On quasi-linear reaction diffusion systems arising from compartmental SEIR models

Juan Yang; Jeff Morgan; Bao Quoc Tang

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arXiv · 2403.15863

On quasi-linear reaction diffusion systems arising from compartmental SEIR models

Juan Yang·Jeff Morgan·Bao Quoc Tang

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Abstract

The global existence and boundedness of solutions to quasi-linear reaction-diffusion systems are investigated. The system arises from compartmental models describing the spread of infectious diseases proposed in [Viguerie et al, Appl. Math. Lett. (2021); Viguerie et al, Comput. Mech. (2020)], where the diffusion rate is assumed to depend on the total population, leading to quasilinear diffusion with possible degeneracy. The mathematical analysis of this model has been addressed recently in [Auricchio et al, Math. Method Appl. Sci. (2023] where it was essentially assumed that all sub-populations diffuse at the same rate, which yields a positive lower bound of the total population, thus removing the degeneracy. In this work, we remove this assumption completely and show the global existence and boundedness of solutions by exploiting a recently developed $L^p$-energy method. Our approach is applicable to a larger class of systems and is sufficiently robust to allow model variants and different boundary conditions.

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Juan Yang, Jeff Morgan, Bao Quoc Tang. 2024-03-23. On quasi-linear reaction diffusion systems arising from compartmental SEIR models. https://arxiv.org/abs/2403.15863

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