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        <title>Qualitative property preservation of high-order operator splitting for the SIR model</title>
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    <abstract>The susceptible-infected-recovered (SIR) model is perhaps the most basic epidemiological model for the evolution of disease spread within a population. Because of its direct representation of fundamental physical quantities, a true solution to an SIR model possesses a number of qualitative properties, such as conservation of the total population or positivity or monotonicity of its constituent populations, that may only be guaranteed to hold numerically under step-size restrictions on the solver. Operator-splitting methods with order greater than two require backward sub-steps in each operator, and the effects of these backward sub-steps on the step-size restrictions for guarantees of qualitative correctness of numerical solutions are not well studied. In this study, we analyze the impact of backward steps on step-size restrictions for guaranteed qualitative properties by applying third- and fourth-order operator-splitting methods to the SIR epidemic model. We find that it is possible to provide step-size restrictions that guarantee qualitative property preservation of the numerical solution despite the negative sub-steps, but care must be taken in the choice of the method. Results such as this open the door for the design and application of high-order operator-splitting methods to other mathematical models in general for which qualitative property preservation is important.</abstract>
    <identifier type="citekey">Wei-2022-Qualitative</identifier>
    <identifier type="doi">10.1016/j.apnum.2021.10.003</identifier>
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        <url>https://gwf-uwaterloo.github.io/gwf-publications/G22-13001</url>
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        <date>2022</date>
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%0 Journal Article
%T Qualitative property preservation of high-order operator splitting for the SIR model
%A Wei, Siqi
%A Spiteri, Raymond J.
%J Applied Numerical Mathematics, Volume 172
%D 2022
%V 172
%I Elsevier BV
%F Wei-2022-Qualitative
%X The susceptible-infected-recovered (SIR) model is perhaps the most basic epidemiological model for the evolution of disease spread within a population. Because of its direct representation of fundamental physical quantities, a true solution to an SIR model possesses a number of qualitative properties, such as conservation of the total population or positivity or monotonicity of its constituent populations, that may only be guaranteed to hold numerically under step-size restrictions on the solver. Operator-splitting methods with order greater than two require backward sub-steps in each operator, and the effects of these backward sub-steps on the step-size restrictions for guarantees of qualitative correctness of numerical solutions are not well studied. In this study, we analyze the impact of backward steps on step-size restrictions for guaranteed qualitative properties by applying third- and fourth-order operator-splitting methods to the SIR epidemic model. We find that it is possible to provide step-size restrictions that guarantee qualitative property preservation of the numerical solution despite the negative sub-steps, but care must be taken in the choice of the method. Results such as this open the door for the design and application of high-order operator-splitting methods to other mathematical models in general for which qualitative property preservation is important.
%R 10.1016/j.apnum.2021.10.003
%U https://gwf-uwaterloo.github.io/gwf-publications/G22-13001
%U https://doi.org/10.1016/j.apnum.2021.10.003
%P 332-350

Markdown (Informal)

[Qualitative property preservation of high-order operator splitting for the SIR model](https://gwf-uwaterloo.github.io/gwf-publications/G22-13001) (Wei & Spiteri, GWF 2022)

• Qualitative property preservation of high-order operator splitting for the SIR model (Wei & Spiteri, GWF 2022)

ACL

• Siqi Wei and Raymond J. Spiteri. 2022. Qualitative property preservation of high-order operator splitting for the SIR model. Applied Numerical Mathematics, Volume 172, 172:332–350.