Staged progression model for epidemic spread on homogeneous and heterogeneous networks

In this paper, epidemic spread with the staged progression model on homogeneous and heterogeneous networks is studied. First, the epidemic threshold of the simple staged progression model is given. Then the staged progression model with birth and death is also considered. The case where infectivity is a nonlinear function of the nodes’ degree is discussed, too. Finally, the analytical results are verified by numerical simulations.

[1]  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.

[2]  Chi K. Tse,et al.  Clustering model for transmission of the SARS virus: application to epidemic control and risk assessment , 2005, Physica A: Statistical Mechanics and its Applications.

[3]  Haifeng Zhang,et al.  Global behavior of epidemic transmission on heterogeneous networks via two distinct routes , 2008, Nonlinear biomedical physics.

[4]  C. K. Michael Tse,et al.  Small World and Scale Free Model of Transmission of SARS , 2005, Int. J. Bifurc. Chaos.

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

[6]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[7]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

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

[9]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

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

[11]  M. Small,et al.  Super-spreaders and the rate of transmission of the SARS virus , 2006, Physica D: Nonlinear Phenomena.

[12]  Guanrong Chen,et al.  Behaviors of susceptible-infected epidemics on scale-free networks with identical infectivity. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Tao Zhou,et al.  Immunization of susceptible–infected model on scale-free networks , 2006, physics/0610138.

[14]  James B. Kadtke,et al.  Enhanced predictability of hierarchical propagation in complex networks , 2007 .

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

[16]  M. Newman.  Spread of epidemic disease on networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[18]  J. Hyman,et al.  An intuitive formulation for the reproductive number for the spread of diseases in heterogeneous populations. , 2000, Mathematical biosciences.