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Mathematical Biosciences and Engineering (MBE)
 

Modelling seasonal influenza in Israel

Pages: 561 - 573, Volume 8, Issue 2, April 2011

doi:10.3934/mbe.2011.8.561       Abstract        References        Full Text (361.6K)       Related Articles

Oren Barnea - Biomathematics Unit, Department of Zoology, Faculty of Life Sciences, Tel Aviv University, Tel Aviv 69978, Israel (email)
Rami Yaari - Biomathematics Unit, Department of Zoology, Faculty of Life Sciences, Tel Aviv University, Tel Aviv 69978, Israel (email)
Guy Katriel - Biomathematics Unit, Department of Zoology, Faculty of Life Sciences, Tel Aviv University, Tel Aviv 69978, Israel (email)
Lewi Stone - Biomathematics Unit, Department of Zoology, Faculty of Life Sciences, Tel Aviv University, Tel Aviv 69978, Israel (email)

Abstract: Mathematical modeling approaches are used to study the epidemic dynamics of seasonal influenza in Israel. The recent availability of highly resolved ten year timeseries of influenza cases provides an opportunity for modeling and estimating important epidemiological parameters in the Israeli population. A simple but well known SIR discrete-time deterministic model was fitted to consecutive epidemics allowing estimation of the initial number of susceptibles in the population $S_0$, as well as the reproductive number $R_0$ each year. The results were corroborated by implementing a stochastic model and using a maximum likelihood approach. The paper discusses the difficulties in estimating these important parameters especially when the reporting rate of influenza cases might only be known with limited accuracy, as is generally the case. In such situations invariant parameters such as the percentage of susceptibles infected, and the effective reproductive rate might be preferred, as they do not depend on reporting rate. Results are given based on the Israeli timeseries.

Keywords:  Epidemiology, influenza, model fitting, basic reproductive ratio, $R_0$, seasonality.
Mathematics Subject Classification:  Primary: 92D30.

Received: March 2010;      Accepted: August 2010;      Published: April 2011.

 References