Oscillatory Behavior of a Network Epidemic SIS Model with Nonlinear Infectivity


In this paper, an epidemic SIS model with nonlinear infectivity on heterogeneous networks and time delays is investigated. The oscillatory behavior of the solutions is studied. Two sufficient conditions are provided to guarantee the oscillatory behavior for the solutions. Some computer simulations are demonstrated.

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C. Feng and C. Pettis, "Oscillatory Behavior of a Network Epidemic SIS Model with Nonlinear Infectivity," Applied Mathematics, Vol. 5 No. 1, 2014, pp. 203-211. doi: 10.4236/am.2014.51021.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] J. S. Zhou, “An SIS Disease Transmission Model with Recruitment-Birth-Death Demographics,” Mathematical and Computer Modelling, Vol. 21, No. 11, 1995, pp. l-11.
[2] Y. N. Xiao and L. S. Chen, “Analysis of a SIS Epidemic Model with Stage Structure and a delay,” Communications in Nonlinear Science and Numerical Simulation, Vol. 6, No. 1, 2001, pp. 35-39. http://dx.doi.org/10.1016/S1007-5704(01)90026-7
[3] M. Safan and F. A. Rihan, “Mathematical Analysis of an SIS Model with Imperfect Vaccination and Backward Bifurcation,” Mathematics and Computers in Simulation, 2011, in Press.
[4] Y. N. Xiao and S. Y. Tang, “Dynamics of Infection with Nonlinear Incidence in a Simple Vaccination Model,” Nonlinear Analysis: RWA, Vol. 11, No. 5, 2010, pp. 4154-4163.
[5] Y. F. Li and J. G. Cui, “The Effect of Constant and Pulse Vaccination on SIS Epidemic Models Incorporating Media Coverage,” Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 5, 2009, pp. 2353-2365.
[6] C. F. Wu and P. X. Weng, “Stability Analysis of a Stage Structured SIS Model with General Incidence Rate,” Nonlinear Analysis: RWA, Vol. 11, No. 3, 2010, pp. 1826-1834.
[7] H. W. Hethcote, W. D. Wang, L. T. Han and Z. E. Ma, “A Predator-Prey Model with Infected Prey,” Theoretical Population Biology, Vol. 66, No. 3, 2004, pp. 259-268.
[8] S. Sinha, O. P. Misra and J. Dhar, “Modelling a Predator-Prey System with Infected Prey in Polluted Environment,” Applied Mathematical Modelling, Vol. 34, No. 7, 2010, pp. 1861-1872.
[9] R. P. Satorras and A. Vespignani, “Epidemic Spreading in Scale-Free Networks,” Physical Review Letters, Vol. 86, No. 3, 2001, p. 3200. http://dx.doi.org/10.1103/PhysRevLett.86.3200
[10] R. P. Satorras and A. Vespignani, “Epidemic Dynamics and Endemic Statesin Complex Networks,” Physical Review E, Vol. 63, No. 6, 2001, Article ID: 066117.
[11] Y. Moreno, R. Pastor-Satorras and A. Vespignani, “Epidemic Outbreaks Incomplex Heterogeneous Networks,” European Journal of Physics, Vol. 26, No. 4, 2002, pp. 521-529.
[12] M. Boguna, R. Pastor-Satorras and A. Vespignani, “Absence of Epidemicthreshold in Scale-Free Networks with Degree Correlations,” Physical Review Letters, Vol. 90, No. 2, 2003, Article ID: 028701. http://dx.doi.org/10.1103/physrevlett.90.028701
[13] H. J. Shi, Z. S. Duan and G. R. Chen, “An SIS Model with Infective medium on Complex Networks,” Physica A, Vol. 387, No. 8-9, 2008, pp. 2133-2144. Http://Dx.Doi.Org/10.1016/J.Physa.2007.11.048
[14] H. F. Zhang and X. C. Fu, “Spreading of Epidemicson Scale-Free Networks with Nonlinear Infectivity,” Nonlinear Analysis: TMA, Vol. 70, No. 9, 2009, pp. 3273-3278.
[15] G. H. Zhu, X. C. Fu and G. R. Chen, “Global Attractivity of a Network-Based Epidemic SIS Model with Nonlinear Infectivity,” Communications in Nonlinear Science and Numerical Simulation, Vol. 17, No. 6, 2012, pp. 2588-2594.
[16] A. d’Onofrio, “A Note on the Global Behavior of the Network-Based SIS Epidemic Model,” Nonlinear Analysis: RWA, Vol. 9, No. 4, 2008, pp. 1567-1572.
[17] R. C. Horn and C. R. Johnson, “Matrix Analysis,” Cambridge University Press, Cambridge, 1985.

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