Existence of periodic solutions for enzyme-catalysed reactions with periodic substrate input
Guy Katriel
Considering a basic enzyme-catalysed reaction, in which the rate of input of the substrate varies periodically in time, we give a necessary and sufficient condition for the existence of a periodic solution of the reaction equations. The proof employs the Leray-Schauder degree, applied to an appropriately constructed homotopy.
keywords: periodic solutions Enzyme kinetics periodic forcing topological degree.
Modelling seasonal influenza in Israel
Oren Barnea Rami Yaari Guy Katriel Lewi Stone
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: seasonality. basic reproductive ratio model fitting Epidemiology $R_0$ influenza
Stability of synchronized oscillations in networks of phase-oscillators
Guy Katriel
We derive simple conditions for the stability or instability of the synchronized oscillation of a class of networks of coupled phase-oscillators, which includes many of the systems used in neural modelling.
keywords: Coupled oscillators Synchronization.

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