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Part of the book series: Texts in Applied Mathematics ((TAM,volume 70))

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Abstract

All the models presented in the previous chapters are parametric. They belong to different types and serve different purposes.

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References

  • Anderson, R. M., & May, R. M. (1991) Infectious diseases of humans, dynamics and control. Oxford: Oxford University Press.

    Google Scholar 

  • Anscombe, F. J. (1953) Contribution to the discussion of H. Hotelling’s paper. Journal of Royal Statistics Society (B), 15, 229–230.

    Google Scholar 

  • Bailey, N. T. J. (1975). The mathematical theory of infectious diseases and its applications (2nd ed.). London: The Griffin & Company Ltd.

    MATH  Google Scholar 

  • Becker, N. G. (1989). Analysis of infectious disease data. London: Chapman and Hall/CRC.

    Google Scholar 

  • Becker, N. G., & Britton, T. (2001). Design issues of studies of infectious diseases. Journal of Statistical Planning and Inference, 96, 41–66.

    Article  Google Scholar 

  • Becker, N. G., & Hasofer, A. M. (1997). Estimation in epidemics with incomplete observations. Journal of the Royal Statistical Society: Series B, 59(2), 415–429.

    Article  MathSciNet  Google Scholar 

  • Becker, N. G., Watson, L. F., & Carlin, J. B. (1991). A method of non-parametric back-projection and its application to AIDS data. Statistics in Medicine, 10, 1527–1542.

    Article  Google Scholar 

  • Brookmeyer, R., & Gail, M. H. (1994). AIDS epidemiology: A quantitative approach. New York, NY: Oxford University Press.

    Google Scholar 

  • Champredon, D., & Dushoff, J. (2015). Intrinsic and realized generation intervals in infectious-disease transmission. Proceedings of the Royal Society B, 282(1821), 2015–2026.

    Article  Google Scholar 

  • Chowell, G., Ammon, C. E., Hengartner, N. W., & Hyman, J. M. (2006). Transmission dynamics of the great influenza pandemic of 1918 in Geneva, Switzerland: Assessing the effects of hypothetical interventions. Journal of Theoretical Biology, 241, 193–204.

    Article  MathSciNet  Google Scholar 

  • Chowell, G., Shim, E., Brauer, F., Diaz-Duenas, P., Hyman, J. M., & Castillo-Chavez, C. (2006). Modelling the transmission dynamics of acute haemorrhagic conjunctivitis: Application to the 2003 outbreak in Mexico. Statistics in Medicine, 25, 1840–1857.

    Article  MathSciNet  Google Scholar 

  • Cook, R. J., & Lawless, J. F. (2007). The statistical analysis of recurrent events. New York, NY: Springer.

    MATH  Google Scholar 

  • Cook, R. J., & Lawless, J. F. (2018). Multistate models for the analysis of life history data. New York, NY: Chapman and Hall/CRC.

    Book  Google Scholar 

  • Cox, D. R., & Donnelly, C. A. (2011). Principles of applied statistics. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Daley, D. J., & Gani, J. (1999). Epidemic modelling, an introduction. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Diekmann, O., Heesterbeek, J. A. P., & Metz, J. A. (1990). On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology, 28, 365–382.

    Article  MathSciNet  Google Scholar 

  • Donnelly, C. A., & Ferguson, N. M. (1999). Statistical aspects of BSE and vCJD, models for epidemics. New York, NY: Chapman and Hall/CRC.

    MATH  Google Scholar 

  • Efron, B., & Tibshirani, R. J. (1994). An introduction to the bootstrap. New York, NY: CRC Press.

    MATH  Google Scholar 

  • Farewell, V. T., Herzberg, A. M., James, K. W., Ho, L. M., & Leung, G. M. (2005). SARS incubation and quarantine times: When is an exposed individual known to be disease free? Statistics in Medicine, 24, 3431–3445.

    Article  MathSciNet  Google Scholar 

  • Fine, P. E. M. (2003). The interval between successive cases of an infectious disease. American Journal of Epidemiology, 158(11), 1039–1047.

    Article  Google Scholar 

  • Godambe, V. P., & Heyde, C. C. (1987). Quasi-likelihood and optimal estimation. International Statistical Review, 55, 231–244.

    Article  MathSciNet  Google Scholar 

  • Hohle, M., & Jørgensen, E. (2003). Estimating parameters for stochastic epidemics. Dina Research Report, 102. http://staff.math.su.se/hoehle/pubs/dina102.pdf

  • Hope Simpson, R. E. (1948). The period of transmission in certain epidemic diseases: An observational method for its discovery. Lancet, 2, 755–760.

    Article  Google Scholar 

  • Kalbfleisch, J. G. (1985). Probability and statistical inference, vol 2: Statistical inference (2nd ed.) New York: Springer.

    Book  Google Scholar 

  • Kalbfleisch, J. D., & Lawless, J. F. (1989). Estimating the incubation time distribution and expected number of cases of transfusion-associated acquired immune deficiency syndrome. Transfusion, 29, 672–676.

    Article  Google Scholar 

  • Kalbfleisch, J. D., & Lawless, J. F. (1991). Regression models for right truncated data with applications to AIDS incubation times and reporting lags. Statistica Sinica, 1, 19–32.

    MATH  Google Scholar 

  • Kenah, E., Lipsitch, M., & Robins, J. M. (2008). Generation interval contraction and epidemic data analysis. Mathematical Biosciences, 213, 71–79.

    Article  MathSciNet  Google Scholar 

  • Kosambi, D. D. (1949). Characteristic properties of series distributions. Proceedings of the National Institute for Science, India, 15, 109–113.

    Google Scholar 

  • Kuhn, M., & Johnson, K. (2013). Applied predictive modeling. New York, NY: Springer.

    Book  Google Scholar 

  • Lagakos, S. W., Rarraj, L. M., & De Gruttola, V. (1988). Nonparametric analysis of truncated survival data, with application to AIDS. Biometrika, 75(5), 15–23.

    MathSciNet  Google Scholar 

  • Lawless, J. F. (1994). Adjustments for reporting delays and the prediction of occurred but not reported events. The Canadian Journal of Statistics, 22(1), 15–31.

    Article  MathSciNet  Google Scholar 

  • Lawless, J. F. (2003). Statistical models and methods for lifetime data (2nd ed.). New York, NY: Wiley.

    MATH  Google Scholar 

  • Liang, K. Y., & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13–22.

    Article  MathSciNet  Google Scholar 

  • Lindsey, J. K. (2001). Nonlinear models in medical statistics. Oxford statistical science series (Vol. 24). Oxford: Oxford University Press.

    Google Scholar 

  • Lipsitch, M., Cohen, T., Cooper, B., Robins, J. M., Ma, S., James, L., et al. (2003). Transmission dynamics and control of severe acute respiratory syndrome. Science, 300, 1966–1970.

    Article  Google Scholar 

  • Lui, K. J., Lawrence, D. N., Morgan, W. M., Peterman, T. A., Haverkos, H. W., & Bregrnan, D. J. (1986). A model-based approach for estimating the mean incubation period of transfusion-associated acquired immunodeficiency syndrome. Proceedings of the National Academy of Sciences, 83, 3051–3055.

    Google Scholar 

  • McCullagh, P., & Nelder, J. A. (1983). Generalized linear models. London: Chapman and Hall.

    Book  Google Scholar 

  • Medley, G. F., Anderson, R. M., Cox, D. R., & Billard, I. (1987). Incubation period of AIDS in patients infected via blood transfusion. Nature, 328(7), 19–21.

    Google Scholar 

  • Neyman, J., & Scott, E. L. (1948). Consistent estimates based on partially consistent observations. Econometrica, 16, 1–32.

    Article  MathSciNet  Google Scholar 

  • Nishiura, H. (2010). Time variations in the generation time of an infectious diseases: Implications for sampling to appropriately quantify transmission potential. Mathematical Biosciences & Engineering, 7(4), 851–869.

    Article  MathSciNet  Google Scholar 

  • Pickles, W. (1939). Epidemiology in country practice. Bristol: John Wright and Sons.

