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The Analysis of a SEIRS Epidemic Model with Time Delay on Complex Networks

DOI: 10.4236/oalib.1103901, PP. 1-10

Subject Areas: Network Modeling and Simulation

Keywords: Epidemic Model, Complex Networks, Time Delay, Permanence, Stability

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Abstract

In this paper, a new epidemic SEIRS model with time delay on complex networks is proposed. Based on the mean field theory, the basic reproductive number and equilibriums of the model are derived. Moreover, the impact of the network topology and time delay on the basic reproductive number is analyzed. Theoretical analyses indicate that the basic reproductive number is dependent on the topology of the underlying networks. The time delay cannot change the basic reproductive number, but it can reduce the endemic level and weaken the epidemic spreading. The global asymptotically stability of the disease-free equilibrium and the permanence of epidemic are proved in detail. Numerical simulations confirm the analytical results.

Cite this paper

Dong, J. , Li, T. , Wan, C. and Liu, X. (2017). The Analysis of a SEIRS Epidemic Model with Time Delay on Complex Networks. Open Access Library Journal, 4, e3901. doi: http://dx.doi.org/10.4236/oalib.1103901.

References

[1]  Anderson, R.M. and May, R.M. (1991) Infectious Diseases of Humans: Dynamics and Control. Oxford University Press Inc., New York.
[2]  Wei, J. and Zou, X. (2006) Bifurcation Analysis of a Population Model and the Resulting SIS Epidemic Model with Delay. Journal of Computational and Applied Mathematics, 197, 169-187.
https://doi.org/10.1016/j.cam.2005.10.037
[3]  Huang, G., Takeuchi, Y., Ma, W., et al. (2010) Global Stability for Delay SIR and SEIR Epidemic Models with Nonlinear Incidence Rate. Bulletin of Mathematical Biology, 72, 1192-1207.
https://doi.org/10.1007/s11538-009-9487-6
[4]  Xiao, Y., Chen, L. and ven den Bosch, F. (2002) Dynamical Behavior for a Stage-Structured SIR Infectious Disease Model. Nonlinear Analysis: Real World Applications, 3, 175-190.
https://doi.org/10.1016/S1468-1218(01)00021-9
[5]  Gao, S., Chen, L. and Teng, Z. (2007) Impulsive Vaccination of an SEIRS Model with Time Delay and Varying Total Population Size. Bulletin of Mathematical Biology, 69, 731-745.
https://doi.org/10.1007/s11538-006-9149-x
[6]  Li, T., Liu, X.D., Wu, J., et al. (2016) An Epidemic Spreading Model on Adaptive Scale-Free Networks with Feedback Mechanism. Physica A: Statistical Mechanics and Its Applications, 450, 649-656.
https://doi.org/10.1016/j.physa.2016.01.045
[7]  Li, J. and Ma, Z. (2006) Analysis of Two SEIS Epidemic Models with Fixed Period of Latency. Journal of Systems Science and Mathematical Sciences, 26, 228-236.
[8]  Enatsu, Y., Nakata, Y. and Muroya, Y. (2012) Global Stability of SIRS Epidemic Models with a Class of Nonlinear Incidence Rates and Distributed Delays. Acta Mathematica Scientia, 32, 851-865. https://doi.org/10.1016/S0252-9602(12)60066-6
[9]  Nakata, Y. (2011) On the Global Stability of a Delayed Epidemic Model with Transport-Related Infection. Nonlinear Analysis: Real World Applications, 12, 3028-3034.
https://doi.org/10.1016/j.nonrwa.2011.05.004
[10]  Zhang, T. and Teng, Z. (2008) Global Behavior and Permanence of SIRS Epidemic mOdel with Time Delay. Nonlinear Analysis: Real World Applications, 9, 1409-1424.
https://doi.org/10.1016/j.nonrwa.2007.03.010
[11]  Liu, Q., Jiang, D., Shi, N., et al. (2016) Asymptotic Behavior of a Stochastic Delayed SEIR Epidemic Model with Nonlinear Incidence. Physica A: Statistical Mechanics and Its Applications, 462, 870-882.
[12]  Sharma, N. and Gupta, A.K. (2017) Impact of Time Delay on the Dynamics of SEIR Epidemic Model using Cellular Automata. Physica A: Statistical Mechanics and Its Applications, 471, 114-125.
[13]  Liu, Q.M., Deng, C.S. and Sun, M.C. (2014) The Analysis of an Epidemic Model with Time Delay on Scale-Free Networks. Physica A: Statistical Mechanics and Its Applications, 410, 79-87.
[14]  Wang, J., Wang, J., Liu, M., et al. (2014) Global Stability Analysis of an SIR Epidemic Model with Demographics and Time Delay on Networks. Physica A: Statistical Mechanics and Its Applications, 410, 268-275.
[15]  Lajmanovich, A. and Yorke, J.A. (1976) A Deterministic Model for Gonorrhea in a Nonhomogeneous Population. Mathematical Biosciences, 28, 221-236.

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