International Journal of Computer
Trends and Technology

Research Article | Open Access | Download PDF

Volume 4 | Issue 3 | Year 2013 | Article Id. IJCTT-V4I3P129 | DOI : https://doi.org/10.14445/22312803/IJCTT-V4I3P129

Vaccination strategies of a modified SIS model on complex networks

Hongxing Yao, Ru Liang

Citation :

Hongxing Yao, Ru Liang, "Vaccination strategies of a modified SIS model on complex networks," International Journal of Computer Trends and Technology (IJCTT), vol. 4, no. 3, pp. 345-351, 2013. Crossref, https://doi.org/10.14445/22312803/IJCTT-V4I3P129

Abstract

A new susceptible-infected-susceptible model is researched in this paper, which has an infective vector. And it describes epidemics (e.g. malaria) transmitted through an infective vector (e.g. mosquitoes) on complex networks. We compare the modified model with the standard SIS model having an infective vector. We also study and compare the effects of the uniform immunization and targeted immunization on complex networks. Then, analytical and simulated results are given to show that the uniform immunization strategy to the modified model is very effective on scale-free networks.

Keywords

Complex network, Disease spread, Immunization, Infective vector.

References

[1] K.Laneri, A.Bhadra, E.L. Lonides, M. Bouma, R.C. Dhiman, R.S. Yaday, M. Pascual, Forcing versus feedback: epidemic malaria and monsoon rains in northwest India. PLoSComput.Biol. 6(2010) e1000898.
[2] P. Rohani, X. Zhong, A.A. King, Contact network structure explains the changing epidemiology of pertussis. Science. 330,982–985(2010).
[3] Kai Diethelm, A fractional calculus based model for the simulation of an out-break of dengue fever. Nonlinear Dyn. (2012). doi:10.1007/ s11071-012-0475-2.
[4] R. Pastor-Satorras, A. Vespignani, Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86, 3200–3203(2001).
[5] R. Pastor-Satorras, A. Vespignani, Immunization of complex networks. Phys. Rev. E65 (2002) 036104. [6] R. Pastor-Satorras, A. Vespignani, Phys. Rev. E65 (2002) 036104.
[7] M. Bogu˜n´an, R. Pastor-Satorras, Phys. Rev. E66 (2002) 047104.
[8] Qiaoling Chen, Zhidong Teng, Lei Wang, Haijun Jiang, The existence of codimension-two bifurcation in a discrete SIS epidemic model with standard incidence. J. Nonlinear Dyn. (2012). doi: 10.1007/ s11071- 012-0641-6.
[9] R. Yang, B.H. Wang, J. Ren, W.J. Bai, Z.W. Shi, W. Xu, T. Zhou, Epidemic spreading on heterogeneous networks with identical infectivity. Phys. Lett. A 364,189–193(2007).
[10] M. Barthélemy, A. Barrat, R. Pastor-Satorras, A. Vespignani, Velocity and hierarchical spread of epidemic outbreaks in scale-free networks. Phys. Rev. Lett. 92, 178701(2004).
[11] M. Barth´elemy, A. Barrat, R. Pastor-Satorras, A. Vespignani. J. Theoet. Biol. 235,275–288 (2005).
[12] T. Zhou, J.G. Liu, W.J. Bai, G.R. Chen, B.H. Wang, Behaviors of susceptible-infected epidemics on scale-free networks with identical infectivity. Phys. Rev. E 74 (2006) 056109.
[13] K.L. Cooke, Stability analysis for a vector disease model. Rocky Mount. J. Math. 9, 31–42(1979). 
[14] S. Busenberg, K.L. Cooke, Periodic solutions of a periodic nonlinear delay differential equation. SIAM. J. Appl. Math. 35,704–721(1978).
[15] P. Marcati, A.M. Pozio, Global asymptotic stability for a vector disease model with spatial spread. J. Math. Biol. 9,179–187 (1980).
[16] R. Volz, Global asymptotic stability of a periodic solution to an epidemic model. J. Math. Biol. 15,319–338 (1982).
[17] Y. Takeuchi, W. Ma, E. Beretta, Global asymptotic properties of a delay SIR epidemic model with finite incubation times. Nonlinear Anal. 42, 931–947(2000).
[18] E. Beretta, Y. Takeuchi, Convergence results in SIR epidemic model with varying population size. Nonlinear Anal. 28, 1909–1921(1997).
[19] E. Beretta, T. Hara, W. Ma, Y. Takeuchi, Global asymptotic stability of an SIR epidemic model with distributed time delay. Nonlinear Anal. 47, 4107–4115(2001).
[20] J.X. Velasco Hernandez, A model for Chagas disease involving transmission by vectors and blood transfusion. Theoret. Popul. Biol. 46, 1–31(1994).
[21] Z. Jin, Z.E. Ma, The stability of an SIR epidemic model with time delays. Math. Biosci. Eng. 3,101–109 (2006).
[22] N. Masuda, N. Konno, Multi-state epidemic processes on complex networks, J. Theoer. Biol. 243, 64–75 (2006).
[23] H.J. Shi, Z.S. Duan, G.R. Chen, An SIS model with infective medium on complex networks. Physica A. 387,2133–2144(2008). [24] M. Yang, G.R. Chen, X.C. Fu, A modified SIS model with an infective medium on complex networks and its global stability. Physica A. 390, 2408–241(2011).