Stochastic infections with carriers on transportation networks

We investigate a stochastic susceptible-infected-carrier-susceptible infection model on transportation networks. The epidemic control measures of the transportation network are modeled under a simple assumption: Detectors of airports and traffic stations prohibit infected individuals from traveling, except the carriers. We focus on the dynamic impact caused by the carrier. By using the method of path integral on Markov chain, the propagation thresholds of the infection model considering carrier state are derived. Research shows that the between-cluster transmission threshold concerns to the population size of cluster, the within-cluster transmission rate and the recovery rate of carriers. Simulation confirmed the correctness of the theoretical calculation result about transmission threshold.