    Google Scholar 

  • Qin, J. (2017). Biased sampling. In Over-identified parameter problems and beyond (ICSA book series in statistics). Springer Nature Singapore. https://doi.org/10.1007/978-981-10-4856-2_1.

    MATH  Google Scholar 

  • Raue, A., Kreutz, C., Maiwald, T., Bachmann, J., Schilling, M., Klingmuller, U., et al. (2009). Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics, 25, 1923–1929.

    Article  Google Scholar 

  • Rida, W. N. (1991). Asymptotic properties of some estimators for the infection rate in the general stochastic epidemic. Journal of Royal Statistical Society (B), 53, 209–283.

    MathSciNet  MATH  Google Scholar 

  • Roberts, G. M., & Heesterbeek, J. A. P. (2007). Model-consistent estimation of the basic reproduction number from the incidence of an emerging infection. Journal of Mathematical Biology, 55, 803–816.

    Article  MathSciNet  Google Scholar 

  • Rohatgi, A., (2018). WebPlotDigitizer Version: 4.1. Austin, TX.

    Google Scholar 

  • Roosa, K., & Chowell, G. (2019). Assessing parameter identifiability in compartmental dynamic models using a computational approach: Application to infectious disease transmission models. Theoretical Biology and Medical Modelling, 16(1), 1.

    Article  Google Scholar 

  • Smirnova, A., & Chowell, G. (2017). A primer on stable parameter estimation and forecasting in epidemiology by a problem-oriented regularized least squares algorithm. Infectious Disease Modeling, 2(2), 268–275.

    Article  Google Scholar 

  • Sprott, D. A. (2000). Statistical inference in science. New York, NY: Springer.

    MATH  Google Scholar 

  • Svensson, A. A. (2007). A note on generation times in epidemic models. Mathematical Biosciences, 208, 300–311.

    Article  MathSciNet  Google Scholar 

  • Tariq, A., Roosa, K., Mizumoto, K., & Chowell, G. (2019). Assessing reporting delays and the effective reproduction number: The 2018–19 Ebola epidemic in DRC, May 2018-January 2019. Epidemics. https://doi.org/10.1016/j.epidem.2019.01.003

    Article  Google Scholar 

  • Tuite, A. R., Greer, A. L., Whelan, M., Winter, A. L., Yan, P., Wu, J, et al. (2010). Estimated epidemiologic parameters and morbidity associated with pandemic H1N1 influenza. Canadian Medical Association Journal, 182, 131–136.

    Article  Google Scholar 

  • van den Driessche, P., & Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180, 29–48.

    Article  MathSciNet  Google Scholar 

  • Wald, A. (1943). A method of estimating plane vulnerability based on damage pf survivors. Statistical Research Group, Columbia University. CRC (Vol. 432). Arlington County, VA: Center for Naval Analyses.

    Google Scholar 

  • Wallinga, J., & Lipsitch, M. (2007). How generation intervals shape the relationship between growth rates and reproductive numbers. Proceedings of Royal Society B, 274, 599–604.

    Google Scholar 

  • Wang, M. C. (2005) Length bias. In Encyclopedia of biostatistics. New York, NY: Wiley. https://doi.org/10.1002/0470011815.b2a11044

  • White, L. F., & Pagano, M. (2008). A likelihood-based method for real-time estimation of the serial interval and reproductive number of an epidemic. Statistics in Medicine, 27, 2999–3016.

    Article  MathSciNet  Google Scholar 

  • Yan, P., & Zhang, F. (2018). A case study of nonlinear programming approach for repeated testing of HIV in a population stratified by subpopulations according to different risks of new infections. Operations Research for Health Care. https://doi.org/10.1016/j.orhc.2018.03.007

    Article  Google Scholar 

  • Yan, P., Zhang, F., & Wand, H. (2011). Using HIV diagnostic data to estimate HIV incidence: Method and simulation. Statistical Communications in Infectious Diseases, 3, 1.

    Article  MathSciNet  Google Scholar 

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Yan, P., Chowell, G. (2019). Some Statistical Issues. In: Quantitative Methods for Investigating Infectious Disease Outbreaks. Texts in Applied Mathematics, vol 70. Springer, Cham. https://doi.org/10.1007/978-3-030-21923-9_7

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