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PreprintCC BY 4.0HAL

Geographic spread of vector borne diseases in periodic heterogeneous environments

  • Antoine Wolff
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Abstract

We consider a reaction-diffusion system that arises in epidemiology to describe the spatial spread of a vector borne disease. Our model is a coupled version of the classical SIR model of Kermack and McKendrick. We study the long-time behavior of the solutions, giving optimal criteria on the propagation or extinction of the disease, and compute the asymptotic speed of spread of solutions, which is given by a Freidlin-Gärtner type formula. We also give some qualitative properties of the model, which yield information on the influence of the parameters on the system's long-time behavior. In particular, we identify the limit of the spreading speed when the diffusions are very large, and we show that the system behaves in this case similarly to a homogenized system.

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Cite

BibTeXRIS
BibTeX
@misc{wolff2026geographic,
  title = {{Geographic spread of vector borne diseases in periodic heterogeneous environments}},
  author = {Antoine Wolff},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26195},
  eprint = {2610.26195},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05803300v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Geographic spread of vector borne diseases in periodic heterogeneous environments
AU  - Antoine Wolff
PY  - 2026
DA  - 2026/10/16
PB  - HAL
DO  - 10.48550/arxiv.2610.26195
UR  - https://hal.science/hal-05803300v1
AB  - We consider a reaction-diffusion system that arises in epidemiology to describe the spatial spread of a vector borne disease. Our model is a coupled version of the classical SIR model of Kermack and McKendrick. We study the long-time behavior of the solutions, giving optimal criteria on the propagation or extinction of the disease, and compute the asymptotic speed of spread of solutions, which is given by a Freidlin-Gärtner type formula. We also give some qualitative properties of the model, which yield information on the influence of the parameters on the system's long-time behavior. In particular, we identify the limit of the spreading speed when the diffusions are very large, and we show that the system behaves in this case similarly to a homogenized system.
ER  -