Global dynamics of a network-based SIQRS epidemic model with demographics and vaccination

Abstract This paper investigates a new SIQRS epidemic model with demographics and vaccination on complex heterogeneous networks. We analytically derive the basic reproduction number R 0 , which determines not only the existence of endemic equilibrium but also the global dynamics of the model. The permanence of the disease and the globally asymptotical stability of disease-free equilibrium are proved in detail. By using a monotone iterative technique, we show that the unique endemic equilibrium is globally attractive under certain conditions. Our results really improve and enrich the results in Li et al (2014) [14]. Interestingly, the basic reproduction number R 0 bears no relation to the degree-dependent birth, but our simulations indicate that the degree-dependent birth does affect the epidemic dynamics. Furthermore, we find that quarantine plays a more active role than vaccination in controlling the disease.

[1]  Lijuan Chen,et al.  Global stability and optimal control of an SIRS epidemic model on heterogeneous networks , 2014 .

[2]  Maoxing Liu,et al.  Global stability analysis of an SIR epidemic model with demographics and time delay on networks , 2014 .

[3]  Xinchu Fu,et al.  Spreading of epidemics on scale-free networks with nonlinear infectivity , 2009 .

[4]  Fengqin Zhang,et al.  Stability analysis and optimal control of a hand-foot-mouth disease (HFMD) model , 2012, Journal of Applied Mathematics and Computing.

[5]  J. Liu,et al.  The spread of disease with birth and death on networks , 2004, q-bio/0402042.

[6]  Fengde Chen.  On a nonlinear nonautonomous predator-prey model with diffusion and distributed delay , 2005 .

[7]  Suh-Yuh Yang,et al.  Analysis of epidemic spreading of an SIRS model in complex heterogeneous networks , 2014, Commun. Nonlinear Sci. Numer. Simul..

[8]  Tao Zhou,et al.  Vaccination intervention on epidemic dynamics in networks , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Horst R. Thieme,et al.  Persistence under relaxed point-dissipativity (with application to an endemic model) , 1993 .

[10]  M. Small,et al.  Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Lewi Stone,et al.  Unexpected epidemic thresholds in heterogeneous networks: the role of disease transmission. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Guanrong Chen,et al.  Global attractivity of a network-based epidemic SIS model with nonlinear infectivity , 2012 .

[13]  Lin Wang,et al.  Global Stability of Virus Spreading in Complex Heterogeneous Networks , 2008, SIAM J. Appl. Math..

[14]  Zhi-Hong Guan,et al.  Spreading dynamics of a SIQRS epidemic model on scale-free networks , 2014, Commun. Nonlinear Sci. Numer. Simul..

[15]  Guanrong Chen,et al.  Spreading dynamics and global stability of a generalized epidemic model on complex heterogeneous networks , 2012 .

[16]  Alessandro Vespignani,et al.  Epidemic spreading in complex networks with degree correlations , 2003, cond-mat/0301149.

[17]  Y. Moreno,et al.  Epidemic outbreaks in complex heterogeneous networks , 2001, cond-mat/0107267.

[18]  Yamir Moreno,et al.  Dynamics of rumor spreading in complex networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Alessandro Vespignani,et al.  Epidemic dynamics and endemic states in complex networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  R. Rothenberg,et al.  Network structural dynamics and infectious disease propagation , 1999, International journal of STD & AIDS.

[21]  Chenquan Gan,et al.  Propagation of computer virus both across the Internet and external computers: A complex-network approach , 2014, Commun. Nonlinear Sci. Numer. Simul..

[22]  Alessandro Vespignani,et al.  Epidemic dynamics in finite size scale-free networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Zhen Jin,et al.  The analysis of an epidemic model on networks , 2011, Appl. Math. Comput..

[24]  Tao Zhou,et al.  Epidemic spreading on heterogeneous networks with identical infectivity , 2007 .

[25]  J. Ripoll,et al.  Spread of epidemic-like failures in telecommunication networks , 2014 .

[26]  Jiajia Wang,et al.  Sentiment contagion in complex networks , 2014 .

[27]  Tailei Zhang,et al.  Epidemic spreading of an SEIRS model in scale-free networks , 2011 .

[28]  Shuigeng Zhou,et al.  Epidemic spreading with nonlinear infectivity in weighted scale-free networks , 2009, 0903.0924.

[29]  Masahiro Kimura,et al.  Tractable Models for Information Diffusion in Social Networks , 2006, PKDD.