Epidemic thresholds in a heterogenous population with competing strains

doi:10.1088/1674-1056/20/4/046401

中国物理B ›› 2011, Vol. 20 ›› Issue (4): 46401-046401.doi: 10.1088/1674-1056/20/4/046401

Epidemic thresholds in a heterogenous population with competing strains

傅新楚¹, 杨孟¹, 吴庆初²

(1)Department of Mathematics, Shanghai University, Shanghai 200444, China; (2)Department of Mathematics, Shanghai University, Shanghai 200444, China;College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China

收稿日期:2010-06-23 修回日期:2010-08-04 出版日期:2011-04-15 发布日期:2011-04-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11072136) and the Shanghai Leading Academic Discipline Project, China (Grant No. S30104).

Epidemic thresholds in a heterogenous population with competing strains

Wu Qing-Chu(吴庆初)^a)b)†, Fu Xin-Chu(傅新楚)^a), and Yang Meng(杨孟)^a)

^a Department of Mathematics, Shanghai University, Shanghai 200444, China; ^b College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China

Received:2010-06-23 Revised:2010-08-04 Online:2011-04-15 Published:2011-04-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11072136) and the Shanghai Leading Academic Discipline Project, China (Grant No. S30104).

摘要/Abstract

摘要： Among many epidemic models, one epidemic disease may transmit with the existence of other pathogens or other strains from the same pathogen. In this paper, we consider the case where all of the strains obey the susceptible-infected-susceptible mechanism and compete with each other at the expense of common susceptible individuals. By using the heterogenous mean-field approach, we discuss the epidemic threshold for one of two strains. We confirm the existence of epidemic threshold in both finite and infinite populations subject to underlying epidemic transmission. Simulations in the Barabasi-Albert (BA) scale-free networks are in good agreement with the analytical results.

关键词: complex network, epidemic threshold, epidemic dynamics

Abstract: Among many epidemic models, one epidemic disease may transmit with the existence of other pathogens or other strains from the same pathogen. In this paper, we consider the case where all of the strains obey the susceptible-infected-susceptible mechanism and compete with each other at the expense of common susceptible individuals. By using the heterogenous mean-field approach, we discuss the epidemic threshold for one of two strains. We confirm the existence of epidemic threshold in both finite and infinite populations subject to underlying epidemic transmission. Simulations in the Barabasi-Albert (BA) scale-free networks are in good agreement with the analytical results.

Key words: complex network, epidemic threshold, epidemic dynamics

中图分类号: (Networks)

64.60.aq

64.60.De (Statistical mechanics of model systems (Ising model, Potts model, field-theory models, Monte Carlo techniques, etc.)) 87.10.Ed (Ordinary differential equations (ODE), partial differential equations (PDE), integrodifferential models)

吴庆初, 傅新楚, 杨孟. Epidemic thresholds in a heterogenous population with competing strains[J]. 中国物理B, 2011, 20(4): 46401-046401.

Wu Qing-Chu(吴庆初), Fu Xin-Chu(傅新楚), and Yang Meng(杨孟) . Epidemic thresholds in a heterogenous population with competing strains[J]. Chin. Phys. B, 2011, 20(4): 46401-046401.

参考文献 29

[1]	Bleed D, Dye C and Raviglione M C 2000 Curr. Opin. Plum. Med. 6 174
[2]	Small M and Tse C K 2005 Int. J. Bifur. Chaos 15 1745
[3]	Small M, Walker D M and Tse C K 2007 Phys. Rev. Lett. 99 188702
[4]	Smith G J D, Vijaykrishna D, Bahl J, Lycett S J, Worobey M, Pybus O G, Ma S K, Cheung C L, Raghwani J, Bhatt S, Peiris J S M, Guan Y and Rambaut A 2009 Nature 459 1122
[5]	Maher B and Butler D 2009 Nature 462 154
[6]	Watts D J and Strogatz S H 1998 Nature 393 440
[7]	Barabasi A L and Albert R 1999 Science 286 509
[8]	Pastor-Satorras R and Vespignani A 2001 Phys. Rev. Lett. 86 3200
[9]	Pastor-Satorras R and Vespignani A 2002 Phys. Rev. E 65 035108
[10]	Santos F C, Rodrigues J F and Pacheco J M 2005 Phys. Rev. E 72 056128
[11]	May R M and Lloyd A L 2001 Phys. Rev. E 64 066112
[12]	Masuda N and Konno N 2006 J. Theor. Biol. 243 64
[13]	Newman M E J 2005 Phys. Rev. Lett. 95 108701
[14]	Thomasey D H and Martcheva M 2008 J. Bio. Sys. 16 255
[15]	NuNo M, Feng Z, Martcheva M and Castillo-Chavez C 2005 SIAM J. Appl. Math. 65 964
[16]	Balter M 1998 Science 281 1425
[17]	Castillo-Chavez C, Huang W and Li J 1996 SIAM J. Appl. Math. 56 494
[18]	Schinazi R B 2001 Markov Processes Relat. Fields 7 595
[19]	Martcheva M and Horst T R 2005 Math. Biosci. 195 23
[20]	Brauer F 2005 Math. Biosci. 198 119
[21]	Zhang H F, Small M, Fu X C and Wang B H 2009 Chin. Phys. B 18 3633
[22]	Fu X C, Small M, Walker D M and Zhang H F 2008 Phys. Rev. E 77 036113
[23]	Barthelémy M, Barrat A, Pastor-Satorras R and Vespignani A 2004 Phys. Rev. Lett. 92 178701
[24]	Pei W D, Liu Z X, Chen Z Q and Yuan Z Z 2008 Acta Phys. Sin. 57 6777 (in Chinese)
[25]	Cai L M, Li X Z and Yu J Y 2007 Math. Appl. 20 328
[26]	Kamo M and Sasaki A 2002 Physica D 165 228
[27]	Liu M X and Ruan J 2009 Chin. Phys. B 18 2115
[28]	Wang L and Dai G Z 2008 SIAM J. Appl. Math. 68 1495
[29]	dónofrio A 2008 Nonlinear Analysis: RWA 9 1567 endfootnotesize

Epidemic thresholds in a heterogenous population with competing strains

Epidemic thresholds in a heterogenous population with competing strains

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