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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Online Access: | http://wrap.warwick.ac.uk/173817/ http://wrap.warwick.ac.uk/173817/1/mathematics-11-00478.pdf https://doi.org/10.3390/math11020478 |
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ftuwarwick:oai:wrap.warwick.ac.uk:173817 2023-05-15T18:30:49+02:00 On the control over the distribution of ticks based on the extensions of the KISS model Kolokoltsov, Vassili N. 2023-01-16 application/pdf http://wrap.warwick.ac.uk/173817/ http://wrap.warwick.ac.uk/173817/1/mathematics-11-00478.pdf https://doi.org/10.3390/math11020478 unknown MDPI http://wrap.warwick.ac.uk/173817/1/mathematics-11-00478.pdf Kolokoltsov, Vassili N. (2023) On the control over the distribution of ticks based on the extensions of the KISS model. Mathematics, 11 (2). 478. doi:10.3390/math11020478 <http://dx.doi.org/10.3390/math11020478> ISSN 2227-7390. QA Mathematics RA0421 Public health. Hygiene. Preventive Medicine Journal Article NonPeerReviewed 2023 ftuwarwick https://doi.org/10.3390/math11020478 2023-03-16T23:42:49Z 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. Article in Journal/Newspaper taiga The University of Warwick: WRAP - Warwick Research Archive Portal Lone ENVELOPE(11.982,11.982,65.105,65.105) Mathematics 11 2 478 |
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The University of Warwick: WRAP - Warwick Research Archive Portal |
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ftuwarwick |
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unknown |
topic |
QA Mathematics RA0421 Public health. Hygiene. Preventive Medicine |
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QA Mathematics RA0421 Public health. Hygiene. Preventive Medicine Kolokoltsov, Vassili N. On the control over the distribution of ticks based on the extensions of the KISS model |
topic_facet |
QA Mathematics RA0421 Public health. Hygiene. Preventive Medicine |
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 |
Article in Journal/Newspaper |
author |
Kolokoltsov, Vassili N. |
author_facet |
Kolokoltsov, Vassili N. |
author_sort |
Kolokoltsov, Vassili N. |
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 |
MDPI |
publishDate |
2023 |
url |
http://wrap.warwick.ac.uk/173817/ http://wrap.warwick.ac.uk/173817/1/mathematics-11-00478.pdf 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_relation |
http://wrap.warwick.ac.uk/173817/1/mathematics-11-00478.pdf Kolokoltsov, Vassili N. (2023) On the control over the distribution of ticks based on the extensions of the KISS model. Mathematics, 11 (2). 478. doi:10.3390/math11020478 <http://dx.doi.org/10.3390/math11020478> ISSN 2227-7390. |
op_doi |
https://doi.org/10.3390/math11020478 |
container_title |
Mathematics |
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11 |
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2 |
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478 |
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1766214422632595456 |