Global stability and optimal control of an SIRS epidemic model on heterogeneous networks

Physica A: Statistical Mechanics and its Applications

Volumn 410, Issue , 2014, Pages 196-204

  Chen, Lijuan ^a,b   Sun, Jitao ^a  

^a TONGJI UNIVERSITY   (China)

^b FUZHOU UNIVERSITY   (China)

Author keywords

Complex networks; Epidemic model; Global stability; Optimal control; SIRS

Indexed keywords

COMPLEX NETWORKS; HETEROGENEOUS NETWORKS; LYAPUNOV FUNCTIONS;

DISEASE-FREE EQUILIBRIUM; ENDEMIC EQUILIBRIUM; EPIDEMIC MODELING; GLOBAL STABILITY; OPTIMAL CONTROLS; SIRS; SIRS EPIDEMIC MODEL; STRUCTURED POPULATION;

DISEASE CONTROL;

EID: 84901653930     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2014.05.034     Document Type: Article

References (25)

1. C. Connell McCluskey Global stability for an SIR epidemic model with delay and nonlinear incidence Nonlinear Anal. RWA 11 4 2010 3106 3109
2. Y. Muroya, H.X. Li, and T. Kuniya Complete global analysis of an SIRS epidemic model with graded cure and incomplete recovery rates J. Math. Anal. Appl. 410 2 2014 719 732
3. L.J. Hao, G.R. Jiang, S.Y. Liu, and L. Ling Global dynamics of an SIRS epidemic model with saturation incidence Biosystems 114 1 2013 56 63
4. Z.Y. Hu, Z.D. Teng, and H.J. Jiang Stability analysis in a class of discrete SIRS epidemic models Nonlinear Anal. RWA 13 5 2012 2017 2033
5. Y. Muroya, Y. Enatsu, and Y. Nakata Monotone iterative techniques to SIRS epidemic models with nonlinear incidence rates and distributed delays Nonlinear Anal. RWA 12 4 2011 1897 1910
6. R. Xu, Z.E. Ma, and Z.P. Wang Global stability of a delayed SIRS epidemic model with saturation incidence and temporary immunity Comput. Math. Appl. 59 9 2010 3211 3221
7. X.J. Yu, C.F. Wu, and P.X. Weng Traveling waves for a SIRS model with nonlocal diffusion Int. J. Biomath. 05 2012 1250036
8. G.H. Zhu, X.C. Fu, and G.R. Chen Spreading dynamics and global stability of a generalized epidemic model on complex heterogeneous networks Appl. Math. Model. 36 2012 5808 5817
9. J.P. Zhang, and Z. Jin The analysis of an epidemic model on networks Appl. Math. Comput. 217 2011 7053 7064
10. M. Yang, and G.R. Chen A modified SIS model with an infective medium on complex networks and its global stability Physica A 390 12 2011 2408 2413
11. H.F. Zhang, M. Small, and X.C. Fu Staged progression model for epidemic spread on homogeneous and hetergeneous networks J. Syst. Sci. Complex 24 2011 619 630
12. Y. Wang, Z. Jin, Z. Yang, Z.K. Zhang, T. Zhou, and G.Q. Sun Global analysis of an SIS model with an infective vector on complex networks Nonlinear Anal. RWA 13 2012 543 557
13. G.H. Zhu, X.C. Fu, and G.R. Chen Global attractivity of a network-based epidemic SIS model with nonlinear infectivity Commun. Nonlinear Sci. Numer. Simul. 17 2012 2588 2594
14. Y. Wang, and Z. Jin Global analysis of multiple routes of disease transmission on hetergeneous networks Physica A 392 18 2013 3869 3880
15. M.E.J. Newman Spread of epidemic disease on networks Phys. Rev. E 66 2002 016128
16. S.C. Ferreira, C. Castellano, and R. Pastor-Satorras Epidemic thresholds of the susceptible-infected-susceptible model on networks: a comparison of numerical and theoretical results Phys. Rev. E 86 2012 041125
17. Q.C. Wu, and X.C. Fu Modelling of discrete-time SIS models with awareness interactions on degree-uncorrelated networks Physica A 390 3 2011 463 470
18. X.L. Peng, X.J. Xu, X.C. Fu, and T. Zhou Vaccination intervention on epidemic dynamics in networks Phys. Rev. E 87 2013 022813
19. R. Pastor-Satorras, and A. Vespignani Epidemic spreading in scale-free networks Phys. Rev. Lett. 86 2001 3200 3203 (Pubitemid 32317894)
20. C.S. Shen, H.S. Chen, and Z.H. Hou Strategy to suppress epidemic explosion in heterogeneous metapopulation networks Phys. Rev. E 86 2012 036114
21. C.H. Li, C.C. Tsai, and S.Y. Yang Analysis of epidemic spreading of an SIRS model in complex heterogeneous networks Commun. Nonlinear Sci. Numer. Simul. 19 2014 1042 1054
22. I.K. Morton, and L.S. Nancy Dynamics Optimization: The Calculus of Variations and Optimal Control in Economics and Management 2000 Elsevier Science The Netherlands 218 234
23. G. Birkhoff, and G.C. Rota Ordinary Differential Equations fourth ed. 1989 John Wiley & Sons New York
24. D.L. Lukes Differential Equations: Classical to Controlled Math. Sci. Eng. vol. 162 1982 Accademic Press
25. S. Lenhart, and J.T. Workman Optimal Control Applied to Biological Models Mathematical and Computational Biology Series 2007 Chapman & Hall/CRC London, UK