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.
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
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
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
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
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
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.
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
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
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
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.
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.
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.
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.
