Stability analysis of an SIS epidemic model with feedback mechanism on networks

In this paper, an epidemic model with feedback mechanism on networks is investigated. We obtain the basic reproductive number R 0 , and analyze the stability behaviors of disease-free equilibrium E 0 and endemic equilibrium E ∗ . When R 0 < 1 , the disease-free equilibrium is globally asymptotically stable, and when R 0 > 1 , the endemic equilibrium is asymptotically stable. Although the feedback mechanism cannot change the basic reproductive number R 0 as we prove, it should be indicated that it can weaken the spreading of diseases and reduce the endemic level. Finally, the results of the stability and the effectiveness of the feedback mechanism are illustrated by some numerical simulations.