Hu Rui, Aziz Muhamad Hifzhudin Noor, Aruchunan Elayaraja, Mohamed Nur Anisah
Institute of Mathematical Sciences, Universiti Malaya, Kuala Lumpur, 50603, Malaysia.
Department of Decision Science, Universiti Malaya, Kuala Lumpur, 50603, Malaysia.
Sci Rep. 2025 Jul 13;15(1):25305. doi: 10.1038/s41598-025-99389-8.
This paper proposed a delayed fractional-order SEIHR-M model incorporating media influence to investigate the transmission dynamics of COVID-19 in Malaysia. By integrating fractional-order dynamics and time-delay media influence into a unified epidemic framework, this novel structure more accurately captures both memory effects and behavioral response lags in the context of COVID-19. Theoretical analysis verified the existence, non-negativity, and boundedness of the solutions, ensuring the biological feasibility of the model. The basic reproduction number [Formula: see text] was derived using the next-generation matrix method, serving as a key metric for evaluating disease transmission and model stability. Furthermore, when [Formula: see text], the disease-free equilibrium is locally asymptotically stable regardless of the value of the delay parameter τ. When [Formula: see text], the stability of the endemic equilibrium exhibits two scenarios: if [Formula: see text], sufficient conditions for local asymptotic stability are provided; if [Formula: see text], there exists a critical delay [Formula: see text]. The endemic equilibrium remains locally asymptotically stable for [Formula: see text] but becomes unstable for [Formula: see text], undergoing a Hopf bifurcation at [Formula: see text], leading to periodic oscillations. The numerical simulation results not only validate the theoretical analysis but also show that as the fractional-order parameter increases, the system exhibits more pronounced oscillations; furthermore, longer delay times facilitate the emergence of these oscillatory behaviors, making the epidemic more prone to recurrent and periodic fluctuations. By fitting the model with early COVID-19 data from Malaysia, the feasibility and applicability of the model are further validated, and the superior fitting performance of the fractional-order delay model compared to the corresponding integer-order model is highlighted. Finally, sensitivity analysis results show that media interventions have a significant impact on epidemic spread, further demonstrating that timely and effective information dissemination plays a crucial role in reducing the peak of infections and controlling the epidemic.
本文提出了一个纳入媒体影响的延迟分数阶SEIHR - M模型，以研究马来西亚新冠肺炎的传播动力学。通过将分数阶动力学和时间延迟媒体影响整合到一个统一的疫情框架中，这种新颖的结构在新冠肺炎的背景下更准确地捕捉了记忆效应和行为反应滞后。理论分析验证了解的存在性、非负性和有界性，确保了模型的生物学可行性。使用下一代矩阵方法推导了基本再生数[公式：见原文]，作为评估疾病传播和模型稳定性的关键指标。此外，当[公式：见原文]时，无论延迟参数τ的值如何，无病平衡点都是局部渐近稳定的。当[公式：见原文]时，地方病平衡点的稳定性表现出两种情况：如果[公式：见原文]，则提供局部渐近稳定的充分条件；如果[公式：见原文]，则存在一个临界延迟[公式：见原文]。地方病平衡点在[公式：见原文]时保持局部渐近稳定，但在[公式：见原文]时变得不稳定，在[公式：见原文]处发生霍普夫分岔，导致周期性振荡。数值模拟结果不仅验证了理论分析，还表明随着分数阶参数的增加，系统表现出更明显的振荡；此外，更长的延迟时间有利于这些振荡行为的出现，使疫情更容易出现反复和周期性波动。通过将该模型与马来西亚早期新冠肺炎数据进行拟合，进一步验证了模型的可行性和适用性，并突出了分数阶延迟模型相对于相应整数阶模型的优越拟合性能。最后，敏感性分析结果表明媒体干预对疫情传播有显著影响，进一步证明及时有效的信息传播在降低感染峰值和控制疫情方面起着至关重要的作用。
