### Mathematical Biosciences and Engineering

2011, Issue 2: 561-573. doi: 10.3934/mbe.2011.8.561

# Modelling seasonal influenza in Israel

• Received: 01 March 2010 Accepted: 29 June 2018 Published: 01 April 2011
• MSC : Primary: 92D30.

• 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.

Citation: Oren Barnea, Rami Yaari, Guy Katriel, Lewi Stone. Modelling seasonal influenza in Israel[J]. Mathematical Biosciences and Engineering, 2011, 8(2): 561-573. doi: 10.3934/mbe.2011.8.561

### Related Papers:

• 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.

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