Epidemic spreading in metapopulation networks with heterogeneous mobility rates

The heterogeneity is a key feature of individual mobility which caused by different comprehensive interferences, including the distinctions of interventions deployed by governments and individuals' self-protection awareness in different regions. Since exposed individuals and infected individuals can infect the susceptible with different transmission rates, we use the Markovian approach to construct a Susceptible-Exposed-Infected-Recovered (SEIR) model with recurrent mobility patterns in the metapopulation network. We first theoretically calculate the epidemic threshold, and then, perform the proposed model in different underlying metapopulation networks, named as ER-like metapopulation network and BA-like metapopulation network. Simulation results indicate that BA-like metapopulation network is more conductive for epidemic spreading. Further research presents that both comprehensive interferences and the initial mobility rate can influence disease propagation heavily. In particular, for ER-like metapopulation network, comprehensive interferences can suppress the disease propagation when the initial mobility rate approaches to one. Whereas for BA-like metapopulation network, comprehensive interferences can contain the disease when the initial mobility rate is greater than a certain value. Meanwhile, implementing stronger interventions in patches with larger populations could reduce epidemic spreading effectively in BA-like metapopulation network. In addition, a long latent period could lead to the spread and infection of disease in both kinds of metapopulation networks.