Mathematical Biosciences and Engineering, 2014, 11(6): 1295-1317. doi: 10.3934/mbe.2014.11.1295.

Primary: 58F15, 58F17; Secondary: 53C35.

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Epidemic models for complex networks with demographics

1. Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030051
2. LAMPS and CDM, Department of Mathematics and Statistics, York University, Toronto, ON, M3J1P3

In this paper, we propose and study network epidemic models withdemographics for disease transmission. We obtain the formula of thebasic reproduction number $R_{0}$ of infection for an SIS model withbirths or recruitment and death rate. We prove that if $R_{0}\leq1$,infection-free equilibrium of SIS model is globally asymptoticallystable; if $R_{0}>1$, there exists a unique endemic equilibrium whichis globally asymptotically stable. It is also found thatdemographics has great effect on basic reproduction number $R_{0}$.Furthermore, the degree distribution of population varies with timebefore it reaches the stationary state.
  Figure/Table
  Supplementary
  Article Metrics

Keywords complex networks; demographics; Epidemic models; basic reproduction number; global stability.

Citation: Zhen Jin, Guiquan Sun, Huaiping Zhu. Epidemic models for complex networks with demographics. Mathematical Biosciences and Engineering, 2014, 11(6): 1295-1317. doi: 10.3934/mbe.2014.11.1295

References

  • 1. Oxford University Press, Oxford, 1992.
  • 2. Science, 286 (1999), 509-511.
  • 3. Journal of Theoretical Biology, 235 (2005), 275-288.
  • 4. J. Phys. A: Math. Theor., 40 (2007), 8607-8619.
  • 5. e-print cond-mat/0301149, (2003).
  • 6. J. Math. Biol., 28 (1990), 257-270.
  • 7. in Mathematical Population Dynamics: Analysis of Heterogeneity (eds. O. Arino, D. Axelrod, M. Kimmel and M. Langlais), Theory of Epidemics, 1, Wuerz, Winnipeg, 1993, 33-50.
  • 8. Applied Mathematics and Computation, 197 (2008), 345-357.
  • 9. J. Math. Biol., 30 (1992), 717-731.
  • 10. Proc. Natl. Acad. Sci. U.S.A., 101 (2004), 15124.
  • 11. J. Math. Anal. Appl., 308 (2005), 343-364.
  • 12. Phys. Rev. E, 69 (2004), 066105.
  • 13. J. R. Soc. Interface, 2 (2005), 295-307.
  • 14. Princeton University Press, 2007.
  • 15. Proc. R. Soc. A, 115 (1927), 700-711.
  • 16. Mathematical Biosciences, 203 (2006), 124-136.
  • 17. Bulletin of Mathematical Biology, 71 (2009), 888-905.
  • 18. Physica D, 238 (2009), 370-378.
  • 19. World Scientific, 2009.
  • 20. Phys. Rev. E, 64 (2001), 066112.
  • 21. Eur. Phys. J. B, 26 (2002), 521-529.
  • 22. Phys. Rev. E, 70 (2004), 030902.
  • 23. Phys. Rev. E, 63 (2001), 066117.
  • 24. Phys. Rev. Let., 86 (2001), 3200.
  • 25. IMA Journal of Mathematics Applied in Medicine & Biology, 13 (1996), 245-257.
  • 26. Phys. Rev. E, 77 (2008), 066101.
  • 27. SIAM J. Appl. Math., 46 (1986), 368-375.
  • 28. Rocky Mountain J. Math., 24 (1994), 351-380.
  • 29. Mathematical Biosciences, 180 (2002), 29-48.
  • 30. Siam J. Appl. Math., 68 (2008), 1495-1502.
  • 31. Mathematical Biosciences, 190 (2004), 97-112.
  • 32. Springer-Verlag, New York, 2003.
  • 33. Canad. Appl. Math. Quart., 4 (1996), 421-444.

 

