Berlin 2024 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 33: Poster: Nonlinear Dynamics, Pattern Formation and Networks

DY 33.10: Poster

Wednesday, March 20, 2024, 15:00–18:00, Poster C

Oscillations in SIRS model with block delay kernels — •Daniel Henrik Nevermann and Claudius Gros — Institut für Theoretische Physik, Goethe-Universität Frankfurt, Deutschland

Oscillations are an omnipresent feature of epidemic dynamics, however, the classical SIRS model with exponentially distributed dwell-times in the compartments is unable to capture stable oscillations. Models with non-exponentially distributed dwell-times, on the other hand, may exhibit periodic outbreaks in its endemic state for certain parameter values. These oscillatory solutions are already present when considering a simple normalized step function kernel, what we call a block delay kernel, for the time of immunity of a recovered individual. We investigate the resulting attractor topology and study the characteristics of the periodic outbreaks, where we use the skewness of the time series as a measure for the shape of the periodic outbreaks.

A continuous approximation to the block delay kernel is given by the normalized sum of N Erlang distributions, where the block delay kernel is recovered in the limit N→∞. We show that this finite sum may be equally represented by an upper incomplete gamma function, which simplifies the derivation of its mathematical properties. We apply the kernel series framework to recast the system with continuous block delay kernel to a set of ordinary differential equations. Using this, we study the onset of periodic outbreaks when systematically decreasing the slope of the block delay kernel. Comparing the skewness of the time series to limiting case of a fixed time in the recovered compartment, we find that the relative deviation scales as a power-law in N.

Keywords: sirs model; block delay kernel; oscillations; kernel series framework