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

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Wacker,  Benjamin
Group Next generation mobility, Department of Dynamics of Complex Fluids, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Schlüter,  Jan Christian
Group Next generation mobility, Department of Dynamics of Complex Fluids, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Wacker, B., & Schlüter, J. C. (2020). An age- and sex-structured SIR model: Theory and an explicit-implicit numerical solution algorithm. Mathematical Biosciences and Engineering, 17, 5752-5801. doi:10.3934/mbe.2020309.


Cite as: http://hdl.handle.net/21.11116/0000-0007-4FFC-6
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.