Epidemiological Model with Fluctuations - Modélisation, Propagation et Imagerie Acoustique Access content directly
Conference Papers Year : 2023

Epidemiological Model with Fluctuations


We study a three-compartment system based on the SIR model [1]. From the view of dynamical systems, the inherent property of SIR and SIRS models is the change of stability. A stable fixed point (healthy state) turns into an unstable saddle if the infection rate reaches a critical value and the trajectories end in a newborn (stable) fixed point, the endemic equilibrium. In our model, noise effects from the environment that allow for a fluctuating infection rate play a crucial role. This results in multiplicative noise terms and our model turns into a set of stochastic nonlinear differential equations (SDEs). A periodic behavior of the infection number is observed that becomes more and more irregular if the noise is increasing. For rather large fluctuations repeated disease outbreaks in the form of sharp pulses with a variety of frequencies and amplitudes are found. The results based on SDEs are confirmed by numerical and approximate analytical solutions of the corresponding Fokker-Planck equation.
Fichier principal
Vignette du fichier
BesMic.pdf (378.38 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04194275 , version 1 (02-09-2023)


  • HAL Id : hal-04194275 , version 1


Michael Bestehorn, Thomas M. Michelitsch. Epidemiological Model with Fluctuations. OttoChaos: From the nonlinear dynamical systems theory to observational chaos, Christophe Letellier Sylvain-Mangiarotti, Denisse Sciamarella, Oct 2023, Toulouse, France. ⟨hal-04194275⟩
80 View
19 Download


Gmail Mastodon Facebook X LinkedIn More