On the Control over the Distribution of Ticks Based on the Extensions of the KISS Model
Ticks and tick-borne diseases present a well-known threat to the health of people in many parts of the globe. The scientific literature devoted both to field observations and to modeling the propagation of ticks continues to grow. To date, the majority of the mathematical studies have been devoted t...
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ftmdpi:oai:mdpi.com:/2227-7390/11/2/478/ 2023-08-20T04:10:06+02:00 On the Control over the Distribution of Ticks Based on the Extensions of the KISS Model Vassili N. Kolokoltsov 2023-01-16 application/pdf https://doi.org/10.3390/math11020478 EN eng Multidisciplinary Digital Publishing Institute https://dx.doi.org/10.3390/math11020478 https://creativecommons.org/licenses/by/4.0/ Mathematics; Volume 11; Issue 2; Pages: 478 propagation of ticks ticks’ growth control critical patch size KISS model control zones vector-valued diffusion models discontinuous diffusion coefficients stability of zero solution Text 2023 ftmdpi https://doi.org/10.3390/math11020478 2023-08-01T08:19:43Z Ticks and tick-borne diseases present a well-known threat to the health of people in many parts of the globe. The scientific literature devoted both to field observations and to modeling the propagation of ticks continues to grow. To date, the majority of the mathematical studies have been devoted to models based on ordinary differential equations, where spatial variability was taken into account by a discrete parameter. Only a few papers use spatially nontrivial diffusion models, and they are devoted mostly to spatially homogeneous equilibria. Here we develop diffusion models for the propagation of ticks stressing spatial heterogeneity. This allows us to assess the sizes of control zones that can be created (using various available techniques) to produce a patchy territory, on which ticks will be eventually eradicated. Using averaged parameters taken from various field observations we apply our theoretical results to the concrete cases of the lone star ticks of North America and of the taiga ticks of Russia. From the mathematical point of view, we give criteria for global stability of the vanishing solution to certain spatially heterogeneous birth and death processes with diffusion. Text taiga MDPI Open Access Publishing Lone ENVELOPE(11.982,11.982,65.105,65.105) Mathematics 11 2 478 |
institution |
Open Polar |
collection |
MDPI Open Access Publishing |
op_collection_id |
ftmdpi |
language |
English |
topic |
propagation of ticks ticks’ growth control critical patch size KISS model control zones vector-valued diffusion models discontinuous diffusion coefficients stability of zero solution |
spellingShingle |
propagation of ticks ticks’ growth control critical patch size KISS model control zones vector-valued diffusion models discontinuous diffusion coefficients stability of zero solution Vassili N. Kolokoltsov On the Control over the Distribution of Ticks Based on the Extensions of the KISS Model |
topic_facet |
propagation of ticks ticks’ growth control critical patch size KISS model control zones vector-valued diffusion models discontinuous diffusion coefficients stability of zero solution |
description |
Ticks and tick-borne diseases present a well-known threat to the health of people in many parts of the globe. The scientific literature devoted both to field observations and to modeling the propagation of ticks continues to grow. To date, the majority of the mathematical studies have been devoted to models based on ordinary differential equations, where spatial variability was taken into account by a discrete parameter. Only a few papers use spatially nontrivial diffusion models, and they are devoted mostly to spatially homogeneous equilibria. Here we develop diffusion models for the propagation of ticks stressing spatial heterogeneity. This allows us to assess the sizes of control zones that can be created (using various available techniques) to produce a patchy territory, on which ticks will be eventually eradicated. Using averaged parameters taken from various field observations we apply our theoretical results to the concrete cases of the lone star ticks of North America and of the taiga ticks of Russia. From the mathematical point of view, we give criteria for global stability of the vanishing solution to certain spatially heterogeneous birth and death processes with diffusion. |
format |
Text |
author |
Vassili N. Kolokoltsov |
author_facet |
Vassili N. Kolokoltsov |
author_sort |
Vassili N. Kolokoltsov |
title |
On the Control over the Distribution of Ticks Based on the Extensions of the KISS Model |
title_short |
On the Control over the Distribution of Ticks Based on the Extensions of the KISS Model |
title_full |
On the Control over the Distribution of Ticks Based on the Extensions of the KISS Model |
title_fullStr |
On the Control over the Distribution of Ticks Based on the Extensions of the KISS Model |
title_full_unstemmed |
On the Control over the Distribution of Ticks Based on the Extensions of the KISS Model |
title_sort |
on the control over the distribution of ticks based on the extensions of the kiss model |
publisher |
Multidisciplinary Digital Publishing Institute |
publishDate |
2023 |
url |
https://doi.org/10.3390/math11020478 |
long_lat |
ENVELOPE(11.982,11.982,65.105,65.105) |
geographic |
Lone |
geographic_facet |
Lone |
genre |
taiga |
genre_facet |
taiga |
op_source |
Mathematics; Volume 11; Issue 2; Pages: 478 |
op_relation |
https://dx.doi.org/10.3390/math11020478 |
op_rights |
https://creativecommons.org/licenses/by/4.0/ |
op_doi |
https://doi.org/10.3390/math11020478 |
container_title |
Mathematics |
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11 |
container_issue |
2 |
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478 |
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1774724045863911424 |