On quasi-linear reaction diffusion systems arising from compartmental SEIR models
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| Format: | Preprint |
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2024
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| _version_ | 1866916173262618624 |
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| author | Yang, Juan Morgan, Jeff Tang, Bao Quoc |
| author_facet | Yang, Juan Morgan, Jeff Tang, Bao Quoc |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_15863 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On quasi-linear reaction diffusion systems arising from compartmental SEIR models Yang, Juan Morgan, Jeff Tang, Bao Quoc Analysis of PDEs 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. |
| title | On quasi-linear reaction diffusion systems arising from compartmental SEIR models |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.15863 |