This article has been cited by

  • 1. Sanling Yuan, P. van den Driessche, Frederick H. Willeboordse, Zhisheng Shuai, Junling Ma, Disease invasion risk in a growing population, Journal of Mathematical Biology, 2016, 73, 3, 665, 10.1007/s00285-015-0962-4
  • 2. Jing Li, Zhen Jin, Yuan Yuan, Gui-Quan Sun, A non-Markovian SIR network model with fixed infectious period and preventive rewiring, Computers & Mathematics with Applications, 2018, 75, 11, 3884, 10.1016/j.camwa.2018.02.035
  • 3. Wei Pan, Gui-Quan Sun, Zhen Jin, How demography-driven evolving networks impact epidemic transmission between communities, Journal of Theoretical Biology, 2015, 382, 309, 10.1016/j.jtbi.2015.07.009
  • 4. Shujuan Zhang, Zhen Jin, Juan Zhang, The dynamical modeling and simulation analysis of the recommendation on the user–movie network, Physica A: Statistical Mechanics and its Applications, 2016, 463, 310, 10.1016/j.physa.2016.07.049
  • 5. Irina Bashkirtseva, Preventing Noise-Induced Extinction in Discrete Population Models, Discrete Dynamics in Nature and Society, 2017, 2017, 1, 10.1155/2017/9610609
  • 6. Wenjun Jing, Zhen Jin, Juping Zhang, An SIR pairwise epidemic model with infection age and demography, Journal of Biological Dynamics, 2018, 12, 1, 486, 10.1080/17513758.2018.1475018
  • 7. Lu-Xing Yang, Moez Draief, Xiaofan Yang, Gui-Quan Sun, The Impact of the Network Topology on the Viral Prevalence: A Node-Based Approach, PLOS ONE, 2015, 10, 7, e0134507, 10.1371/journal.pone.0134507
  • 8. Hendrik Baumann, Werner Sandmann, Gui-Quan Sun, Structured Modeling and Analysis of Stochastic Epidemics with Immigration and Demographic Effects, PLOS ONE, 2016, 11, 3, e0152144, 10.1371/journal.pone.0152144
  • 9. Junyuan Yang, Yuming Chen, Effect of infection age on an SIR epidemic model with demography on complex networks, Physica A: Statistical Mechanics and its Applications, 2017, 479, 527, 10.1016/j.physa.2017.03.006
  • 10. XIAOFENG LUO, LILI CHANG, ZHEN JIN, DEMOGRAPHICS INDUCE EXTINCTION OF DISEASE IN AN SIS MODEL BASED ON CONDITIONAL MARKOV CHAIN, Journal of Biological Systems, 2017, 25, 01, 145, 10.1142/S0218339017500085
  • 11. WENJUN JING, ZHEN JIN, XIAO-LONG PENG, ADAPTIVE SIS EPIDEMIC MODELS ON HETEROGENEOUS NETWORKS WITH DEMOGRAPHICS AND RISK PERCEPTION, Journal of Biological Systems, 2018, 26, 02, 247, 10.1142/S0218339018500122
  • 12. Yi Wang, Jinde Cao, Ahmed Alsaedi, Tasawar Hayat, The spreading dynamics of sexually transmitted diseases with birth and death on heterogeneous networks, Journal of Statistical Mechanics: Theory and Experiment, 2017, 2017, 2, 023502, 10.1088/1742-5468/aa58a6
  • 13. Wei Gou, Zhen Jin, How heterogeneous susceptibility and recovery rates affect the spread of epidemics on networks, Infectious Disease Modelling, 2017, 2, 3, 353, 10.1016/j.idm.2017.07.001
  • 14. Yang Qin, Xiaoxiong Zhong, Hao Jiang, Yibin Ye, An environment aware epidemic spreading model and immune strategy in complex networks, Applied Mathematics and Computation, 2015, 261, 206, 10.1016/j.amc.2015.03.110
  • 15. Hai-Feng Huo, Fang-Fang Cui, Hong Xiang, Dynamics of an SAITS alcoholism model on unweighted and weighted networks, Physica A: Statistical Mechanics and its Applications, 2018, 496, 249, 10.1016/j.physa.2018.01.003
  • 16. YANRU YAO, JUPING ZHANG, A TWO-STRAIN EPIDEMIC MODEL ON COMPLEX NETWORKS WITH DEMOGRAPHICS, Journal of Biological Systems, 2016, 24, 04, 577, 10.1142/S0218339016500297
  • 17. Shouying Huang, Jifa Jiang, Global stability of a network-based sis epidemic model with a general nonlinear incidence rate, Mathematical Biosciences and Engineering, 2016, 13, 4, 723, 10.3934/mbe.2016016
  • 18. Hai-Feng Huo, Hui-Ning Xue, Hong Xiang, Dynamics of an alcoholism model on complex networks with community structure and voluntary drinking, Physica A: Statistical Mechanics and its Applications, 2018, 505, 880, 10.1016/j.physa.2018.04.024
  • 19. Raul Nistal, Manuel de la Sen, Santiago Alonso-Quesada, Asier Ibeas, Aitor J. Garrido, On the Stability and Equilibrium Points of MultistagedSI(n)REpidemic Models, Discrete Dynamics in Nature and Society, 2015, 2015, 1, 10.1155/2015/379576
  • 20. LI LI, MONTHLY PERIODIC OUTBREAK OF HEMORRHAGIC FEVER WITH RENAL SYNDROME IN CHINA, Journal of Biological Systems, 2016, 24, 04, 519, 10.1142/S0218339016500261
  • 21. Junyuan Yang, Fei Xu, Global stability of two SIS epidemic mean-field models on complex networks: Lyapunov functional approach, Journal of the Franklin Institute, 2018, 10.1016/j.jfranklin.2018.06.040
  • 22. Wenjun Jing, Zhen Jin, Juping Zhang, Low-Dimensional SIR Epidemic Models with Demographics on Heterogeneous Networks, Journal of Systems Science and Complexity, 2018, 31, 5, 1103, 10.1007/s11424-018-7029-8
  • 23. Junyuan Yang, Fei Xu, The computational approach for the basic reproduction number of epidemic models on complex networks, IEEE Access, 2019, 1, 10.1109/ACCESS.2019.2898639
  • 24. Zhen Jin, Shuping Li, Xiaoguang Zhang, Juping Zhang, Xiao-Long Peng, , Complex Systems and Networks, 2016, Chapter 3, 51, 10.1007/978-3-662-47824-0_3
  • 25. Hai-Feng Huo, Peng Yang, Hong Xiang, Dynamics for an SIRS epidemic model with infection age and relapse on a scale-free network, Journal of the Franklin Institute, 2019, 10.1016/j.jfranklin.2019.03.034
  • 26. Hong Xiang, Fang-Fang Cui, Hai-Feng Huo, Analysis of the SAITS alcoholism model on scale-free networks with demographic and nonlinear infectivity, Journal of Biological Dynamics, 2019, 13, 1, 621, 10.1080/17513758.2019.1683629

Reader Comments

your name: *   your email: *  

Copyright Info: 2014, Zhen Jin, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved