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Stability analysis of a two-strain epidemic model on complex networks with latency
1. | Department of Applied Mathematics, Yuncheng University, Yuncheng 044000, Shanxi |
2. | Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5 |
3. | Department of Computer Science, Hongkong Baptist University, Kowloon Tong, Hongkong, China |
References:
[1] |
A. L. Barabási and R. Albert, Emergence of scaling in random networks, Science, 286 (1999), 509-512.
doi: 10.1126/science.286.5439.509. |
[2] |
T. Cohen and M. Murray, Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness, Nat Med., 10 (2004), 1117-1121.
doi: 10.1038/nm1110. |
[3] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[4] |
Z. Feng, C. Castillo-Chavez and A. Capurro, A model for Tuberculosis with exogenous reinfection, Theoretical Population Biology, 57 (2000), 235-247.
doi: 10.1006/tpbi.2000.1451. |
[5] |
Z. Feng, M. Iannelli and F. A. Milner, A two-strain tuberculosis model with age of infection, SIAM J. Appl. Math., 62 (2002), 1634-1656.
doi: 10.1137/S003613990038205X. |
[6] |
X. C. Fu, S. Michael and G. R. Chen, Propagation Dynamics on Complex Networks, Models, Methods and Stability Analysis, Higher Education Press. Beijing, 2014.
doi: 10.1002/9781118762783. |
[7] |
J. K. Hale and P. Waltman, Persistence in infinite dimensional systems, SIAM J. Math. Anal., 20 (1989), 388-395.
doi: 10.1137/0520025. |
[8] |
C. H. Li, C. C. Tsai and S. Y. Yang, Analysis of epidemic spreading of an SIRS model in complex heterogeneous networks, Commun. Nonlinear Sci. Numer. Simul., 19 (2014), 1042-1054.
doi: 10.1016/j.cnsns.2013.08.033. |
[9] |
M. E. J. Newman, Threshold effects for two pathogens spreading on a network, Phys. Rev. Lett., 95 (2005), 108701.
doi: 10.1103/PhysRevLett.95.108701. |
[10] |
R. Pastor-Satorras and A. Vespignani, Epidemic spreading in scale-free networks, Phys. Rev. Lett., 86 (2001), 3200-3203.
doi: 10.1103/PhysRevLett.86.3200. |
[11] |
R. Pastor-Satorras and A. Vespignani, Epidemic dynamics and endemic states in complex networks, Phys. Rev. E., 63 (2001), 066117.
doi: 10.1103/PhysRevE.63.066117. |
[12] |
R. Pastor-Satorras and A. Vespignani, Immunization of complex networks, Phys. Rev. E., 65 (2002), 036104.
doi: 10.1103/PhysRevE.65.036104. |
[13] |
L. Perko, Differential Equations and Dynamical Systems, Springer-Verlag, New York, 1991.
doi: 10.1007/978-1-4684-0392-3. |
[14] |
R. J. Smith, J. T. Okano, J. S. Kahn, E. N. Bodine and S. Blower, Evolutionary dynamics of complex networks of HIV drug-resistant strains: The case of San Francisco, Science, 327 (2010), 697-701.
doi: 10.1126/science.1180556. |
[15] |
H. R. Thieme, Persistence under relaxed point-dissipativity with application to an endemic model, SIAM J Math Anal., 24 (1993), 407-435.
doi: 10.1137/0524026. |
[16] |
Y. Wang, J. Cao, Z. Jin, H. Zhang and G. Sun, Impact of media coverage on epidemic spreading in complex networks, Phys. A., 392 (2013), 5824-5835.
doi: 10.1016/j.physa.2013.07.067. |
[17] |
L. Wang and G. Z. Dai, Global stability of virus spreading in complex heterogeneous networks, SIAM J. Appl. Math., 68 (2008), 1495-1502.
doi: 10.1137/070694582. |
[18] |
L. Wang and G. Z. Dai, Scale-free Phenomanas of Complex Network, Science Press. Beijing, 2009. |
[19] |
Y. Wang and Z. Jin, Global analysis of multiple routes of disease transmission on heterogeneous networks, Physica A, 392 (2013), 3869-3880.
doi: 10.1016/j.physa.2013.03.042. |
[20] |
Y. Wang, Z. Jin, Z. Yang, Z. Zhang, T. Zhou and G. Sun, Global analysis of an SIS model with an infective vector on complex networks, Nonlinear Anal. Real World Appl., 13 (2012), 543-557.
doi: 10.1016/j.nonrwa.2011.07.033. |
[21] |
Y. B. Wang, G. X. Xiao and J. Liu, Dynamics of competing ideas in complex social systems, New J. Phys., 14 (2012), 013015.
doi: 10.1088/1367-2630/14/1/013015. |
[22] |
Q. C. Wu, X. C. Fu and M. Yang, Epidemic thresholds in a heterogenous population with competing strains, Chin. Phys. B., 20 (2011), 046401.
doi: 10.1088/1674-1056/20/4/046401. |
[23] |
Q. Wu, M. Small and H. Liu, Superinfection behaviors on scale-free networks with competing strains, J. Nonlinear Sci., 23 (2013), 113-127.
doi: 10.1007/s00332-012-9146-1. |
[24] |
H. Zhang and X. Fu, Spreading of epidemics on scale-free networks with nonlinear infectivity, Nonlinear Anal., 70 (2009), 3273-3278.
doi: 10.1016/j.na.2008.04.031. |
[25] |
J. Zhang, Z. Jin and Y. Chen, Analysis of sexually transmitted disease spreading in heterosexual and homosexual populations, Math. Biosci., 242 (2013), 143-152.
