Dynamic Processes on Complex Networks
Network-based analysis offers a new perspective in studying complex biological systems. This chapter describes the scaled SIS process, a continuous-time Markov process on networks, which models the spread of contagion in a finite-sized population with arbitrary heterogeneous interactions; this is in contrast to classical epidemics models based on the thermodynamic principle of full mixing. An individual’s probability of being infected is dependent on the number of infected neighbors. The inclusion of a finite-sized network introduces combinatorial complexity in the analysis. We show that the scaled SIS process has a closed-form steady-state characterization (i.e., equilibrium distribution) of the Gibbs form. The equilibrium distribution allows us to study the effects of network topology and infection/healing dynamics on the steady-state behavior of the process. We use the equilibrium distribution to formulate and analyze the vulnerability of the population to infection. Using the most-probable configuration, we show that individuals in densely connected subgraphs may be more vulnerable to infection depending on network topology and dynamics parameters.