Speaker
Description
Vector-borne diseases are infections transmitted between two interacting biological populations: a host, such as birds, and a vector, typically mosquitoes. The dynamics of these types of diseases can be linked to seasonal fluctuations, which in turn influence the spatial spread of the infection.
To this end, following Lewis et al.~\cite{Lewis_2006}, we couple an SIS model for the host population with an SI model for the vector population. Spatial terms are included, leading to a system of reaction–diffusion equations that describe random movement in space.
To incorporate both epidemic spatial spread and seasonal dynamics, we assume that no transmission occurs during the winter season, while epidemiological parameters remain constant during the summer season. Consequently, the inter-annual dynamics are governed by the survival rates of the infected populations.
First, we consider the non-spatial model and demonstrate, following Hethcote~\cite{Hethcote_1985}, the existence of a unique periodic dynamics, providing a clear threshold for disease persistence.
Extending the analysis to the spatial model, and following the framework established by Lui~\cite{Lui_1989_I, Lui_1989_II} and Li et al.~\cite{Li_2005}, we derive that the epidemic spreads from year to year with an asymptotic propagation speed $c^*$.
Finally, we illustrate the results through numerical simulations, comparing the speed of propagation $c^*$ obtained from numerical solutions with its analytical estimate.
Bibliography
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title = {Traveling waves and spread rates for a {West} {Nile} virus model},
volume = {68},
copyright = {http://www.springer.com/tdm},
issn = {0092-8240, 1522-9602},
url = {http://link.springer.com/10.1007/s11538-005-9018-z},
doi = {10.1007/s11538-005-9018-z},
language = {en},
number = {1},
urldate = {2026-03-10},
journal = {Bulletin of Mathematical Biology},
author = {Lewis, Mark and Rencławowicz, Joanna and Den Driessche, P. Van},
month = jan,
year = {2006},
pages = {3--23},
}
@article{Hethcote_1985,
title = {Stability of the endemic equilibrium in epidemic models with subpopulations},
volume = {75},
copyright = {https://www.elsevier.com/tdm/userlicense/1.0/},
issn = {00255564},
url = {https://linkinghub.elsevier.com/retrieve/pii/0025556485900380},
doi = {10.1016/0025-5564(85)90038-0},
language = {en},
number = {2},
urldate = {2026-03-10},
journal = {Mathematical Biosciences},
author = {Hethcote, Herbert W. and Thieme, Horst R.},
month = aug,
year = {1985},
pages = {205--227},
}
@article{Lui_1989_I,
title = {Biological growth and spread modeled by systems of recursions. {I}. mathematical theory},
volume = {93},
copyright = {https://www.elsevier.com/tdm/userlicense/1.0/},
issn = {00255564},
url = {https://linkinghub.elsevier.com/retrieve/pii/0025556489900266},
doi = {10.1016/0025-5564(89)90026-6},
language = {en},
number = {2},
urldate = {2026-03-10},
journal = {Mathematical Biosciences},
author = {Lui, Roger},
month = apr,
year = {1989},
pages = {269--295},
}
@article{Lui_1989_II,
title = {Biological growth and spread modeled by systems of recursions. {II}. biological theory},
volume = {93},
copyright = {https://www.elsevier.com/tdm/userlicense/1.0/},
issn = {00255564},
url = {https://linkinghub.elsevier.com/retrieve/pii/0025556489900278},
doi = {10.1016/0025-5564(89)90027-8},
language = {en},
number = {2},
urldate = {2026-03-10},
journal = {Mathematical Biosciences},
author = {Lui, Roger},
month = apr,
year = {1989},
pages = {297--311},
}
@article{Li_2005,
title = {Spreading speeds as slowest wave speeds for cooperative systems},
volume = {196},
copyright = {https://www.elsevier.com/tdm/userlicense/1.0/},
issn = {00255564},
url = {https://linkinghub.elsevier.com/retrieve/pii/S002555640500060X},
doi = {10.1016/j.mbs.2005.03.008},
language = {en},
number = {1},
urldate = {2026-03-10},
journal = {Mathematical Biosciences},
author = {Li, Bingtuan and Weinberger, Hans F. and Lewis, Mark A.},
month = jul,
year = {2005},
pages = {82--98},
}
