Grimm, Viktor, Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin and Weber, Janine (2020). Estimating the time-dependent contact rate of SIR and SEIR models in mathematical epidemiology using physics-informed neural networks. Technical Report.


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The course of an epidemic can be often successfully described mathematically using compartment models. These models result in a system of ordinary differential equations. Two well-known examples are the SIR and the SEIR models. The transition rates between the different compartments are defined by certain parameters which are specific for the respective virus. Often, these parameters can be taken from the literature or can be determined from statistics. However, the contact rate or the related effective reproduction number are in general not constant and thus cannot easily be determined. Here, a new machine learning approach based on physics-informed neural networks is presented that can learn the contact rate from given data for the dynamical systems given by the SIR and SEIR models. The new method generalizes an already known approach for the identification of constant parameters to the variable or time-dependent case. After introducing the new method, it is tested for synthetic data generated by the numerical solution of SIR and SEIR models. Here, the case of exact and perturbed data is considered. In all cases, the contact rate can be learned very satisfactorily. Finally, the SEIR model in combination with physics-informed neural networks is used to learn the contact rate for COVID-19 data given by the course of the epidemic in Germany. The simulation of the number of infected individuals over the course of the epidemic, using the learned contact rate, is very promising.

Item Type: Preprints, Working Papers or Reports (Technical Report)
CreatorsEmailORCIDORCID Put Code
Grimm, Viktorviktor.grimm@uni-koeln.deUNSPECIFIEDUNSPECIFIED
Lanser, Martinmartin.lanser@uni-koeln.deUNSPECIFIEDUNSPECIFIED
URN: urn:nbn:de:hbz:38-121595
Series Name at the University of Cologne: Technical report series. Center for Data and Simulation Science
Volume: 2020,5
Date: 22 September 2020
Language: English
Faculty: Central Institutions / Interdisciplinary Research Centers
Divisions: Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Subjects: Data processing Computer science
Natural sciences and mathematics
Life sciences
Technology (Applied sciences)
Uncontrolled Keywords:
machine learningEnglish
physics-informed neural networksEnglish
SIR modelEnglish
SEIR modelEnglish
epidemic modelingEnglish
parameter estimationEnglish
scientific machine learningEnglish
Refereed: No


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