publication . Preprint . 2019

Survival Dynamical Systems for the Population-level Analysis of Epidemics

KhudaBukhsh, Wasiur R.; Choi, Boseung; Kenah, Eben; Rempala, Grzegorz A.;
Open Access English
  • Published: 02 Jan 2019
Abstract
Comment: 27 pages and 6 figures
Subjects
free text keywords: Quantitative Biology - Populations and Evolution, Mathematics - Dynamical Systems, Statistics - Methodology, 92D30, 60J27, 62N02
Related Organizations
Funded by
NIH| Understanding Transmission with Integrated Genetic and Epidemiologic Inference
Project
  • Funder: National Institutes of Health (NIH)
  • Project Code: 5U54GM111274-02
  • Funding stream: NATIONAL INSTITUTE OF GENERAL MEDICAL SCIENCES
,
NSF| RAPID: Stochastic Ebola Modeling on Dynamic Contact Networks
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1513489
,
NSF| Mathematical Biosciences Institute
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1440386
,
NIH| Regression, Phylogenetics, and Study Design in Infectious Disease Epidemiology
Project
  • Funder: National Institutes of Health (NIH)
  • Project Code: 7R01AI116770-03
  • Funding stream: NATIONAL INSTITUTE OF ALLERGY AND INFECTIOUS DISEASES
Download from
44 references, page 1 of 3

[1] O. O. Aalen, . Borgan, and H. K. Gjessing. Survival and event history analysis: a process point of View. Springer Science & Business Media, 2008. [OpenAIRE]

[3] D. F. Anderson and T. G. Kurtz. Stochastic Analysis of Biochemical Systems, volume 1. Springer, 2015.

[4] H. Anderson and T. Britton. Stochastic Epidemic Models and Their Statistical Analysis. Springer-Verlag New York, 2000.

[5] Y. F. Atchade, J. S. Rosenthal, et al. On adaptive markov chain monte carlo algorithms. Bernoulli, volume 11(5):pp. 815{828, 2005. [OpenAIRE]

[6] J. Baladron, D. Fasoli, O. Faugeras, and J. Touboul. Mean- eld description and propagation of chaos in networks of hodgkin-huxley and tzhugh-nagumo neurons. The Journal of Mathematical Neuroscience, volume 2(1):p. 10, 2012. [OpenAIRE]

[7] S. Banisch. Markov Chain Aggregation for Agent-Based Models. Springer International Publishing, 2016.

[8] P. Buchholz. Exact and ordinary lumpability in nite markov chains. Journal of Applied Probability, volume 31(1):pp. 59{75, 1994.

[9] M. G. Burch, K. A. Jacobsen, J. H. Tien, and G. A. Rempala. Network-based analysis of a small ebola outbreak. Mathematical Biosciences & Engineering, volume 14:p. 67, 2017.

[10] B. Choi and G. A. Rempala. Inference for discretely observed stochastic kinetic networks with applications to epidemic modeling. Biostatistics, volume 13(1):pp. 153{165, 2012.

[11] A. Dembo and O. Zeitouni. Large Deviations Techniques and Applications. Springer, 2010.

[12] B. Djehiche and A. Schied. Large deviations for hierarchical systems of interacting jump processes. Journal of Theoretical Probability, volume 11(1):pp. 1{24, 1998.

[16] J. Feng and T. G. Kurtz. Large Deviations for Stochastic Processes. 131. American Mathematical Soc., 2006.

[17] T. R. Fleming and D. P. Harrington. Counting processes and survival analysis. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. John Wiley & Sons, Inc., New York, 1991.

[18] W. M. Getz and E. R. Dougherty. Discrete stochastic analogs of erlang epidemic models. Journal of biological dynamics, volume 12(1):pp. 16{38, 2018.

[19] D. T. Gillespie. Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry, volume 81(25):pp. 2340{2361, 1977.

44 references, page 1 of 3
Abstract
Comment: 27 pages and 6 figures
Subjects
free text keywords: Quantitative Biology - Populations and Evolution, Mathematics - Dynamical Systems, Statistics - Methodology, 92D30, 60J27, 62N02
Related Organizations
Funded by
NIH| Understanding Transmission with Integrated Genetic and Epidemiologic Inference
Project
  • Funder: National Institutes of Health (NIH)
  • Project Code: 5U54GM111274-02
  • Funding stream: NATIONAL INSTITUTE OF GENERAL MEDICAL SCIENCES
,
NSF| RAPID: Stochastic Ebola Modeling on Dynamic Contact Networks
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1513489
,
NSF| Mathematical Biosciences Institute
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1440386
,
NIH| Regression, Phylogenetics, and Study Design in Infectious Disease Epidemiology
Project
  • Funder: National Institutes of Health (NIH)
  • Project Code: 7R01AI116770-03
  • Funding stream: NATIONAL INSTITUTE OF ALLERGY AND INFECTIOUS DISEASES
Download from
44 references, page 1 of 3

[1] O. O. Aalen, . Borgan, and H. K. Gjessing. Survival and event history analysis: a process point of View. Springer Science & Business Media, 2008. [OpenAIRE]

[3] D. F. Anderson and T. G. Kurtz. Stochastic Analysis of Biochemical Systems, volume 1. Springer, 2015.

[4] H. Anderson and T. Britton. Stochastic Epidemic Models and Their Statistical Analysis. Springer-Verlag New York, 2000.

[5] Y. F. Atchade, J. S. Rosenthal, et al. On adaptive markov chain monte carlo algorithms. Bernoulli, volume 11(5):pp. 815{828, 2005. [OpenAIRE]

[6] J. Baladron, D. Fasoli, O. Faugeras, and J. Touboul. Mean- eld description and propagation of chaos in networks of hodgkin-huxley and tzhugh-nagumo neurons. The Journal of Mathematical Neuroscience, volume 2(1):p. 10, 2012. [OpenAIRE]

[7] S. Banisch. Markov Chain Aggregation for Agent-Based Models. Springer International Publishing, 2016.

[8] P. Buchholz. Exact and ordinary lumpability in nite markov chains. Journal of Applied Probability, volume 31(1):pp. 59{75, 1994.

[9] M. G. Burch, K. A. Jacobsen, J. H. Tien, and G. A. Rempala. Network-based analysis of a small ebola outbreak. Mathematical Biosciences & Engineering, volume 14:p. 67, 2017.

[10] B. Choi and G. A. Rempala. Inference for discretely observed stochastic kinetic networks with applications to epidemic modeling. Biostatistics, volume 13(1):pp. 153{165, 2012.

[11] A. Dembo and O. Zeitouni. Large Deviations Techniques and Applications. Springer, 2010.

[12] B. Djehiche and A. Schied. Large deviations for hierarchical systems of interacting jump processes. Journal of Theoretical Probability, volume 11(1):pp. 1{24, 1998.

[16] J. Feng and T. G. Kurtz. Large Deviations for Stochastic Processes. 131. American Mathematical Soc., 2006.

[17] T. R. Fleming and D. P. Harrington. Counting processes and survival analysis. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. John Wiley & Sons, Inc., New York, 1991.

[18] W. M. Getz and E. R. Dougherty. Discrete stochastic analogs of erlang epidemic models. Journal of biological dynamics, volume 12(1):pp. 16{38, 2018.

[19] D. T. Gillespie. Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry, volume 81(25):pp. 2340{2361, 1977.

44 references, page 1 of 3
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