Effects of Variant Rates and Noise on Epidemic Spreading
LI Wei1,2**, GAO Zong-Mao1, GU Jiao1,2
1Complexity Science Center and Institute of Particle Physics, Huazhong Normal University, Wuhan 430079 2Max-Planck-Institute for Mathematics in the Sciences
Effects of Variant Rates and Noise on Epidemic Spreading
LI Wei1,2**, GAO Zong-Mao1, GU Jiao1,2
1Complexity Science Center and Institute of Particle Physics, Huazhong Normal University, Wuhan 430079 2Max-Planck-Institute for Mathematics in the Sciences
摘要We introduce variant rates, for both infection and recovery and noise into the susceptible-infected-removed (SIR) model for epidemic spreading. The changing rates are taken mainly due to the changing profiles of an epidemic during its evolution. However, the noise parameter which is taken from a given distribution, i.e. Gaussian can describe the fluctuations of the infection and recovery rates. The numerical simulations show that the SIR model with variant rates and noise and can improve the fitting with real SARS data in the near-stationary stage.
Abstract：We introduce variant rates, for both infection and recovery and noise into the susceptible-infected-removed (SIR) model for epidemic spreading. The changing rates are taken mainly due to the changing profiles of an epidemic during its evolution. However, the noise parameter which is taken from a given distribution, i.e. Gaussian can describe the fluctuations of the infection and recovery rates. The numerical simulations show that the SIR model with variant rates and noise and can improve the fitting with real SARS data in the near-stationary stage.
[1] Weiss G H and Dishon M 1971 Math. Biosici. 11 261
[2] Bailey N T 1975 The Mathematical Theory of Infectious Diseases and Its Applications (London: Griffin)
[3] Murray J D 1993 Mathematical Biology (New York: Springer)
[4] Lin G Jia X and Ouyang Q 2003 J. Peking Universtity (Health Sciences) Suppl. 35 66 (in Chinese)
[5] Zhou T, Fu Z Q and Wang B H 2006 Prog. Natural Sci. 16 5
[6] Zhou J and Liu Z H 2008 Front. Phys. Chin. 3 331
[7] Liu Z R, Yan J R and Zhang J G 2006 Chin. Phys. Lett. 23 1343
[8] Gu J, Li w and Cai X 2008 Eur. Phys. J. B 62 247
[9] Li W, Gu J and Cai X 2008 Chin. Phys. Lett. 25 2303
[10] Romualdo P S and Alessandro V 2001 Phys. Rev. Lett. 86 3200
[11] Fu X C, Small M, Walker D M and Zhang H F 2008 Phys. Rev. E 77 036113
[12] Zhou Y Z, Liu Z H and Zhou J 2007 Chin. Phys. Lett. 24 581
[13] Yamir M, Romualdo P S and Alessandro V 2002 Eur. Phys. J. B 26 521
[14] Hong L, Ouyang M, Mao Z J and Chen X G 2009 Sixth International Symposium on Neural Networks (Wuhan, China 26–29 May 2009) p 937
[15] Wang Y and Wang C 2003 Proceedings of the 2003 ACM workshop on Rapid Malcode (Washington, DC, USA 27–30 October 2003) p 61
[16] Newman M E J 2002 Phys. Rev. E 66 016128
[17] Wu X Y and Liu Z H 2007 Chin. Phys. Lett. 24 1118
[18] Bao J D 2005 Prog. Phys. 25 359 (in Chinese)
[19] Yang R, Wang B H, Ren J, Bai W J, Shi Z W, Xu W and Zhou T 2007 Phys. Lett. A 364 189
[20] Zhou T, Jian G L, Bai W J, Chen G and Wang B H 2006 Phys. Rev. E 74 056109 5
[21] Pang G P and Chen L S 2007 Chao Solitons and Fractals 34 1629
2011, Vol. 28 
