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Volumn 2, Issue 2, 2012, Pages 156-169

Dynamic noise, chaos and parameter estimation in population biology

Author keywords

Dengue fever; Deterministic chaos; Epidemiology; Influenza; Likelihood; Master equation

Indexed keywords


EID: 84860896719     PISSN: 20428898     EISSN: 20428901     Source Type: Journal    
DOI: 10.1098/rsfs.2011.0103     Document Type: Review
Times cited : (37)

References (41)
  • 5
    • 67650417452 scopus 로고    scopus 로고
    • Epidemiology of dengue fever: A model with temporary cross-immunity and possible secondary infection shows bifurcations and chaotic behaviour in wide parameter regions
    • (doi:10.1051/mmnp:2008070)
    • Aguiar, M., Kooi, B. & Stollenwerk, N. 2008 Epidemiology of dengue fever: a model with temporary cross-immunity and possible secondary infection shows bifurcations and chaotic behaviour in wide parameter regions. Math. Model. Nat. Phenom. 3, 48-70. (doi:10.1051/mmnp:2008070)
    • (2008) Math. Model. Nat. Phenom , vol.3 , pp. 48-70
    • Aguiar, M.1    Kooi, B.2    Stollenwerk, N.3
  • 6
    • 0142071883 scopus 로고    scopus 로고
    • Master equation solution of a plant disease model
    • (doi:10.1016/S0375-9601(00)00520-X)
    • Stollenwerk, N. & Briggs, K. M. 2000 Master equation solution of a plant disease model. Phys. Lett. A 274, 84-91. (doi:10.1016/S0375-9601(00)00520-X)
    • (2000) Phys Lett. A , vol.274 , pp. 84-91
    • Stollenwerk, N.1    Briggs, K.M.2
  • 7
    • 80052707832 scopus 로고    scopus 로고
    • The role of seasonality and import in a minimalistic multi-strain dengue model capturing differences between primary and secondary infections: Complex dynamics and its implications for data analysis
    • (doi:10.1016/j.jtbi.2011.08.043)
    • Aguiar, M., Ballesteros, S., Kooi, B. W. & Stollenwerk, N. 2011 The role of seasonality and import in a minimalistic multi-strain dengue model capturing differences between primary and secondary infections: complex dynamics and its implications for data analysis. J. Theoret. Biol. 86, 181-196. (doi:10.1016/j.jtbi.2011.08.043).
    • (2011) J. Theoret. Biol , vol.86 , pp. 181-196
    • Aguiar, M.1    Ballesteros, S.2    Kooi, B.W.3    Stollenwerk, N.4
  • 8
    • 76249131779 scopus 로고    scopus 로고
    • Torus bifurcations, isolas and chaotic attractors in a simple dengue fever model with ADE and temporary cross immunity
    • ., (doi:10.1080/ 00207160902783532)
    • Aguiar, M., Stollenwerk, N. & Kooi, B. 2009 Torus bifurcations, isolas and chaotic attractors in a simple dengue fever model with ADE and temporary cross immunity. Int. J. Comput. Math. 86, 1867-1877. (doi:10.1080/ 00207160902783532)
    • (2009) Int. J. Comput. Math , vol.86 , pp. 1867-1877
    • Aguiar, M.1    Stollenwerk, N.2    Kooi, B.3
  • 10
    • 0003582543 scopus 로고    scopus 로고
    • Cambridge, UK: Cambridge University Press
    • Ott, E. 2002 Chaos in dynamical systems. Cambridge, UK: Cambridge University Press.
    • (2002) Chaos In Dynamical Systems
    • Ott, E.1
  • 12
    • 36049030270 scopus 로고    scopus 로고
    • The phase transition lines in pair approximation for the basic reinfection model SIRI
    • (doi:10. 1016/j.physleta.2007.06.040)
    • Stollenwerk, N., Martins, J. & Pinto, A. 2007 The phase transition lines in pair approximation for the basic reinfection model SIRI. Phys. Lett. A 371, 379-388. (doi:10. 1016/j.physleta.2007.06.040)
    • (2007) Phys. Lett. A , vol.371 , pp. 379-388
    • Stollenwerk, N.1    Martins, J.2    Pinto, A.3
  • 13
    • 79960727107 scopus 로고    scopus 로고
    • On the series expansion of the spatial SIS evolution operator
    • (doi:10.1080/ 10236190903153884)
    • Martins, J., Aguiar, M., Pinto, A. & Stollenwerk, N. 2011 On the series expansion of the spatial SIS evolution operator. J. Diff. Equ. Appl. 17, 1107-1118. (doi:10.1080/ 10236190903153884)
    • (2011) J. Diff. Equ. Appl , vol.17 , pp. 1107-1118
    • Martins, J.1    Aguiar, M.2    Pinto, A.3    Stollenwerk, N.4
  • 15
    • 84860900807 scopus 로고    scopus 로고
