Interacting viruses in networks: can both survive?

Suppose we have two competing ideas/products/viruses, that propagate over a social or other network. Suppose that they are strong/virulent enough, so that each, if left alone, could lead to an epidemic. What will happen when both operate on the network? Earlier models assume that there is perfect competition: if a user buys product 'A' (or gets infected with virus 'X'), she will never buy product 'B' (or virus 'Y'). This is not always true: for example, a user could install and use both Firefox and Google Chrome as browsers. Similarly, one type of flu may give partial immunity against some other similar disease. In the case of full competition, it is known that 'winner takes all,' that is the weaker virus/product will become extinct. In the case of no competition, both viruses survive, ignoring each other. What happens in-between these two extremes? We show that there is a phase transition: if the competition is harsher than a critical level, then 'winner takes all;' otherwise, the weaker virus survives. These are the contributions of this paper (a) the problem definition, which is novel even in epidemiology literature (b) the phase-transition result and (c) experiments on real data, illustrating the suitability of our results.

[1]  Shishir Bharathi,et al.  Competitive Influence Maximization in Social Networks , 2007, WINE.

[2]  Mark S. Granovetter.  Threshold Models of Collective Behavior , 1978, American Journal of Sociology.

[3]  Matthew Richardson,et al.  Mining the network value of customers , 2001, KDD '01.

[4]  Devavrat Shah,et al.  Rumors in a Network: Who's the Culprit? , 2009, IEEE Transactions on Information Theory.

[5]  Marc Lipsitch,et al.  What is the mechanism for persistent coexistence of drug-susceptible and drug-resistant strains of Streptococcus pneumoniae? , 2009, Journal of The Royal Society Interface.

[6]  Ramanathan V. Guha,et al.  Information diffusion through blogspace , 2004, WWW '04.

[7]  Martin A Nowak,et al.  THE EVOLUTION OF VIRULENCE IN PATHOGENS WITH VERTICAL AND HORIZONTAL TRANSMISSION , 1996, Evolution; international journal of organic evolution.

[8]  Jaideep Srivastava,et al.  A Generalized Linear Threshold Model for Multiple Cascades , 2010, 2010 IEEE International Conference on Data Mining.

[9]  Christos Faloutsos,et al.  Patterns of Cascading Behavior in Large Blog Graphs , 2007, SDM.

[10]  Carlos Castillo-Chavez,et al.  Competitive Exclusion and Coexistence of Multiple Strains in an SIS STD Model , 1999, SIAM J. Appl. Math..

[11]  Matthew Richardson,et al.  Mining knowledge-sharing sites for viral marketing , 2002, KDD.

[12]  Roger Wattenhofer,et al.  Word of Mouth: Rumor Dissemination in Social Networks , 2008, SIROCCO.

[13]  Christos Faloutsos,et al.  Winner takes all: competing viruses or ideas on fair-play networks , 2012, WWW.

[14]  S. Bikhchandani,et al.  You have printed the following article : A Theory of Fads , Fashion , Custom , and Cultural Change as Informational Cascades , 2007 .

[15]  R M May,et al.  Coevolution of hosts and parasites , 1982, Parasitology.

[16]  Michalis Faloutsos,et al.  Virus Propagation on Time-Varying Networks: Theory and Immunization Algorithms , 2010, ECML/PKDD.

[17]  Carlos Castillo-Chavez,et al.  Competitive Exclusion in Gonorrhea Models and Other Sexually Transmitted Diseases , 1996, SIAM J. Appl. Math..

[18]  Linda J. S. Allen,et al.  Competitive exclusion in SIS and SIR epidemic models with total cross immunity and density-dependent host mortality , 2005 .

[19]  Kendrick,et al.  Applications of Mathematics to Medical Problems , 1925, Proceedings of the Edinburgh Mathematical Society.

[20]  Jacob Goldenberg,et al.  Talk of the Network: A Complex Systems Look at the Underlying Process of Word-of-Mouth , 2001 .

[21]  Christos Faloutsos,et al.  Epidemic thresholds in real networks , 2008, TSEC.

[22]  Herbert W. Hethcote,et al.  The Mathematics of Infectious Diseases , 2000, SIAM Rev..

[23]  Marc Lipsitch,et al.  No coexistence for free: neutral null models for multistrain pathogens. , 2009, Epidemics.

[24]  A. M'Kendrick.  Applications of Mathematics to Medical Problems , 1925, Proceedings of the Edinburgh Mathematical Society.

[25]  P. Bearman,et al.  After the promise: the STD consequences of adolescent virginity pledges. , 2005, The Journal of adolescent health : official publication of the Society for Adolescent Medicine.

[26]  Ravi Kumar,et al.  On the Bursty Evolution of Blogspace , 2003, WWW '03.

[27]  Jeffrey O. Kephart,et al.  Measuring and modeling computer virus prevalence , 1993, Proceedings 1993 IEEE Computer Society Symposium on Research in Security and Privacy.

[28]  Dimitrios Gunopulos,et al.  Finding effectors in social networks , 2010, KDD.

[29]  A. J. Hall.  Infectious diseases of humans: R. M. Anderson & R. M. May. Oxford etc.: Oxford University Press, 1991. viii + 757 pp. Price £50. ISBN 0-19-854599-1 , 1992 .

[30]  N. Ling.  The Mathematical Theory of Infectious Diseases and its applications , 1978 .

[31]  Alexander Grey,et al.  The Mathematical Theory of Infectious Diseases and Its Applications , 1977 .

[32]  Donald F. Towsley,et al.  The effect of network topology on the spread of epidemics , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[33]  J. Leskovec,et al.  Cascading Behavior in Large Blog Graphs Patterns and a model , 2006 .

[34]  Christos Faloutsos,et al.  On the Vulnerability of Large Graphs , 2010, 2010 IEEE International Conference on Data Mining.

[35]  M. Henry,et al.  A Primer of Ecology with R , 2009 .

[36]  Jure Leskovec,et al.  The dynamics of viral marketing , 2005, EC '06.

[37]  Karline Soetaert.  A Primer of Ecology with R , 2010 .

[38]  Michalis Faloutsos,et al.  Threshold conditions for arbitrary cascade models on arbitrary networks , 2011, 2011 IEEE 11th International Conference on Data Mining.

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