Dynamical epidemic suppression using stochastic prediction and control.

We consider the effects of noise on a model of epidemic outbreaks, where the outbreaks appear randomly. Using a constructive transition approach that predicts large outbreaks prior to their occurrence, we derive an adaptive control scheme that prevents large outbreaks from occurring. The theory is applicable to a wide range of stochastic processes with underlying deterministic structure.

[1]  A L Lloyd,et al.  Spatial heterogeneity in epidemic models. , 1996, Journal of theoretical biology.

[2]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .

[3]  P. Kaye.  Infectious diseases of humans: Dynamics and control , 1993 .

[4]  Y. Moreno,et al.  Epidemic outbreaks in complex heterogeneous networks , 2001, cond-mat/0107267.

[5]  Ott,et al.  Preserving chaos: Control strategies to preserve complex dynamics with potential relevance to biological disorders. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  L Billings,et al.  Exciting chaos with noise: unexpected dynamics in epidemic outbreaks , 2002, Journal of mathematical biology.

[7]  David L. Craft,et al.  Emergency response to a smallpox attack: The case for mass vaccination , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[8]  A Magnifying Glass for the Milky Way , 2000, Science.

[9]  E. Bollt,et al.  A manifold independent approach to understanding transport in stochastic dynamical systems , 2002 .

[10]  J. Aron,et al.  Multiple attractors in the response to a vaccination program. , 1990, Theoretical population biology.

[11]  Ira B Schwartz,et al.  Phase-space transport of stochastic chaos in population dynamics of virus spread. , 2002, Physical review letters.

[12]  Vadim N. Smelyanskiy,et al.  Optimal Control of Large Fluctuations. , 1997 .

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

[14]  V. Araújo.  Random Dynamical Systems , 2006, math/0608162.

[15]  R. Anderson,et al.  Pulse mass measles vaccination across age cohorts. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[16]  J. Patz,et al.  A human disease indicator for the effects of recent global climate change , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[17]  H. B. Wilson,et al.  Chaotic stochasticity: a ubiquitous source of unpredictability in epidemics , 1991, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[18]  D. Earn,et al.  A simple model for complex dynamical transitions in epidemics. , 2000, Science.

[19]  B. Bolker,et al.  Chaos and biological complexity in measles dynamics , 1993, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[20]  B. Øksendal.  Stochastic differential equations : an introduction with applications , 1987 .

[21]  I B Schwartz,et al.  Infinite subharmonic bifurcation in an SEIR epidemic model , 1983, Journal of mathematical biology.

[22]  I B Schwartz,et al.  Multiple stable recurrent outbreaks and predictability in seasonally forced nonlinear epidemic models , 1985, Journal of mathematical biology.

[23]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[24]  Measles immunization strategies for an epidemiologically heterogeneous population: the Israeli case study , 1993, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[25]  Stephen Wiggins,et al.  Chaotic transport in dynamical systems , 1991 .