    • Dynamic noise and its role in understanding epidemiological processes
    • (eds T. E. Simos, G. Psi-hoyios & Ch. Tsitouras). College Park, MD: American Institute of Physics
    • Aguiar, M. & Stollenwerk, N. 2010 Dynamic noise and its role in understanding epidemiological processes. In Proc. ICNAAM, Numerical Analysis and Applied Mathematics, Int. Conf. 2010, Rhodes, Greece (eds T. E. Simos, G. Psi-hoyios & Ch. Tsitouras). College Park, MD: American Institute of Physics.
    • (2010) Proc. ICNAAM, Numerical Analysis and Applied Mathematics, Int
    • Aguiar, M.1    Stollenwerk, N.2
  • 16
    • 0017030517 scopus 로고
    • A general method for numerically simulating the stochastic time evolution of coupled chemical reactions
    • (doi:10.1016/ 0021-9991(76)90041-3)
    • Gillespie, D. T. 1976 A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22, 403-434. (doi:10.1016/ 0021-9991(76)90041-3)
    • (1976) J. Comput. Phys , vol.22 , pp. 403-434
    • Gillespie, D.T.1
  • 17
    • 0001645085 scopus 로고
    • Monte Carlo simulation of random walks with residence time dependent transition probability rates
    • (doi:10. 1016/0021-9991(78)90060-8)
    • Gillespie, D. T. 1978 Monte Carlo simulation of random walks with residence time dependent transition probability rates. J. Comput. Phys. 28, 395-407. (doi:10. 1016/0021-9991(78)90060-8)
    • (1978) J. Comput. Phys , vol.28 , pp. 395-407
    • Gillespie, D.T.1
  • 18
    • 33845508786 scopus 로고    scopus 로고
    • Inference for nonlinear dynamical systems
    • (doi:10.1073/pnas.063181103
    • Ionides, E. L., Breto, C. & King, A. A. 2006 Inference for nonlinear dynamical systems. Proc. Natl Acad. Sci. USA 103, 18438-18443. (doi:10.1073/pnas.063181103)
    • (2006) Proc. Natl Acad. Sci. USA , vol.103 , pp. 18438-18443
    • Ionides, E.L.1    Breto, C.2    King, A.A.3
  • 19
    • 73949147171 scopus 로고    scopus 로고
    • Time series analysis via mechanistic models
    • (doi:10.1214/08-AOAS201)
    • Breto, C., He, D., Ionides, E. L. & King, A. A. 2009 Time series analysis via mechanistic models. Ann. Appl. Stat. 3, 319-348. (doi:10.1214/08-AOAS201)
    • (2009) Ann. Appl. Stat , vol.3 , pp. 319-348
    • Breto, C.1    He, D.2    Ionides, E.L.3    King, A.A.4
  • 20
    • 74049096785 scopus 로고    scopus 로고
    • Plug-and-play inference for disease dynamics: Measles in large and small towns as a case study
    • (doi:10.1098/rsif.2009.0151)
    • He, D., Ionides, E. L. & King, A. A. 2010 Plug-and-play inference for disease dynamics: measles in large and small towns as a case study. J. R. Soc. Interface 7, 271-283. (doi:10.1098/rsif.2009.0151)
    • (2010) J. R. Soc. Interface , vol.7 , pp. 271-283
    • He, D.1    Ionides, E.L.2    King, A.A.3
  • 21
    • 80052459646 scopus 로고    scopus 로고
    • Iterated filtering
    • (doi:10.1214/ 11-AOS886)
    • Ionides, E. L., Bhadra, A., Atchade, Y. & King, A. A. 2011 Iterated filtering. Ann. Stat. 39, 1776-1802. (doi:10.1214/ 11-AOS886)
    • (2011) Ann. Stat , vol.39 , pp. 1776-1802
    • Ionides, E.L.1    Bhadra, A.2    Atchade, Y.3    King, A.A.4
  • 23
    • 84863755349 scopus 로고    scopus 로고
    • In press. Scaling of stochasticity in dengue hemorrhagic fever epidemics. Math. Model. Nat. Phenom
    • Aguiar, M., Kooi, B. W., Martins, J. & Stollenwerk, N. In press. Scaling of stochasticity in dengue hemorrhagic fever epidemics. Math. Model. Nat. Phenom.
    • Aguiar, M.1    Kooi, B.W.2    Martins, J.3    Stollenwerk, N.4
  • 24
    • 33747453222 scopus 로고
    • Optimum nonlinear systems which bring about a separation of a signal with constant parameters from noise
    • Stratonovich, R. L. 1959 Optimum nonlinear systems which bring about a separation of a signal with constant parameters from noise. Radiofizika 2, 892-901.
    • (1959) Radiofizika , vol.2 , pp. 892-901
    • Stratonovich, R.L.1
  • 25
    • 0141532332 scopus 로고
    • On the theory of optimal non-linear filtering of random functions
    • Stratonovich, R. L. 1959 On the theory of optimal non-linear filtering of random functions. Theory Probab. Appl. 4, 223-225.
