The Influence Of The Size And Structure Of Epidemic Networks On The Stochastic Extinction Of Infections

The stochastic extinction of epidemic infections is commonly observed in small communities, and its underlying mechanisms have been studied in classical compartmentalized epidemic models in which hosts are assumed to be perfectly mixed. However, epidemic networks are complicated and perfectly mixing is not always the case. This suggests the necessity to investigate how the contact patterns affect the stochastic extinction by a network approach. To investigate the mechanisms of stochastic extinction in epidemic networks, a Susceptible-Infected-Recovered-Susceptible (SIRS) epidemic model of one-pathogen strain is considered. To illustrate how the size and structure of contact networks affect the stochastic extinction of infection, four typical types of networks are examined: the globally coupled network, the nearest-neighbor coupled network, the Newman-Watts (NW) small-world network and the Barabasi-Albert (BA) scale-free network. The major concern of this thesis is the stochastic extinction rate (the probability of stochastic extinction to happen in one step of simulation). In the globally coupled network, it is found that the stochastic extinction rate decreases exponentially as the size of the network grows. While in the nearest-neighbor coupled network, the NW small-world network and the BA scale-free network, it is found that the stochastic extinction rate decreases as the connectivity parameters grow (different networks have their own connectivity parameters).