Epidemic spread in adaptive networks with multitype agents

In this paper we study the epidemic spread in adaptive networks with multitype agents. We assume that the infection probability as well as the rewiring probability between agents is type-dependent. Under this assumption we analyze a system of M-type networks with mean-field approximation. These general expressions apply to networks with various choices of infection mechanisms and rewiring rules. We explicitly evaluate the infection level for two-type networks with intratype/intertype infecting and rewiring and investigate their impacts on the epidemic threshold. By plotting the bifurcation diagram for various parameters, we find a bistability region where both the disease-free state and the endemic state co-exist for appropriate rewiring dynamics. The area of each phase depends on the corresponding interaction modes. We show that consistency between infecting and rewiring modes speeds up the disease spread, while inconsistency contributes to halting the outbreak.

[1]  C. Watkins,et al.  The spread of awareness and its impact on epidemic outbreaks , 2009, Proceedings of the National Academy of Sciences.

[2]  R. May,et al.  Infection dynamics on scale-free networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Thilo Gross,et al.  Adaptive Networks: Theory, Models and Applications , 2009 .

[4]  C. Macken,et al.  Mitigation strategies for pandemic influenza in the United States. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[5]  Antoine Allard,et al.  Heterogeneous bond percolation on multitype networks with an application to epidemic dynamics. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  S. Bornholdt,et al.  Topological evolution of dynamical networks: global criticality from local dynamics. , 2000, Physical review letters.

[7]  D. Zanette,et al.  Infection Spreading in a Population with Evolving Contacts , 2007, Journal of biological physics.

[8]  Thilo Gross,et al.  Adaptive coevolutionary networks: a review , 2007, Journal of The Royal Society Interface.

[9]  Alexei Vazquez,et al.  Spreading dynamics on heterogeneous populations: multitype network approach. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[11]  M E J Newman,et al.  Finding and evaluating community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  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.

[13]  Alessandro Vespignani,et al.  Dynamical Patterns of Epidemic Outbreaks in Complex Heterogeneous Networks , 1999 .

[14]  Viktor Nagy.  Mean-field theory of a recurrent epidemiological model. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Shlomo Havlin,et al.  Improving immunization strategies. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[17]  Ira B Schwartz,et al.  Fluctuating epidemics on adaptive networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  F. C. Santos,et al.  Evolutionary games in self-organizing populations , 2008 .

[19]  Paul R. Cohen,et al.  Maximizing Influence Propagation in Networks with Community Structure , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Gourab Ghoshal,et al.  Dynamics of networking agents competing for high centrality and low degree. , 2005, Physical review letters.

[21]  M E J Newman,et al.  Modularity and community structure in networks. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[22]  Alex Arenas,et al.  Traffic-driven epidemic spreading in finite-size scale-free networks , 2009, Proceedings of the National Academy of Sciences.

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

[24]  Sebastian Funk,et al.  Interacting epidemics on overlay networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Adriano Lazzarin,et al.  The Efficiency of Male‐to Female and Female‐to‐Male Sexual Transmission of the Human Immunodeficiency Virus: A Study of 730 Stable Couples , 1994, Epidemiology.

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

[27]  Shlomo Havlin,et al.  Finding a better immunization strategy. , 2008, Physical review letters.

[28]  Alessandro Vespignani,et al.  The role of the airline transportation network in the prediction and predictability of global epidemics , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[29]  M. Newman,et al.  Nonequilibrium phase transition in the coevolution of networks and opinions. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Naoki Masuda,et al.  Immunization of networks with community structure , 2009, 0909.1945.

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

[32]  Thilo Gross,et al.  Robust oscillations in SIS epidemics on adaptive networks: Coarse graining by automated moment closure , 2008 .

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

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