical Analysis and Optimal Control of a Transmission Model for Respiratory Syncytial Virus

Zakaria S. Al Ajlan, Moustafa El-Shahed and Yousef Alnafisah ()
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Zakaria S. Al Ajlan: Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
Moustafa El-Shahed: Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
Yousef Alnafisah: Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia

Mathematics, 2025, vol. 13, issue 18, 1-25

Abstract: In this study, we develop a mathematical model to describe the transmission dynamics of the Respiratory Syncytial Virus (RSV), incorporating the coexistence of two distinct strains. The global stability of the disease-free and endemic equilibria is analyzed. Bifurcation analysis reveals the occurrence of a forward bifurcation. To control the spread of the infection, Pontryagin’s maximum principle is applied within the framework of optimal control theory, considering intervention strategies such as isolation, treatment, and vaccination. A detailed evaluation of the effectiveness of these control strategies is conducted for a specific population based on a nonlinear optimal control model. Moreover, a cost-effectiveness analysis is performed to identify the most economically viable intervention. The findings indicate that, among the studied interventions, isolation is the most cost-effective strategy for reducing RSV prevalence. The model is numerically solved using the fourth-order Runge–Kutta method, coupled with the forward–backward sweep algorithm, to assess the impact of various control combinations on the transmission dynamics of RSV.

Keywords: mathematical model; stability; respiratory syncytial virus (RSV); optimal control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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