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Reconstruction of the seasonally varying contact rate for measles. (English) Zbl 0818.92021
Summary: With the extended Kalman filter the time dependent contact rate for measles in the SEIR-model is reconstructed from data of the incidence of this infectious disease in the city of New York. It is concluded that although these data show through the years an irregular change in the number of infected children the contact rate is definitely periodic and follows the season. The analysis gives improved values of the parameters in the SEIR-model for this special problem.

MSC:
92D30 Epidemiology
93E11 Filtering in stochastic control theory
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[1] Aron, J.L.; Schwartz, I.B., Seasonality and periodic-doubling bifurcations in an epidemic model, J. theor. biology, 110, 665-679, (1984)
[2] Dietz, K., The incidence of infectious diseases under the influence of seasonal fluctuations, Lecture notes in biomath, 11, 1-15, (1976) · Zbl 0333.92014
[3] Engbert, R.; Drepper, F.R., Quantitative analysis of unpredictability; A case study from childhood epidemics, (), 204-215 · Zbl 1102.92303
[4] Farmer, J.D.; Sidorowich, J.J., Optimal shadowing and noise reduction, Physica D, 47, 373-392, (1992) · Zbl 0729.65501
[5] Fine, P.E.M.; Clarkson, J.A., Measles in england and wales I: an analysis of factors underlying seasonal patterns, Internat. J. epidemiology, 11, 5-14, (1982)
[6] Jazwinski, A.H., Stochastic processes and filtering theory, (1970), Academic Press New York · Zbl 0203.50101
[7] Kendall, B.E.; Schaffer, W.M.; Olsen, L.F.; Tidd, C.W.; Jorgensen, B.L., Using chaos to understand biological dynamics, (), 184-203 · Zbl 0878.92002
[8] London, W.P.; Yorke, J.A., Recurrent outbreaks of measles, chickenpox, and mumps I: seasonal variation in contact rates, Amer. J. epidemiol., 98, 453-468, (1973)
[9] Olsen, L.F.; Truty, G.L.; Schaffer, W.M., Oscillations and chaos in epidemics: A nonlinear dynamic study of six childhood diseases in Copenhagen, Denmark, Theor. pop. biology, 33, 344-370, (1988) · Zbl 0639.92012
[10] Soper, M.A., The interpretation of periodicity in deseases prevalence, J. roy. stat. soc. A, 92, 34-61, (1929) · JFM 55.0941.13
[11] Winfree, A.T., The geometry of biological time, (1980), Springer-Verlag New York · Zbl 0856.92002
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