Dynamics of an SEIRM Epidemic Model with Disease Awareness, Saturation Treatment, and Contagious Incubation Period

Recognizing the crucial roles of media-driven awareness in shaping public responses to precautionary measures, we propose and analyse an SEIRM epidemic model with infectious force in incubation period affected by the intensity of the disease awareness through a novel media function. We discuss the existence and stability of disease free and endemic equilibrium, and establish conditions for periodic oscillations. When awareness growth surpasses a critical threshold, Hopf bifurcation induces limit cycles with amplitude increasing as awareness intensifies.