| Issue |
Math. Model. Nat. Phenom.
Volume 20, 2025
Special Issue to honour Vitaly's work
|
|
|---|---|---|
| Article Number | 12 | |
| Number of page(s) | 38 | |
| DOI | https://doi.org/10.1051/mmnp/2024024 | |
| Published online | 14 May 2025 | |
Spreading speed for a time-periodic vector-borne disease system on a growing domain
Université Le Havre Normandie, Normandie Univ., LMAH UR 3821,
76600
Le Havre, France
* Corresponding author: arnaud.ducrot@univ-lehavre.fr
Received:
24
July
2024
Accepted:
8
November
2024
This paper is concerned with the study of the asymptotic speed of spread for a timeperiodic vector-borne disease system posed on the whole space for the host population and on a time varying domain for the vector population.We firstly examine the spreading properties of a time-periodic Fisher-KPP equation posed on a growing domain by constructing appropriate sub- and super-solutions. Then, using the basic reproduction number of the corresponding kinetic system, we describe the long time behavior of the system. In particular when this basic reproduction number is larger than one, we prove that the epidemic is endemic and we derive some estimates for the spreading speed of the invasion of the disease. Finally, numerical simulations are carried out to illustrate our theoretical results.
Mathematics Subject Classification: 35K51 / 35K57 / 35R37 / 92D30
Key words: Vector-borne disease system / spreading speed / moving domain / sub- and super-solutions
© The authors. Published by EDP Sciences, 2025
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