Epidemic spreading of an SEIRS model in scale-free networks |
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| Affiliation: | 1. Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan;2. Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh;3. Faculty of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan;1. School of Science, Chongqing University of Technology, Chongqing 400054, China;2. Department of Mathematics, Sichuan Normal University, Chengdu 610066, China;1. School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, PR China;2. Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006, PR China;1. Business School, University of Shanghai for Science and Technology, 334 Jungong Road, Shanghai, 200093, China;2. School of Physics Science and Engineering, Tongji University, 1239 Siping Road, Shanghai, 200092, Western Australia, China;3. Complex Systems Group, Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley, 6009, Australia;4. Mineral Resources, CSIRO, 26 Dick Perry Ave, Kensington, 6151, Western Australia, Australia;5. School of Economics and Management, Beihang University, 37 Xueyuan Road, Beijing, 100191, China |
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| Abstract: | An SEIRS epidemic model on the scale-free networks is presented, where the active contact number of each vertex is assumed to be either constant or proportional to its degree for this model. Using the analytical method, we obtain the two threshold values for above two cases and find that the threshold value for constant contact is independent of the topology of the underlying networks. The existence of positive equilibrium is determined by threshold value. For a finite size of scale-free network, we prove the local stability of disease-free equilibrium and the permanence of the disease on the network. Furthermore, we investigate two major immunization strategies, random immunization and targeted immunization, some similar results are obtained. The simulation shows the positive equilibrium is stable. |
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