Title: Interaction between cluster synchronization and epidemic spread in community networks,
Abstract: In real world, there is a significant relation between human behaviors and
epidemic spread. Especially, the reactions among individuals in different
communities to epidemics may be different, which lead to cluster
synchronization of human behaviors. So, a mathematical model that embeds
community structures, behavioral evolution and epidemic transmission is
constructed to study the interaction between cluster synchronization and
epidemic spread. The epidemic threshold of the model is obtained by using
Gersgorin Lemma and dynamical system theory. By applying the Lyapunov stability
method, the stability analysis of cluster synchronization and spreading
dynamics are presented. Then, some numerical simulations are performed to
illustrate and complement our theoretical results. As far as we know, this work
is the first one to address the interplay between cluster synchronization and
epidemic transmission in community networks, so it may deepen the understanding
of the impact of cluster behaviors on infectious disease dynamics.