doi: 10.1016/j.mbs.2013.01.005. |
show all references
References:
[1] |
A. L. Barabási and R. Albert, Emergence of scaling in random networks, Science, 286 (1999), 509-512.
doi: 10.1126/science.286.5439.509. |
[2] |
T. Cohen and M. Murray, Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness, Nat Med., 10 (2004), 1117-1121.
doi: 10.1038/nm1110. |
[3] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[4] |
Z. Feng, C. Castillo-Chavez and A. Capurro, A model for Tuberculosis with exogenous reinfection, Theoretical Population Biology, 57 (2000), 235-247.
doi: 10.1006/tpbi.2000.1451. |
[5] |
Z. Feng, M. Iannelli and F. A. Milner, A two-strain tuberculosis model with age of infection, SIAM J. Appl. Math., 62 (2002), 1634-1656.
doi: 10.1137/S003613990038205X. |
[6] |
X. C. Fu, S. Michael and G. R. Chen, Propagation Dynamics on Complex Networks, Models, Methods and Stability Analysis, Higher Education Press. Beijing, 2014.
doi: 10.1002/9781118762783. |
[7] |
J. K. Hale and P. Waltman, Persistence in infinite dimensional systems, SIAM J. Math. Anal., 20 (1989), 388-395.
doi: 10.1137/0520025. |
[8] |
C. H. Li, C. C. Tsai and S. Y. Yang, Analysis of epidemic spreading of an SIRS model in complex heterogeneous networks, Commun. Nonlinear Sci. Numer. Simul., 19 (2014), 1042-1054.
doi: 10.1016/j.cnsns.2013.08.033. |
[9] |
M. E. J. Newman, Threshold effects for two pathogens spreading on a network, Phys. Rev. Lett., 95 (2005), 108701.
doi: 10.1103/PhysRevLett.95.108701. |
[10] |
R. Pastor-Satorras and A. Vespignani, Epidemic spreading in scale-free networks, Phys. Rev. Lett., 86 (2001), 3200-3203.
doi: 10.1103/PhysRevLett.86.3200. |
[11] |
R. Pastor-Satorras and A. Vespignani, Epidemic dynamics and endemic states in complex networks, Phys. Rev. E., 63 (2001), 066117.
doi: 10.1103/PhysRevE.63.066117. |
[12] |
R. Pastor-Satorras and A. Vespignani, Immunization of complex networks, Phys. Rev. E., 65 (2002), 036104.
doi: 10.1103/PhysRevE.65.036104. |
[13] |
L. Perko, Differential Equations and Dynamical Systems, Springer-Verlag, New York, 1991.
doi: 10.1007/978-1-4684-0392-3. |
[14] |
R. J. Smith, J. T. Okano, J. S. Kahn, E. N. Bodine and S. Blower, Evolutionary dynamics of complex networks of HIV drug-resistant strains: The case of San Francisco, Science, 327 (2010), 697-701.
doi: 10.1126/science.1180556. |
[15] |
H. R. Thieme, Persistence under relaxed point-dissipativity with application to an endemic model, SIAM J Math Anal., 24 (1993), 407-435.
doi: 10.1137/0524026. |
[16] |
Y. Wang, J. Cao, Z. Jin, H. Zhang and G. Sun, Impact of media coverage on epidemic spreading in complex networks, Phys. A., 392 (2013), 5824-5835.
doi: 10.1016/j.physa.2013.07.067. |
[17] |
L. Wang and G. Z. Dai, Global stability of virus spreading in complex heterogeneous networks, SIAM J. Appl. Math., 68 (2008), 1495-1502.
doi: 10.1137/070694582. |
[18] |
L. Wang and G. Z. Dai, Scale-free Phenomanas of Complex Network, Science Press. Beijing, 2009. |
[19] |
Y. Wang and Z. Jin, Global analysis of multiple routes of disease transmission on heterogeneous networks, Physica A, 392 (2013), 3869-3880.
doi: 10.1016/j.physa.2013.03.042. |
[20] |
Y. Wang, Z. Jin, Z. Yang, Z. Zhang, T. Zhou and G. Sun, Global analysis of an SIS model with an infective vector on complex networks, Nonlinear Anal. Real World Appl., 13 (2012), 543-557.
doi: 10.1016/j.nonrwa.2011.07.033. |
[21] |
Y. B. Wang, G. X. Xiao and J. Liu, Dynamics of competing ideas in complex social systems, New J. Phys., 14 (2012), 013015.
doi: 10.1088/1367-2630/14/1/013015. |
[22] |
Q. C. Wu, X. C. Fu and M. Yang, Epidemic thresholds in a heterogenous population with competing strains, Chin. Phys. B., 20 (2011), 046401.
doi: 10.1088/1674-1056/20/4/046401. |
[23] |
Q. Wu, M. Small and H. Liu, Superinfection behaviors on scale-free networks with competing strains, J. Nonlinear Sci., 23 (2013), 113-127.
doi: 10.1007/s00332-012-9146-1. |
[24] |
H. Zhang and X. Fu, Spreading of epidemics on scale-free networks with nonlinear infectivity, Nonlinear Anal., 70 (2009), 3273-3278.
doi: 10.1016/j.na.2008.04.031. |
[25] |
J. Zhang, Z. Jin and Y. Chen, Analysis of sexually transmitted disease spreading in heterosexual and homosexual populations, Math. Biosci., 242 (2013), 143-152.
doi: 10.1016/j.mbs.2013.01.005. |
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