The dynamics of an HBV epidemic model on complex heterogeneous networks

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July 2015, 20(5): 1393-1404. doi: 10.3934/dcdsb.2015.20.1393

The dynamics of an HBV epidemic model on complex heterogeneous networks

Meihong Qiao ^1, , Anping Liu ^1, and Qing Tang ^1,

1.	School of Mathematics & Physics, China University of Geoscience, Wuhan 430074, Hubei Province, China, China, China

Received April 2014 Revised January 2015 Published May 2015

Abstract
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In this paper, an HBV epidemic model on complex heterogeneous networks is proposed. Theoretical analysis of the HBV spreading dynamics is presented via mean-field approximation. Stabilities of the disease-free equilibrium and the endemic equilibrium are studied. The theoretical results reveal that disease propagation is impacted by the heterogeneous connectivity patterns and the underlying network structures.

Keywords: mathematical model, Heterogeneous network, equilibrium., HBV, global stability.

Mathematics Subject Classification: Primary: 32G3.

Citation: Meihong Qiao, Anping Liu, Qing Tang. The dynamics of an HBV epidemic model on complex heterogeneous networks. Discrete & Continuous Dynamical Systems - B, 2015, 20 (5) : 1393-1404. doi: 10.3934/dcdsb.2015.20.1393

References:

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[10]	R. Pastor-Satorras and A. Vespignani, Epidemic dynamics in scale-free networks,, Phys Rev Lett, 86 (2001). Google Scholar
[11]	A. L. Barabási and R. Albert, Emergence of scaling in random networks,, Science, 286 (1999), 509. doi: 10.1126/science.286.5439.509. Google Scholar
[12]	Y. Moreno, R. Pastor-Satorras and A. Vespignani, Epidemic outbreaks in complex heterogeneous networks,, Eur Phys J. B., 26 (2002), 521. doi: 10.1140/epjb/e20020122. Google Scholar
[13]	L. Wang and G. Z. Dai. Global, stability of virus spreading in complex heterogeneous networks,, SIAM J. Appl. Math., 68 (2008), 1495. doi: 10.1137/070694582. Google Scholar
[14]	J. Liu and T. Zhang, Epidemic spreading of an SEIRS model in scale-free networks,, Commun Nonlinear Sci Numer Simul, 16 (2011), 3375. doi: 10.1016/j.cnsns.2010.11.019. Google Scholar

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References:

[1]	H. W. Hethcote, The mathematics of infectious diseases,, SIAM Rev, 42 (2000), 599. doi: 10.1137/S0036144500371907. Google Scholar
[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. doi: 10.1016/S0252-9602(11)60294-4. Google Scholar
[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. doi: 10.1002/mma.2620. Google Scholar
[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. doi: 10.1016/j.amc.2014.12.022. Google Scholar
[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. doi: 10.1098/rsif.2007.1100. Google Scholar
[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). doi: 10.1103/PhysRevE.77.036113. Google Scholar
[7]	J. Joo and J. L. Lebowitz, Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation,, Phys Rev E, 69 (2004). doi: 10.1103/PhysRevE.69.066105. Google Scholar
[8]	Z. Liu and B. Hu, Epidemic spreading in community networks,, Europhys Lett, 72 (2005), 315. doi: 10.1209/epl/i2004-10550-5. Google Scholar
[9]	R. Olinky and L. Stone, Unexpected epidemic thresholds in heterogeneous networks: The role of disease transmission,, Phys Rev E, 70 (2004). doi: 10.1103/PhysRevE.70.030902. Google Scholar
[10]	R. Pastor-Satorras and A. Vespignani, Epidemic dynamics in scale-free networks,, Phys Rev Lett, 86 (2001). Google Scholar
[11]	A. L. Barabási and R. Albert, Emergence of scaling in random networks,, Science, 286 (1999), 509. doi: 10.1126/science.286.5439.509. Google Scholar
[12]	Y. Moreno, R. Pastor-Satorras and A. Vespignani, Epidemic outbreaks in complex heterogeneous networks,, Eur Phys J. B., 26 (2002), 521. doi: 10.1140/epjb/e20020122. Google Scholar
[13]	L. Wang and G. Z. Dai. Global, stability of virus spreading in complex heterogeneous networks,, SIAM J. Appl. Math., 68 (2008), 1495. doi: 10.1137/070694582. Google Scholar
[14]	J. Liu and T. Zhang, Epidemic spreading of an SEIRS model in scale-free networks,, Commun Nonlinear Sci Numer Simul, 16 (2011), 3375. doi: 10.1016/j.cnsns.2010.11.019. Google Scholar

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