Modeling and analysis of a delayed fractional order COVID-19 SEIHRM model with media coverage in Malaysia.

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.