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 \(R_0\) was derived using the next-generation matrix method, serving as a key metric for evaluating disease transmission and model stability. Furthermore, when \(R_0 < 1\) , the disease-free equilibrium is locally asymptotically stable regardless of the value of the delay parameter \(\tau\) . When \(R_0 > 1\) , the stability of the endemic equilibrium exhibits two scenarios: if \(\tau = 0\) , sufficient conditions for local asymptotic stability are provided; if \(\tau > 0\) , there exists a critical delay \(\tau _0\) . The endemic equilibrium remains locally asymptotically stable for \(0< \tau < \tau _0\) but becomes unstable for \(\tau > \tau _0\) , undergoing a Hopf bifurcation at \(\tau = \tau _0\) , 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.
