A Non-Local Fractional-Order Mathematical Model Quantifying the Long-Term Memory Effect of Respiratory Syncytial Virus (RSV) Infection on Childhood Asthma Dynamics
Abstract
Respiratory Syncytial Virus (RSV) infection in infancy is strongly correlated with an increased risk of childhood asthma, presenting a complex public health challenge involving both transient infectious dynamics and long-term chronic sequelae. To address this gap, this study develops a novel seven-compartmental model, utilizing the Caputo fractional derivative. The Disease-Free Equilibrium (E0) and the Basic Reproduction Number (R0) were derived using the Next-Generation Matrix (NGM) method. The result proves that the persistence of both RSV and the resultant endemic asthma burden depend exclusively on parameters governing the primary RSV infection. Numerical simulations, employing the generalized Adams-Bashforth-Moulton (ABM) method was used to validate the analytical threshold and illustrate the dynamics. A sensitivity analysis also identified the RSV treatment rate ($\alpha_{R}$) and vaccination rate (p) as the most critical policy levers for reducing R0. Furthermore, quantitative results demonstrate that a stronger memory effect (lower $\alpha$) reduces long-term endemic prevalence of chronic asthma ($I_{A}^{*}$). The findings provide quantitative evidence that public health strategies targeting the prevention and mitigation of acute RSV infection offer the most effective dual-benefit approach for reducing the combined acute and chronic disease burdens.
Keywords
Fractional-Order Calculus; Caputo Derivative; Respiratory Syncytial Virus (RSV); Childhood Asthma; Basic Reproduction Number (Ro); Next-Generation Matrix (NGM); Biological Memory; Sensitivity Analysis
References
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