American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Polynomial preserving recovery of an over-penalized symmetric interior penalty Galerkin method for elliptic problems
  • DCDS-B Home
  • This Issue
  • Next Article
    A posteriori eigenvalue error estimation for a Schrödinger operator with inverse square potential
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

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:
[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

show all references

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

[1]

Ting Guo, Haihong Liu, Chenglin Xu, Fang Yan. Global stability of a diffusive and delayed HBV infection model with HBV DNA-containing capsids and general incidence rate. Discrete & Continuous Dynamical Systems - B, 2018, 23 (10) : 4223-4242. doi: 10.3934/dcdsb.2018134
[2]

Leonid Shaikhet. Stability of a positive equilibrium state for a stochastically perturbed mathematical model of glassy-winged sharpshooter population. Mathematical Biosciences & Engineering, 2014, 11 (5) : 1167-1174. doi: 10.3934/mbe.2014.11.1167
[3]

Liping Zhang. A nonlinear complementarity model for supply chain network equilibrium. Journal of Industrial & Management Optimization, 2007, 3 (4) : 727-737. doi: 10.3934/jimo.2007.3.727
[4]

Svetlana Bunimovich-Mendrazitsky, Yakov Goltser. Use of quasi-normal form to examine stability of tumor-free equilibrium in a mathematical model of bcg treatment of bladder cancer. Mathematical Biosciences & Engineering, 2011, 8 (2) : 529-547. doi: 10.3934/mbe.2011.8.529
[5]

Saif Ullah, Muhammad Altaf Khan, Muhammad Farooq, Taza Gul, Fawad Hussain. A fractional order HBV model with hospitalization. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 957-974. doi: 10.3934/dcdss.2020056
[6]

Shouying Huang, Jifa Jiang. Global stability of a network-based SIS epidemic model with a general nonlinear incidence rate. Mathematical Biosciences & Engineering, 2016, 13 (4) : 723-739. doi: 10.3934/mbe.2016016
[7]

V. Lanza, D. Ambrosi, L. Preziosi. Exogenous control of vascular network formation in vitro: a mathematical model. Networks & Heterogeneous Media, 2006, 1 (4) : 621-637. doi: 10.3934/nhm.2006.1.621
[8]

Thomas Hillen, Peter Hinow, Zhi-An Wang. Mathematical analysis of a kinetic model for cell movement in network tissues. Discrete & Continuous Dynamical Systems - B, 2010, 14 (3) : 1055-1080. doi: 10.3934/dcdsb.2010.14.1055
[9]

Shu Liao, Jin Wang. Stability analysis and application of a mathematical cholera model. Mathematical Biosciences & Engineering, 2011, 8 (3) : 733-752. doi: 10.3934/mbe.2011.8.733
[10]

Abdul M. Kamareddine, Roger L. Hughes. Towards a mathematical model for stability in pedestrian flows. Networks & Heterogeneous Media, 2011, 6 (3) : 465-483. doi: 10.3934/nhm.2011.6.465
[11]

Yunan Wu, T. C. Edwin Cheng. Classical duality and existence results for a multi-criteria supply-demand network equilibrium model. Journal of Industrial & Management Optimization, 2009, 5 (3) : 615-628. doi: 10.3934/jimo.2009.5.615
[12]

T.C. Edwin Cheng, Yunan Wu. Henig efficiency of a multi-criterion supply-demand network equilibrium model. Journal of Industrial & Management Optimization, 2006, 2 (3) : 269-286. doi: 10.3934/jimo.2006.2.269
[13]

Wenbin Wang, Peng Zhang, Junfei Ding, Jian Li, Hao Sun, Lingyun He. Closed-loop supply chain network equilibrium model with retailer-collection under legislation. Journal of Industrial & Management Optimization, 2019, 15 (1) : 199-219. doi: 10.3934/jimo.2018039
[14]

Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. Conference Publications, 2009, 2009 (Special) : 367-376. doi: 10.3934/proc.2009.2009.367
[15]

A. Chauviere, T. Hillen, L. Preziosi. Modeling cell movement in anisotropic and heterogeneous network tissues. Networks & Heterogeneous Media, 2007, 2 (2) : 333-357. doi: 10.3934/nhm.2007.2.333
[16]

Junyoung Jang, Kihoon Jang, Hee-Dae Kwon, Jeehyun Lee. Feedback control of an HBV model based on ensemble kalman filter and differential evolution. Mathematical Biosciences & Engineering, 2018, 15 (3) : 667-691. doi: 10.3934/mbe.2018030
[17]

Xichao Duan, Sanling Yuan, Kaifa Wang. Dynamics of a diffusive age-structured HBV model with saturating incidence. Mathematical Biosciences & Engineering, 2016, 13 (5) : 935-968. doi: 10.3934/mbe.2016024
[18]

Boguslaw Twarog, Robert Pekala, Jacek Bartman, Zbigniew Gomolka. The changes of air gap in inductive engines as vibration indicator aided by mathematical model and artificial neural network. Conference Publications, 2007, 2007 (Special) : 1005-1012. doi: 10.3934/proc.2007.2007.1005
[19]

Youshan Tao, J. Ignacio Tello. Nonlinear stability of a heterogeneous state in a PDE-ODE model for acid-mediated tumor invasion. Mathematical Biosciences & Engineering, 2016, 13 (1) : 193-207. doi: 10.3934/mbe.2016.13.193
[20]

Kousuke Kuto. Stability and Hopf bifurcation of coexistence steady-states to an SKT model in spatially heterogeneous environment. Discrete & Continuous Dynamical Systems - A, 2009, 24 (2) : 489-509. doi: 10.3934/dcds.2009.24.489

2018 Impact Factor: 1.008

Tools

Metrics

  • PDF downloads (13)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences