Controlling disease spread on networks with feedback mechanism

Many real-world networks have the ability to adapt themselves in response to the state of their nodes. This paper studies controlling disease spread on network with feedback mechanism, where the susceptible nodes are able to avoid contact with the infected ones by cutting their connections with probability when the density of infected nodes reaches a certain value in the network. Such feedback mechanism considers the networks' own adaptivity and the cost of immunization. The dynamical equations about immunization with feedback mechanism are solved and theoretical predictions are in agreement with the results of large scale simulations. It shows that when the lethality α increases, the prevalence decreases more greatly with the same immunization g. That is, with the same cost, a better controlling result can be obtained. This approach offers an effective and practical policy to control disease spread, and also may be relevant to other similar networks.

[1]  Huijie Yang,et al.  Temporal series analysis approach to spectra of complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[3]  A. Barabasi,et al.  Halting viruses in scale-free networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Márton Karsai,et al.  Nonequilibrium phase transitions and finite-size scaling in weighted scale-free networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  A Flahault,et al.  A mathematical model for evaluating the impact of vaccination schedules: application to Neisseria meningitidis , 2003, Epidemiology and Infection.

[6]  Thilo Gross,et al.  Epidemic dynamics on an adaptive network. , 2005, Physical review letters.

[7]  Reuven Cohen,et al.  Efficient immunization strategies for computer networks and populations. , 2002, Physical review letters.

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

[9]  Dai Shuo,et al.  Mirror nodes in growing random networks , 2004 .

[10]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[11]  B. Dybiec,et al.  Controlling disease spread on networks with incomplete knowledge. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  M. Newman,et al.  Epidemics and percolation in small-world networks. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  Alessandro Vespignani,et al.  Immunization of complex networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.