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On parameter estimation in population models II: Multi-dimensional processes and transient dynamics

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  • Ross, J.V.
  • Pagendam, D.E.
  • Pollett, P.K.

Abstract

Recently, a computationally-efficient method was presented for calibrating a wide-class of Markov processes from discrete-sampled abundance data. The method was illustrated with respect to one-dimensional processes and required the assumption of stationarity. Here we demonstrate that the approach may be directly extended to multi-dimensional processes, and two analogous computationally-efficient methods for non-stationary processes are developed. These methods are illustrated with respect to disease and population models, including application to infectious count data from an outbreak of “Russian influenza†(A/USSR/1977 H1N1) in an educational institution. The methodology is also shown to provide an efficient, simple and yet rigorous approach to calibrating disease processes with gamma-distributed infectious period.

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  • Ross, J.V. & Pagendam, D.E. & Pollett, P.K., 2009. "On parameter estimation in population models II: Multi-dimensional processes and transient dynamics," Theoretical Population Biology, Elsevier, vol. 75(2), pages 123-132.
    • Handle: RePEc:eee:thpobi:v:75:y:2009:i:2:p:123-132
    DOI: 10.1016/j.tpb.2008.12.002
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    References listed on IDEAS

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    1. Aaron A. King & Edward L. Ionides & Mercedes Pascual & Menno J. Bouma, 2008. "Inapparent infections and cholera dynamics," Nature, Nature, vol. 454(7206), pages 877-880, August.
    2. Helen J Wearing & Pejman Rohani & Matt J Keeling, 2005. "Appropriate Models for the Management of Infectious Diseases," PLOS Medicine, Public Library of Science, vol. 2(7), pages 1-1, July.
    3. Simon Cauchemez & Alain-Jacques Valleron & Pierre-Yves Boëlle & Antoine Flahault & Neil M. Ferguson, 2008. "Estimating the impact of school closure on influenza transmission from Sentinel data," Nature, Nature, vol. 452(7188), pages 750-754, April.
    4. P. D. O’Neill & G. O. Roberts, 1999. "Bayesian inference for partially observed stochastic epidemics," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(1), pages 121-129.
    5. Alex R. Cook & Gavin J. Gibson & Christopher A. Gilligan, 2008. "Optimal Observation Times in Experimental Epidemic Processes," Biometrics, The International Biometric Society, vol. 64(3), pages 860-868, September.
    6. Mogens Bladt & Michael Sørensen, 2005. "Statistical inference for discretely observed Markov jump processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 395-410, June.
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    Citations

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    Cited by:

    1. Rebuli, Nicolas P. & Bean, N.G. & Ross, J.V., 2018. "Estimating the basic reproductive number during the early stages of an emerging epidemic," Theoretical Population Biology, Elsevier, vol. 119(C), pages 26-36.
    2. Jonathan Fintzi & Jon Wakefield & Vladimir N. Minin, 2022. "A linear noise approximation for stochastic epidemic models fit to partially observed incidence counts," Biometrics, The International Biometric Society, vol. 78(4), pages 1530-1541, December.
    3. Artalejo, J.R. & Lopez-Herrero, M.J., 2011. "The SIS and SIR stochastic epidemic models: A maximum entropy approach," Theoretical Population Biology, Elsevier, vol. 80(4), pages 256-264.
    4. Campillo, F. & Joannides, M. & Larramendy-Valverde, I., 2011. "Stochastic modeling of the chemostat," Ecological Modelling, Elsevier, vol. 222(15), pages 2676-2689.
    5. Keeling, M.J. & Ross, J.V., 2009. "Efficient methods for studying stochastic disease and population dynamics," Theoretical Population Biology, Elsevier, vol. 75(2), pages 133-141.
    6. Gamboa, M. & López-García, M. & Lopez-Herrero, M.J., 2024. "On the exact and population bi-dimensional reproduction numbers in a stochastic SVIR model with imperfect vaccine," Applied Mathematics and Computation, Elsevier, vol. 468(C).
    7. Ross, J.V., 2012. "On parameter estimation in population models III: Time-inhomogeneous processes and observation error," Theoretical Population Biology, Elsevier, vol. 82(1), pages 1-17.
    8. Christian H. Weiß & Philip K. Pollett, 2012. "Chain Binomial Models and Binomial Autoregressive Processes," Biometrics, The International Biometric Society, vol. 68(3), pages 815-824, September.

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