The Effects Of Clustering On SIR-type Epidemic Dynamics

Considering the spread of epidemic on complex networks has been significant part of research on epidemic dynamics,however,network structure plays a crucial role in disease spread.It has been proved that network clustering has nonnegligible effect on network structure and epidemic dynamics.In chapter two,the paper first develops a SIR-type epidemic model on random networks with clustering,i.e.,Next,the comparison between the results of stochastic and numerical simulations confirms the validity of the system of equations;meanwhile,the analytical result of the model reveals that clustering slows epidemic rate and decreases the final size of epidemic.Finally,the paper investigates the implication of the difference between the distribution of local clustering for the spread of disease by stochastic simulations:although the speeds of disease spread between the networks with different distributions of local clustering diverge,there is a small gap between the values of the final size of epidemic,while keeping the degree distribution and the value of clustering of the networks almost same.In chapter three,in order to make it clear that the structure difference between two kinds of networks generated by the algorithm the paper suggests and the widely used "big V" rewiring algorithm,the paper compares some large-scale structure properties,including average path length,assortative mixing by degree and giant connected component size.The results show that,there exist tiny distinction between those in properties of average path length and component size,except one of assortative mixing by degree.In contrast to "big V" rewiring algorithm,the algorithm the paper suggests not only introduces the clustering into networks but also brings higher assortative mixing by degree into networks.