Quantifying the Effect of Metapopulation Size on the Persistence of Infectious Diseases in a Metapopulation

We investigate the special role of the three-dimensional relationship between periodicity, persistence and synchronization on its ability of disease persistence in a meta-population. Persistence is dominated by synchronization effects, but synchronization is dominated by the coupling strength and the interaction between local population size and human movement. Here we focus on the quite important role of population size on the ability of disease persistence. We implement the simulations of stochastic dynamics in a susceptible-exposed-infectious-recovered (SEIR) metapopulation model in space. Applying the continuous-time Markov description of the model of deterministic equations, the direct method of Gillespie [10] in the class of Monte-Carlo simulation methods allows us to simulate exactly the transmission of diseases through the seasonally forced and spatially structured SEIR meta-population model. Our finding shows the ability of the disease persistence in the meta-population is formulated as an exponential survival model on data simulated by the stochastic model. Increasing the meta-population size leads to the clearly decrease of the extinction rates local as well as global. The curve of the coupling rate against the extinction rate which looks like a convex functions, gains the minimum value in the medium interval, and its curvature is directly proportional to the meta-population size.