Analytical model of spread of epidemics in open finite regions

Epidemic dynamics, a kind of biological mechanisms describing microorganism propagation within populations, can inspire a wide range of novel designs of engineering technologies, such as advanced wireless communication and networking, global immunization on complex systems, and so on. There have been many studies on epidemic spread, but most of them focus on closed regions where the population size is fixed. In this paper, we proposed a susceptible-exposed-infected-recovered model with a variable contact rate to depict the dynamic spread processes of epidemics among heterogeneous individuals in open finite regions. We took the varied number of individuals and the dynamic migration rate into account in the model. We validated the effectiveness of our proposed model by simulating epidemics spread in different scenarios. We found that the average infected possibility of individuals, the population size of infectious individuals in the regions, and the infection ability of epidemics have great impact on the outbreak sizes of epidemics. The results demonstrate that the proposed model can well describe epidemics spread in open finite regions.