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The dynamics of an HBV epidemic model on complex heterogeneous networks
| 1. | School of Mathematics & Physics, China University of Geoscience, Wuhan 430074, Hubei Province, China, China, China |
References:
| [1] |
H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev, 42 (2000), 599-653.
doi: 10.1137/S0036144500371907. |
| [2] |
M. H. Qiao, H. Qi and Y. C. Chen, Qualitative analysis of hepatitis B virus infection model with impulsive vaccination and time delay, Acta Mathematica Scientia, 31 (2011), 1020-1034.
doi: 10.1016/S0252-9602(11)60294-4. |
| [3] |
M. H. Qiao, A. P. Liu and U. Fory's, Qualitative analysis of the SICR epidemic model with impulsive vaccinations, Math. Meth. Appl. Sci., 36 (2013), 695-706.
doi: 10.1002/mma.2620. |
| [4] |
M. H. Qiao, A. P. Liu and U. Fory's, The dynamics of a time delayed epidemic model on a population with birth pulse, Applied Mathematics and Computation, 252 (2015), 166-174.
doi: 10.1016/j.amc.2014.12.022. |
| [5] |
S. Bansal, B. T. Grenfell and L. A. Meyers, When individual behaviour matters: Homogeneous and network models in epidemiology, J R Soc Interface, 4 (2007), 879-891.
doi: 10.1098/rsif.2007.1100. |
| [6] |
X. Fu, M. Small, D. M. Walker and H. Zhang, Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization, Phys Rev E, 77 (2008), 036113, 8pp.
doi: 10.1103/PhysRevE.77.036113. |
| [7] |
J. Joo and J. L. Lebowitz, Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation, Phys Rev E, 69 (2004), 066105.
doi: 10.1103/PhysRevE.69.066105. |
| [8] |
Z. Liu and B. Hu, Epidemic spreading in community networks, Europhys Lett, 72 (2005), 315-321.
doi: 10.1209/epl/i2004-10550-5. |
| [9] |
R. Olinky and L. Stone, Unexpected epidemic thresholds in heterogeneous networks: The role of disease transmission, Phys Rev E, 70 (2004), 030902(R).
doi: 10.1103/PhysRevE.70.030902. |
| [10] |
R. Pastor-Satorras and A. Vespignani, Epidemic dynamics in scale-free networks, Phys Rev Lett, 86 (2001), p3200. |
| [11] |
A. L. Barabási and R. Albert, Emergence of scaling in random networks, Science, 286 (1999), 509-512.
doi: 10.1126/science.286.5439.509. |
| [12] |
Y. Moreno, R. Pastor-Satorras and A. Vespignani, Epidemic outbreaks in complex heterogeneous networks, Eur Phys J. B., 26 (2002), 521-529.
doi: 10.1140/epjb/e20020122. |
| [13] |
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. |
| [14] |
J. Liu and T. Zhang, Epidemic spreading of an SEIRS model in scale-free networks, Commun Nonlinear Sci Numer Simul, 16 (2011), 3375-3384.
doi: 10.1016/j.cnsns.2010.11.019. |
show all references
References:
| [1] |
H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev, 42 (2000), 599-653.
doi: 10.1137/S0036144500371907. |
| [2] |
M. H. Qiao, H. Qi and Y. C. Chen, Qualitative analysis of hepatitis B virus infection model with impulsive vaccination and time delay, Acta Mathematica Scientia, 31 (2011), 1020-1034.
doi: 10.1016/S0252-9602(11)60294-4. |
| [3] |
M. H. Qiao, A. P. Liu and U. Fory's, Qualitative analysis of the SICR epidemic model with impulsive vaccinations, Math. Meth. Appl. Sci., 36 (2013), 695-706.
doi: 10.1002/mma.2620. |
| [4] |
M. H. Qiao, A. P. Liu and U. Fory's, The dynamics of a time delayed epidemic model on a population with birth pulse, Applied Mathematics and Computation, 252 (2015), 166-174.
doi: 10.1016/j.amc.2014.12.022. |
| [5] |
S. Bansal, B. T. Grenfell and L. A. Meyers, When individual behaviour matters: Homogeneous and network models in epidemiology, J R Soc Interface, 4 (2007), 879-891.
doi: 10.1098/rsif.2007.1100. |
| [6] |
X. Fu, M. Small, D. M. Walker and H. Zhang, Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization, Phys Rev E, 77 (2008), 036113, 8pp.
doi: 10.1103/PhysRevE.77.036113. |
| [7] |
J. Joo and J. L. Lebowitz, Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation, Phys Rev E, 69 (2004), 066105.
doi: 10.1103/PhysRevE.69.066105. |
| [8] |
Z. Liu and B. Hu, Epidemic spreading in community networks, Europhys Lett, 72 (2005), 315-321.
doi: 10.1209/epl/i2004-10550-5. |
| [9] |
R. Olinky and L. Stone, Unexpected epidemic thresholds in heterogeneous networks: The role of disease transmission, Phys Rev E, 70 (2004), 030902(R).
doi: 10.1103/PhysRevE.70.030902. |
| [10] |
R. Pastor-Satorras and A. Vespignani, Epidemic dynamics in scale-free networks, Phys Rev Lett, 86 (2001), p3200. |
| [11] |
A. L. Barabási and R. Albert, Emergence of scaling in random networks, Science, 286 (1999), 509-512.
doi: 10.1126/science.286.5439.509. |
| [12] |
Y. Moreno, R. Pastor-Satorras and A. Vespignani, Epidemic outbreaks in complex heterogeneous networks, Eur Phys J. B., 26 (2002), 521-529.
doi: 10.1140/epjb/e20020122. |
| [13] |
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. |
| [14] |
J. Liu and T. Zhang, Epidemic spreading of an SEIRS model in scale-free networks, Commun Nonlinear Sci Numer Simul, 16 (2011), 3375-3384.
doi: 10.1016/j.cnsns.2010.11.019. |
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