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Compartment SIS and SEIR mathematical models are utilized in recent 3–4 years, to investigate the impact of COVID-19. We consider models that account the space diffusion of the disease. The article is devoted to construction of integral conservative finite difference schemes, that preserves the basic biological property - positivity of the solution. The proposed schemes have usual first in time and second in space orders of approximation. We construct iterative algorithms, which also satisfy the conservation and positivity properties of the difference scheme. The numerical experiments confirm the theoretical results and the efficiency of the algorithms.

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Positive Conservative Difference Schemes for SIS and SEIR Models with Spatial Diffusion

  • 会议论文

  • 发表日期：

    2025年

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  • Miglena N. Koleva,
  • Lubin G. Vulkov

摘要

Compartment SIS and SEIR mathematical models are utilized in recent 3–4 years, to investigate the impact of COVID-19. We consider models that account the space diffusion of the disease. The article is devoted to construction of integral conservative finite difference schemes, that preserves the basic biological property - positivity of the solution. The proposed schemes have usual first in time and second in space orders of approximation. We construct iterative algorithms, which also satisfy the conservation and positivity properties of the difference scheme. The numerical experiments confirm the theoretical results and the efficiency of the algorithms.