SI based disease model over signed network

Signed network is a kind of network that associates each edge a positive or negative sign which could express friendly or unfriendly relationship between individuals. When diseases spreading over the signed network, some unfriendly edges may refuse to spread. Moreover, the signed network is dynamic, according to the structure balance theory which is the most important theory in the study of signed network, edges in the signed network will flip their signs over time. How does disease spreading interact with signed network evolving becomes a challenging issue. In this paper, we propose an energy function to describe the disease spreading and network evolving together, and we introduce the notion of Structure and Spreading Balanced. We extend the structure balance theory of Cartwright and propose a Structure and Spreading theorem. Finally, we carry out Monte-Carlo simulations on complete signed network to validate our theorem. In the experiment, we find that the signed network has self-immunity during disease spreading, which can be used explain the phenomenon of isolating the virulent virus by isolation.