Berlin 2012 – wissenschaftliches Programm

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BP: Fachverband Biologische Physik

BP 18: Posters: Statistical Physics in Biological Systems

BP 18.2: Poster

Mittwoch, 28. März 2012, 17:30–19:30, Poster A

Emergence of stable epidemic oscillations due to a small weather-based parametric excitation — •Eugene Postnikov and Dmitry Tatarenkov — Staatliche Universität Kursk, Kursk, Russland

The problem of mathematical description of seasonal epidemics of common diseases, e.g. flu, is one of hot topics joining mathematical epidemiology and theory of dynamical systems. The known results of stochastic simulations [Dushoff et al., 2004] demonstrate an evidence of 1:1 dynamical resonance between periods of parameter and solution variations. At the same time a deterministic model revealing this property is still an open problem.

We present the model based on SIRS (Susceptible-Infected-Recovered-Susceptible) approach: Ṡ=−kIS+θ⁻¹R,İdt=kIS−τ⁻¹I, Ṙ=τ⁻¹I−θ⁻¹R (S+I+R=1) with the variable parameter k=k₀[1+δsin(ω t)]. It has been shown that that this system can be transformed into the second-order non-autonomous ODE with free the term R_sθ⁻¹τ⁻¹sin(ω t), where R_s is a fixed point for R in the case k=k₀=const. In other words, the proposed coordinate transformation reveals the used parametrical excitation as a kind of outer one that allow us to clarify 1:1 character of the resonance.

To prove the obtained model, we analyze data on flu dynamics obtained from Google Flu Trends and corresponding weather conditions (mean temperature and humidity) from European Climate Assessment & Dataset. The processing of these curves confirms the proposed mathematical model.