SKM 2021 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 4: Poster Session II: Nonlinear Dynamics, Simulations and Machine Learning

DY 4.2: Poster

Dienstag, 28. September 2021, 17:30–19:30, P

Epidemic modeling with delay-differential equations including saturation effects by isolation and contact restriction — •Susanne Kiefer and Edeltraud Gehrig — RheinMain University of Applied Science, Germany

Delay differential equation enable a realistic modeling of epidemics since they allow the inclusion of incubation periods, recovery times or the influence of a quarantine. A systematic modelling of the influence of parameters and their mutual dependence is of high importance when analyzing the behavior of the numbers of infected, susceptible and recovered persons. In this work we present and compare epidemic models with variable delays and saturation parameters. Thereby we consider both, a delay term describing the influence of incubation time as well as a delay for an inclusion of recovery. Our stability analysis and modeling of the temporal behavior allow for a determination of critical regimes where, depending on model approach, a delay may turn the system into instable behavior. A rise in amplitude of the characteristic oscillations shows a strong dependence on delay. This behavior may be controlled by parameters describing quarantine rules. Results of our simulations reveal an influence of parameters describing isolation of infected persons and contact restrictions on the dynamics and particularly on the transition to unstable behavior. A thorough adjustment of contact restriction and isolation may allow to shift the onset of instability and to adjust restriction rules. Thereby the range of control options of each of these parameters critically depends on initial values, infection and recovery rates as well on the delays.