An age- and sex-structured SIR model: Theory and an explicit-implicit numerical solution algorithm

Benjamin Wacker; Jan Schlüter; Benjamin Wacker; Jan Schlüter

doi:10.3934/mbe.2020309

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 5752-5801. doi: 10.3934/mbe.2020309

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Research article

An age- and sex-structured SIR model: Theory and an explicit-implicit numerical solution algorithm

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

1.
Next Generation Mobility Group, Max-Planck-Institute for Dynamics and Self-Organization, Department of Dynamics of Complex Fluids, Am Fassberg 17, D-37077 Göttingen, Germany
2.
Institute for Dynamics of Complex Systems, Faculty of Physics, Georg-August-University of Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany

Received: 26 May 2020 Accepted: 03 August 2020 Published: 31 August 2020

Since age and sex play an important role in transmission of diseases, we propose a SIR (susceptible-infectious-recovered) model for short-term predictions where the population is divided into subgroups based on both factors without taking into account vital dynamics. After stating our model and its underlining assumptions, we analyze its qualitative behavior thoroughly. We prove global existence and uniqueness, non-negativity, boundedness and certain monotonicity properties of the solution. Furthermore, we develop an explicit-implicit numerical solution algorithm and show that all properties of the continuous solution transfer to its time-discrete version. Finally, we provide one numerical example to illustrate our theoretical findings.
- age structure,
- existence and uniqueness,
- nonlinear ordinary differential equations,
- numerical algorithm,
- sex structure,
- SIR model
Citation: Benjamin Wacker, Jan Schlüter. An age- and sex-structured SIR model: Theory and an explicit-implicit numerical solution algorithm[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5752-5801. doi: 10.3934/mbe.2020309

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Abstract

Since age and sex play an important role in transmission of diseases, we propose a SIR (susceptible-infectious-recovered) model for short-term predictions where the population is divided into subgroups based on both factors without taking into account vital dynamics. After stating our model and its underlining assumptions, we analyze its qualitative behavior thoroughly. We prove global existence and uniqueness, non-negativity, boundedness and certain monotonicity properties of the solution. Furthermore, we develop an explicit-implicit numerical solution algorithm and show that all properties of the continuous solution transfer to its time-discrete version. Finally, we provide one numerical example to illustrate our theoretical findings.

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