基于复杂网络,建立了多染病阶段的传染病动力学模型,通过对模型的动力学性态分析获得了基本再生数和最终规模。发现疾病在复杂网络中传播时,早期患者会加剧其传播。数值模拟验证了所得结论的正确性。
We establish a staged progression epidemic model on complex networks. With the analysis of dynamical behavior, the basic reproduction number and final size are obtained. We discover that the early stage patients can intensify the disease when it is spreading on the heterogeneous networks. The correctness of our theoretical results are validated by numerical simulations.
[1] Kermack W O, McKendrick A G. A Contribution to the mathematical theory of epidemics[J]. Proceedings of the Royal Society Series A, 1927, 115（772):700-721.
[2] Hyman J M, Li J, Stanley E A. The differential infectivity and staged progression models for the transmission of HIV[J]. Mathematical Biosciences, 1999, 155（2):77-109.
[3] Wearing H J, Rohani P, Keeling M J. Appropriate models for the management of infectious diseases[J]. PLoS Medicine, 2005, 2（7):621-627.
[4] Pastor-Satorras R, Vespignani A. Epidemic dynamics and endemic states in complex networks[J]. Physical Review E, 2001, 63（6):066117-24.
[5] 汪小帆,李翔,陈关荣.网络科学导论[M].北京:高等教育出版社, 2012.
[6] 杨慧,唐明,许伯铭.自适应网络中的流行病传播动力学研究综述[J]. 复杂系统与复杂性科学, 2012, 9（4):63-83.
Yang Hui, Tang ming, Hui Pak-ming. Epidemic dynamics on adaptive networks-a short review[J].Complex Systems and Complexity Science, 2012, 9（4):63-83.
[7] Zhang H F, Small M, Fu X C. Staged progression model for epidemic spread on homogeneous and heterogeneous networks[J]. Journal of Systems Science and Complexity, 2011, 24（4):619-630.
[8] Driessche V D P, Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission[J]. Mathematical Biosciences, 2002, 180（1/2):29-48.
[9] Jin Z, Zhang J P, Song L P, et al. Modelling and analysis of influenza A（H1N1) on networks[J]. BMC Public Health, 2011, 11（suppl 1):S9.
