It is well known that both media coverage and the presence of asymptomatic patients have a significant impact on the spread and control of infectious diseases. Therefore, this paper proposes a class of fractional epidemic models that incorporate media coverage and asymptomatic infection. Also, the time delay for individuals’ response to the current media coverage, as well as the time delay of media coverage, are incorporated in our proposed model to make it more practical. Based on fractional proportional-derivative (PD) control method, Hopf bifurcation is investigated by taking the sum of the two time delays and the order of the fractional derivatives as bifurcation parameters, respectively. Some sufficient delayed-induced and order-induced bifurcation conditions are given. The application and effectiveness of the presented theoretical results are illustrated through a simulation example. Furthermore, the impact of the feedback control gains and the media effect weight on the stability and Hopf bifurcation of the considered epidemic model is explored.
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