Article Contents
Article Contents

# The dynamics of an HBV epidemic model on complex heterogeneous networks

• 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.
Mathematics Subject Classification: Primary: 32G34.

 Citation:

•  [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.