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<p>In this work, we analyze the stiffness properties of systems of ordinary differential equations originating from the SIR-type epidemiological model. We illustrate that the stiffness effect influences the numerical approximation of the SIR-type model solution via the Euler method, contingent on the contagion rates in the classical SIR model or the presence of numerous distinct neighboring populations interacting within the SIR-type model. This highlights the necessity for an appropriate selection of time-step size in numerical approximations. We present a theoretical <i>a priori</i> upper bound for the Euler method’s time-step size, formulated in terms of the model parameters and the number of interacting neighboring populations, to avoid negative values in the numerical solution for the SIR-type models.</p>

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On an a priori upper bound for the time-step size for the numerical solution of epidemiological SIR-type models

  • 期刊论文

  • 发表日期：

    2025年7月11日

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  • Marline Ilha da Silva,
  • Joice Chaves Marques,
  • Adriano De Cezaro,
  • Adelaida Otazu Conza

摘要

In this work, we analyze the stiffness properties of systems of ordinary differential equations originating from the SIR-type epidemiological model. We illustrate that the stiffness effect influences the numerical approximation of the SIR-type model solution via the Euler method, contingent on the contagion rates in the classical SIR model or the presence of numerous distinct neighboring populations interacting within the SIR-type model. This highlights the necessity for an appropriate selection of time-step size in numerical approximations. We present a theoretical a priori upper bound for the Euler method’s time-step size, formulated in terms of the model parameters and the number of interacting neighboring populations, to avoid negative values in the numerical solution for the SIR-type models.