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From the SIR/SEIR/SVEIR Model to a Chemotactic System: Analysis of Spatiotemporal Mechanisms of Infection Spread within the Einstein Paradigm

  • Yizhou Wang
  • Evgenia Echkina
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Abstract

This work investigates the class of SIR/SEIR models and their extension to an ODE-based SVEIR system, whose parameters are calibrated and validated using real influenza outbreak data. The theoretical part establishes existence and uniqueness of solutions for the SVEIR model via the Picard-Lindelof theorem and analyzes invariance of the admissible region. To describe spatiotemporal infection spread in an urban setting, a diffusion-chemotaxis extension of the SIR framework is formulated as a PDE system; an additional term is introduced to represent fear/avoidance effects in the system dynamics. A numerical workflow is proposed, including grid discretization, Neumann boundary conditions enforced by mirror extension, a semi-implicit IMEX time-stepping scheme, and sparse linear solves; computational correctness is monitored, in particular, by checking conservation of the total population.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026from,
  title = {{From the SIR/SEIR/SVEIR Model to a Chemotactic System: Analysis of Spatiotemporal Mechanisms of Infection Spread within the Einstein Paradigm}},
  author = {Yizhou Wang and Evgenia Echkina},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.15164},
  eprint = {2608.15164},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.15164},
}
RIS
TY  - UNPB
TI  - From the SIR/SEIR/SVEIR Model to a Chemotactic System: Analysis of Spatiotemporal Mechanisms of Infection Spread within the Einstein Paradigm
AU  - Yizhou Wang
AU  - Evgenia Echkina
PY  - 2026
DA  - 2026/08/15
PB  - arXiv
DO  - 10.48550/arxiv.2608.15164
UR  - https://arxiv.org/abs/2608.15164
AB  - This work investigates the class of SIR/SEIR models and their extension to an ODE-based SVEIR system, whose parameters are calibrated and validated using real influenza outbreak data. The theoretical part establishes existence and uniqueness of solutions for the SVEIR model via the Picard-Lindelof theorem and analyzes invariance of the admissible region. To describe spatiotemporal infection spread in an urban setting, a diffusion-chemotaxis extension of the SIR framework is formulated as a PDE system; an additional term is introduced to represent fear/avoidance effects in the system dynamics. A numerical workflow is proposed, including grid discretization, Neumann boundary conditions enforced by mirror extension, a semi-implicit IMEX time-stepping scheme, and sparse linear solves; computational correctness is monitored, in particular, by checking conservation of the total population.
ER  -