Abstract:We present an epidemiological model for vector-borne diseases that includes within-host viral load and antibody dynamics using structured transport equations. By incorporating the internal dynamics into the infected and recovered host compartments, the formulation introduces nonlinearities and nonlocalities. We establish analytical properties, including well-posedness and mass conservation, and characterize its characteristic curves. Furthermore, we derive a simplified Uniform Host Response (UHR) model featuring delay-type terms. For both the full and UHR frameworks, the basic reproduction number is determined and shown to serve as a threshold for the existence of an endemic equilibrium, and is related to the linear stability of the disease-free state. Finally, numerical experiments, parameterized specifically for Dengue fever, demonstrate how within-host mechanisms influence population-level epidemiological outcomes.
| Subjects: | Analysis of PDEs (math.AP); Numerical Analysis (math.NA) |
| MSC classes: | 92D30, 35Q49, 35Q92 |
| Cite as: | arXiv:2605.25370 [math.AP] |
| (or arXiv:2605.25370v1 [math.AP] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25370 arXiv-issued DOI via DataCite (pending registration) |
From: Débora De Oliveira Medeiros [view email]
[v1]
Mon, 25 May 2026 02:50:32 UTC (9,011 KB)
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