    • (1959) Theory Probab. Appl , vol.4 , pp. 223-225
    • Stratonovich, R.L.1
  • 26
    • 78651477722 scopus 로고
    • Application of the Markov processes theory to optimal filtering
    • Stratonovich, R. L. 1960 Application of the Markov processes theory to optimal filtering. Radio Eng. Electron. Phys. 5, 1-19.
    • (1960) Radio Eng. Electron. Phys , vol.5 , pp. 1-19
    • Stratonovich, R.L.1
  • 27
    • 0001355394 scopus 로고
    • Conditional Markov processes
    • (doi:10.1137/1105015)
    • Stratonovich, R. L. 1960 Conditional Markov processes. Theory Probab. Appl. 5, 156-178. (doi:10.1137/1105015)
    • (1960) Theory Probab. Appl , vol.5 , pp. 156-178
    • Stratonovich, R.L.1
  • 28
    • 85024429815 scopus 로고
    • A new approach to linear filtering and prediction problems
    • (doi:10. 1115/1.3662552)
    • Kalman, R. E. 1960 A new approach to linear filtering and prediction problems. J. Basic Eng. 82, 35-45. (doi:10. 1115/1.3662552)
    • (1960) J. Basic Eng , vol.82 , pp. 35-45
    • Kalman, R.E.1
  • 29
    • 85024423711 scopus 로고
    • New results in linear filtering and prediction theory
    • Kalman, R. E. & Bucy, R. S. 1961 New results in linear filtering and prediction theory. Trans. ASME Ser. D. J. Basic Eng. 83, 95-108.
    • (1961) Trans. ASME Ser. D. J. Basic Eng , vol.83 , pp. 95-108
    • Kalman, R.E.1    Bucy, R.S.2
  • 31
    • 0001460136 scopus 로고    scopus 로고
    • On sequential Monte Carlo sampling methods for Bayesian filtering
    • (doi:10.1023/A:1008935410038)
    • Doucet, A., Godsill, S. & Andrieu, C. 2000 On sequential Monte Carlo sampling methods for Bayesian filtering.Stat. Comput. 10, 197-208. (doi:10.1023/A:1008935410038)
    • (2000) Stat. Comput , vol.10 , pp. 197-208
    • Doucet, A.1    Godsill, S.2    Andrieu, C.3
  • 34
    • 58149142997 scopus 로고    scopus 로고
    • Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems
    • (doi:10.1098/rsif.2008.0172)
    • Toni, T., Welch, D., Strelkowa, N., Ipsen, A. & Stumpf, M. P. H. 2009.Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J. R. Soc. Interface 6, 18-202. (doi:10.1098/rsif.2008.0172)
    • (2009) J. R. Soc. Interface , vol.6 , pp. 18-202
    • Toni, T.1    Welch, D.2    Strelkowa, N.3    Ipsen, A.4    Stumpf, M.P.H.5
  • 36
    • 80055040254 scopus 로고    scopus 로고
    • Designing attractive models via automated identification of chaotic and oscillatory dynamical regimes
    • (doi:10.1038/ncomms1496)
    • Silk, D., Kirk, P. D. W., Barnes, C. P., Toni, T., Rose, A., Moon, S., Dallman, M. J. & Stumpf, M. P. H. 2011 Designing attractive models via automated identification of chaotic and oscillatory dynamical regimes. Nat. Commun. 2, 1-6. (doi:10.1038/ncomms1496)
    • (2011) Nat. Commun , vol.2 , pp. 1-6
    • Silk, D.1    Kirk, P.D.W.2    Barnes, C.P.3    Toni, T.4    Rose, A.5    Moon, S.6    Dallman, M.J.7    Stumpf, M.P.H.8
  • 37
    • 0035888797 scopus 로고    scopus 로고
    • Testing nonlinear stochastic models on phytoplankton biomass time series
    • (doi:10.1016/ S0304-3800(01)00377-5)
    • Stollenwerk, N., Drepper, F. & Siegel, H. 2001 Testing nonlinear stochastic models on phytoplankton biomass time series. Ecol. Modell. 144, 261-277. (doi:10.1016/ S0304-3800(01)00377-5)
    • (2001) Ecol. Modell , vol.144 , pp. 261-277
    • Stollenwerk, N.1    Drepper, F.2    Siegel, H.3
  • 40
    • 79960504031 scopus 로고    scopus 로고
    • A spatially stochastic epidemic model with partial immunization shows in mean field approximation the reinfection threshold
    • (doi:10.1080/17513758.2010. 487159)
    • Stollenwerk, N., van Noort, S., Martins, J., Aguiar, M., Hilker, F., Pinto, A. & Gomes, G. 2010 A spatially stochastic epidemic model with partial immunization shows in mean field approximation the reinfection threshold. J. Biol. Dyn. 4, 634-649. (doi:10.1080/17513758.2010. 487159)
    • (2010) J. Biol. Dyn , vol.4 , pp. 634-649
    • Stollenwerk, N.1    van Noort, S.2    Martins, J.3    Aguiar, M.4    Hilker, F.5    Pinto, A.6    Gomes, G.7


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