How to distribute antidote to control epidemics

We give a rigorous analysis of variations of the contact process on a finite graph in which the cure rate is allowed to vary from one vertex to the next, and even to depend on the current state of the system. In particular, we study the epidemic threshold in the models where the cure rate is proportional to the degree of the node or when it is proportional to the number of its infected neighbors. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010

[1]  Derek de Solla Price,et al.  A general theory of bibliometric and other cumulative advantage processes , 1976, J. Am. Soc. Inf. Sci..

[2]  A. Stacey.  The existence of an intermediate phase for the contact process on trees , 1996 .

[3]  T. Liggett,et al.  Stochastic Interacting Systems: Contact, Voter and Exclusion Processes , 1999 .

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

[5]  L. Amaral,et al.  The web of human sexual contacts , 2001, Nature.

[6]  A. Stacey.  The contact process on finite homogeneous trees , 2001 .

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

[8]  Fan Chung Graham,et al.  A Random Graph Model for Power Law Graphs , 2001, Exp. Math..

[9]  Béla Bollobás,et al.  The degree sequence of a scale‐free random graph process , 2001, Random Struct. Algorithms.

[10]  Vern Paxson,et al.  How to Own the Internet in Your Spare Time , 2002, USENIX Security Symposium.

[11]  David Moore,et al.  Code-Red: a case study on the spread and victims of an internet worm , 2002, IMW '02.

[12]  Lev S. Tsimring,et al.  Modeling of contact tracing in social networks , 2003 .

[13]  Amin Saberi,et al.  On certain connectivity properties of the Internet topology , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[14]  Matthew C. Elder,et al.  Recent worms: a survey and trends , 2003, WORM '03.

[15]  Christos Gkantsidis,et al.  Conductance and congestion in power law graphs , 2003, SIGMETRICS '03.

[16]  M. Newman,et al.  Network theory and SARS: predicting outbreak diversity , 2004, Journal of Theoretical Biology.

[17]  R. Christley,et al.  Network analysis of cattle movement in Great Britain. , 2005 .

[18]  Amin Saberi,et al.  On the spread of viruses on the internet , 2005, SODA '05.

[19]  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..

[20]  I. Kiss,et al.  Infectious disease control using contact tracing in random and scale-free networks , 2006, Journal of The Royal Society Interface.

[21]  M. Keeling,et al.  Networks and epidemic models , 2005, Journal of The Royal Society Interface.

[22]  V. Anantharam,et al.  Designing a contact process: the piecewise-homogeneous process on a finite set with applications , 2005 .

[23]  Kiyosi Itô,et al.  Essentials of Stochastic Processes , 2006 .

[24]  Christopher A Gilligan,et al.  Optimizing the control of disease infestations at the landscape scale , 2007, Proceedings of the National Academy of Sciences.