On stochastic models for the spread of infections

I returned, and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all.

[1]  David Gamarnik,et al.  The diameter of a long range percolation graph , 2002, SODA '02.

[2]  Harry Kesten,et al.  Geometry of the Uniform Spanning Forest: Transitions in Dimensions 4, 8, 12 , 2001 .

[3]  van Marie-Colette Lieshout,et al.  Markov Point Processes and Their Applications , 2000 .

[4]  Noam Berger,et al.  The diameter of long-range percolation clusters on finite cycles , 2001, Random Struct. Algorithms.

[5]  M. D. de Jong,et al.  Quantification of the effect of control strategies on classical swine fever epidemics. , 2003, Mathematical biosciences.

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

[7]  Christl A. Donnelly,et al.  Transmission intensity and impact of control policies on the foot and mouth epidemic in Great Britain , 2001, Nature.

[8]  R. Durrett.  Random Graph Dynamics: References , 2006 .

[9]  Jason Lowther.  Statistical Inference for Branching Processes , 1992 .

[10]  Daryl J. Daley,et al.  Epidemic Modelling: An Introduction , 1999 .

[11]  F. Ball.  A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models , 1986, Advances in Applied Probability.

[12]  Harry Kesten,et al.  Geometry of the uniform spanning forest: Transitions in dimensions 4, 8, 12 ,... , 2004 .

[13]  Christl A. Donnelly,et al.  The Foot-and-Mouth Epidemic in Great Britain: Pattern of Spread and Impact of Interventions , 2001, Science.

[14]  Chris T Bauch,et al.  The spread of infectious diseases in spatially structured populations: an invasory pair approximation. , 2005, Mathematical biosciences.

[15]  Piet Van Mieghem,et al.  Three-query PCPs with perfect completeness over non-Boolean domains , 2005 .

[16]  R M May,et al.  The influence of concurrent partnerships on the dynamics of HIV/AIDS. , 1992, Mathematical biosciences.

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

[18]  H. Kesten.  The critical probability of bond percolation on the square lattice equals 1/2 , 1980 .

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

[20]  M. Keeling,et al.  The effects of local spatial structure on epidemiological invasions , 1999, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[21]  S. Utev,et al.  Protective Vaccine Efficacy when Vaccine Response is Random , 2002 .

[22]  P. Hall,et al.  Martingale Limit Theory and Its Application , 1980 .

[23]  Kari Kuulasmaa,et al.  The spatial general epidemic and locally dependent random graphs , 1982, Journal of Applied Probability.

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

[25]  Estimation in branching processes with restricted observations , 2006 .

[26]  Rowland R Kao,et al.  The role of mathematical modelling in the control of the 2001 FMD epidemic in the UK. , 2002, Trends in microbiology.

[27]  Paolo De Los Rios,et al.  Cluster approximations for epidemic processes: a systematic description of correlations beyond the pair level. , 2004, Journal of theoretical biology.

[28]  W. O. Kermack,et al.  Contributions to the mathematical theory of epidemics--I. 1927. , 1991, Bulletin of mathematical biology.

[29]  W. O. Kermack,et al.  Contributions to the mathematical theory of epidemics—I , 1991, Bulletin of mathematical biology.

[30]  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..

[31]  J. Peccoud,et al.  Estimation of the parameters of a branching process from migrating binomial observations , 1998, Advances in Applied Probability.

[32]  Paul Ormerod,et al.  The Medieval inquisition: scale-free networks and the suppression of heresy , 2004 .

[33]  N G Becker,et al.  The effect of random vaccine response on the vaccination coverage required to prevent epidemics. , 1998, Mathematical biosciences.

[34]  Piet Van Mieghem,et al.  Distances in random graphs with finite variance degrees , 2005, Random Struct. Algorithms.

[35]  M. Keeling.  The implications of network structure for epidemic dynamics. , 2005, Theoretical population biology.

[36]  Peter Donnelly,et al.  Strong approximations for epidemic models , 1995 .

[37]  H. Knolle,et al.  A discrete branching process model for the spread of HIV via steady sexual partnerships , 2004, Journal of mathematical biology.

[38]  N. Rashevsky,et al.  Mathematical biology , 1961, Connecticut medicine.

[39]  Leeat Yariv,et al.  Diusion on Social Networks , 2006 .

[40]  F. Ball,et al.  Epidemics with two levels of mixing , 1997 .

[41]  A. M. Hasofer,et al.  Estimation in Epidemics with Incomplete Observations , 1997 .

[42]  Ulf Dieckmann,et al.  On moment closures for population dynamics in continuous space. , 2004, Journal of theoretical biology.

[43]  Mark E. J. Newman,et al.  Ego-centered networks and the ripple effect , 2001, Soc. Networks.

[44]  A branching model for the spread of infectious animal diseases in varying environments , 2004, Journal of mathematical biology.

[45]  O. Diekmann.  Mathematical Epidemiology of Infectious Diseases , 1996 .

[46]  D Mollison,et al.  Dependence of epidemic and population velocities on basic parameters. , 1991, Mathematical biosciences.

[47]  A. Martin-Löf,et al.  Generating Simple Random Graphs with Prescribed Degree Distribution , 2006, 1509.06985.

[48]  P. Bearman,et al.  Chains of Affection: The Structure of Adolescent Romantic and Sexual Networks1 , 2004, American Journal of Sociology.

[49]  Thomas Sellke,et al.  On the asymptotic distribution of the size of a stochastic epidemic , 1983, Journal of Applied Probability.

[50]  S. Cornell,et al.  Dynamics of the 2001 UK Foot and Mouth Epidemic: Stochastic Dispersal in a Heterogeneous Landscape , 2001, Science.

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

[52]  Modelling and prediction of classical swine fever epidemics , 2007 .

[53]  D. Klinkenberg.  Mathematical epidemiology and the conctrol of classical swine fever virus , 2003 .

[54]  Rick Durrett,et al.  Limit theorems for the spread of epidemics and forest fires , 1988 .

[55]  M. D. de Jong,et al.  Quantification of the transmission of classical swine fever virus between herds during the 1997-1998 epidemic in The Netherlands. , 1999, Preventive veterinary medicine.

[56]  Denis Mollison,et al.  Spatial Contact Models for Ecological and Epidemic Spread , 1977 .

[57]  H. Andersson,et al.  Stochastic Epidemic Models and Their Statistical Analysis , 2000 .

[58]  M. Biskup.  On the scaling of the chemical distance in long-range percolation models , 2003, math/0304418.

[59]  F. Chung,et al.  Connected Components in Random Graphs with Given Expected Degree Sequences , 2002 .

[60]  An epidemic model with exposure-dependent severities , 2005 .

[61]  Frank Ball,et al.  The distribution of general final state random variables for stochastic epidemic models , 1999 .

[62]  J. Murray,et al.  On the spatial spread of rabies among foxes. , 1992, Proceedings of the Royal Society of London. Series B, Biological sciences.

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

[64]  David A. Rand,et al.  Correlation Equations and Pair Approximations for Spatial Ecologies , 1999 .

[65]  Béla Bollobás,et al.  The phase transition in inhomogeneous random graphs , 2007, Random Struct. Algorithms.