A non-standard finite-difference-method for a non-autonomous epidemiological model: analysis, parameter identification and applications

Benjamin Wacker; Jan Christian Schlüter; Benjamin Wacker; Jan Christian Schlüter

doi:10.3934/mbe.2023577

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 7: 12923-12954. doi: 10.3934/mbe.2023577

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A non-standard finite-difference-method for a non-autonomous epidemiological model: analysis, parameter identification and applications

Benjamin Wacker ^{1,2
,
,},
Jan Christian Schlüter ^{2,3
,
,}

1.
Department of Engineering and Natural Sciences, University of Applied Sciences Merseburg, Eberhard-Leibnitz-Str. 2, D-06217 Merseburg, Germany
2.
Chair of Data Science, Faculty of Management, Social Work and Construction, HAWK, Haarmannplatz 3, D-37603 Holzminden, Germany
3.
Computational Epidemiology and Public Health Research Group, Institute for Medical Epidemiology, Biometrics and Informatics, Interdisciplinary Center for Health Sciences, Martin Luther University Halle-Wittenberg, Magdeburger Str. 8, D-06112 Halle, Germany

Academic Editor: Frank Werner

Received: 16 March 2023 Revised: 17 May 2023 Accepted: 19 May 2023 Published: 05 June 2023

In this work, we propose a new non-standard finite-difference-method for the numerical solution of the time-continuous non-autonomous susceptible-infected-recovered model. For our time-discrete numerical solution algorithm, we prove preservation of non-negativity and show that the unique time-discrete solution converges linearly towards the time-continuous unique solution. In addition to that, we introduce a parameter identification algorithm for the susceptible-infected-recovered model. Finally, we provide two numerical examples to stress our theoretical findings.
- convergence,
- COVID-19,
- epidemiology,
- non-negativity,
- non-standard finite-difference-method,
- SIR model
Citation: Benjamin Wacker, Jan Christian Schlüter. A non-standard finite-difference-method for a non-autonomous epidemiological model: analysis, parameter identification and applications[J]. Mathematical Biosciences and Engineering, 2023, 20(7): 12923-12954. doi: 10.3934/mbe.2023577

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Abstract

In this work, we propose a new non-standard finite-difference-method for the numerical solution of the time-continuous non-autonomous susceptible-infected-recovered model. For our time-discrete numerical solution algorithm, we prove preservation of non-negativity and show that the unique time-discrete solution converges linearly towards the time-continuous unique solution. In addition to that, we introduce a parameter identification algorithm for the susceptible-infected-recovered model. Finally, we provide two numerical examples to stress our theoretical findings.

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