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arXiv · 2608.15164

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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Yizhou Wang, Evgenia Echkina. 2026-08-15. From the SIR/SEIR/SVEIR Model to a Chemotactic System: Analysis of Spatiotemporal Mechanisms of Infection Spread within the Einstein Paradigm. https://arxiv.org/abs/2608.15164

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