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In this paper, considering the random motion of nodes, we propose an epidemic spreading model on network of mobile environment based on the mean-filed theory. Using the theory of differential dynamical system, the behaviors of epidemic spreading are further analyzed. It is shown that if R0 1, the epidemic always dies out and the disease-free equilibrium is globally asymptotically stable; and if R0 1, the epidemic is uniformly persistent and the endemic equilibrium is globally asymptotically stable. Numerical simulations are given to validate the results of theoretical analysis.
[1] Zhou T, Liu J G, Bai W J, Chen G R, Wang B H 2006 Phys.Rev.E 74 056109
[2] Song Y R, Jiang G P 2010 Acta Phys.Sin. 59 7546 (in Chinese) [宋玉蓉, 蒋国平 2010 59 7546]
[3] Wu Q C, Fu X C, Yang M 2011 Chin.Phys. B 20 046401
[4] Pastor-Statorras R, Vespignani A 2001 Phys.Rev. E 63 066117
[5] Castellano C, Pastor-Satorras R 2010 Phys.Rev.Lett.105 218701
[6] Wang Y, Zheng Z G 2009 Acta Phys.Sin. 58 4421 (in Chinese) [王延, 郑志刚 2009 58 4421]
[7] Shi H J, Duan Z S, Chen G R 2008 Physica A 387 2133
[8] Wang Y Q, Jiang G P 2010 Acta Phys.Sin. 59 6734 (in Chinese) [王亚奇, 蒋国平 2010 59 6734]
[9] Ball F G, Knock E S, O'Neill P D 2008 Math.Biosci.216 100
[10] Wang J Z, Liu Z R, Xu J H 2007 Physica A 382 715
[11] Zhang H F, Fu X C 2009 Nonlinear Anal.: Theor. Meth. Appl. 70 3273
[12] Pastor-Satorras R, Vespignani A 2001 Phys.Rev.E 65 036134
[13] Madar N, Kalisky T, Cohen R, Been-Avraham, Havlin S 2004 Eur.Phys.J.B 38 269
[14] Peng C B, Jin X G, Shi M X 2010 Physica A 389 549
[15] Wang L, Zhu C P 2010 Phys. Proc. 3 1819
[16] Wang P, Gonzalez M C, Hidalgo C A, Barabasi A L 2009 Science 324 1071
[17] Buscarino A, Fortuna L, Frasca M, Latora V 2008 Euro. Phys. Lett. 82 38002
[18] Frasca M, Buscarino A, Rizzo A, Fortuna L, Boccaletti S 2006 Phys.Rev.E 74 036110
[19] Gonzalez M C, Herrmann H J 2004 Physica A 340 741
[20] Rhodes C J, Nekovee M 2008 Physica A 387 6837
[21] Yang H X, Wang W X, Xie Y B, Lai Y C, Wang B H 2011 Phys.Rev.E 83 016102
[22] Van den Driessche P, Watmough J 2002 Math.Biosci. 180 29
[23] Li M Y, Smith H L, Wang L 2001 SIAM J. Appl. Math. 62 58
[24] Li M Y, Muldowney J S 1996 SIAM J.Math.Anal. 27 1070
[25] Martin Jr R H 1974 J.Math.Anal.Appl. 45 432
[26] Muldowney J S 1990 Rocky Mountain J. Math. 20 857
[27] Xiang H J 2005 Appl.Math.J.Chin. Univ.Ser.A 20 284 (in Chinese) [向红军 2005 高校应用数学学报A辑 20 284]
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[1] Zhou T, Liu J G, Bai W J, Chen G R, Wang B H 2006 Phys.Rev.E 74 056109
[2] Song Y R, Jiang G P 2010 Acta Phys.Sin. 59 7546 (in Chinese) [宋玉蓉, 蒋国平 2010 59 7546]
[3] Wu Q C, Fu X C, Yang M 2011 Chin.Phys. B 20 046401
[4] Pastor-Statorras R, Vespignani A 2001 Phys.Rev. E 63 066117
[5] Castellano C, Pastor-Satorras R 2010 Phys.Rev.Lett.105 218701
[6] Wang Y, Zheng Z G 2009 Acta Phys.Sin. 58 4421 (in Chinese) [王延, 郑志刚 2009 58 4421]
[7] Shi H J, Duan Z S, Chen G R 2008 Physica A 387 2133
[8] Wang Y Q, Jiang G P 2010 Acta Phys.Sin. 59 6734 (in Chinese) [王亚奇, 蒋国平 2010 59 6734]
[9] Ball F G, Knock E S, O'Neill P D 2008 Math.Biosci.216 100
[10] Wang J Z, Liu Z R, Xu J H 2007 Physica A 382 715
[11] Zhang H F, Fu X C 2009 Nonlinear Anal.: Theor. Meth. Appl. 70 3273
[12] Pastor-Satorras R, Vespignani A 2001 Phys.Rev.E 65 036134
[13] Madar N, Kalisky T, Cohen R, Been-Avraham, Havlin S 2004 Eur.Phys.J.B 38 269
[14] Peng C B, Jin X G, Shi M X 2010 Physica A 389 549
[15] Wang L, Zhu C P 2010 Phys. Proc. 3 1819
[16] Wang P, Gonzalez M C, Hidalgo C A, Barabasi A L 2009 Science 324 1071
[17] Buscarino A, Fortuna L, Frasca M, Latora V 2008 Euro. Phys. Lett. 82 38002
[18] Frasca M, Buscarino A, Rizzo A, Fortuna L, Boccaletti S 2006 Phys.Rev.E 74 036110
[19] Gonzalez M C, Herrmann H J 2004 Physica A 340 741
[20] Rhodes C J, Nekovee M 2008 Physica A 387 6837
[21] Yang H X, Wang W X, Xie Y B, Lai Y C, Wang B H 2011 Phys.Rev.E 83 016102
[22] Van den Driessche P, Watmough J 2002 Math.Biosci. 180 29
[23] Li M Y, Smith H L, Wang L 2001 SIAM J. Appl. Math. 62 58
[24] Li M Y, Muldowney J S 1996 SIAM J.Math.Anal. 27 1070
[25] Martin Jr R H 1974 J.Math.Anal.Appl. 45 432
[26] Muldowney J S 1990 Rocky Mountain J. Math. 20 857
[27] Xiang H J 2005 Appl.Math.J.Chin. Univ.Ser.A 20 284 (in Chinese) [向红军 2005 高校应用数学学报A辑 20 284]
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