The Generalized Multistate Complex Network Contagion Dynamics Model and Its Stability

In this paper, we propose a new and fairly general network-based contagion dynamics model framework. In the model framework, each node in the network can be in one of multiple secure (or good) and infected (or bad) states. We characterize the dynamics of our model framework, by presenting the following: (i) a sufficient condition under which the dynamics are globally asymptotically stable; (ii) a sufficient condition under which the dynamics are locally asymptotically stable; and (iii) a sufficient condition for the persistence of bad states. Finally, we implemented three operations on the transition diagram. These three operations can help eliminate the bad states and help the model achieve the stability conditions.