Threshold phenomena with respect to the initiation of depopulation in a simple model of foot-and-mouth disease
Depopulation is one of the important interventions for the outbreak of animal diseases. Simulation models using actual case scenarios conclude that early depopulation is the most efficient in preventing the spread of foot-and-mouth disease (FMD). However, the long delay in its initiation was often s...
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| Format: | Article |
| Language: | English |
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AIMS Press
2019-06-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2019297?viewType=HTML |
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| author | Kenji Itao Fumiya Omata Yoshitaka Nishikawa Tetsuro Oda Toshiharu Sasaki Cherri Zhang John Solomon Maninang Takayuki Yamaguchi |
| author_facet | Kenji Itao Fumiya Omata Yoshitaka Nishikawa Tetsuro Oda Toshiharu Sasaki Cherri Zhang John Solomon Maninang Takayuki Yamaguchi |
| author_sort | Kenji Itao |
| collection | DOAJ |
| description | Depopulation is one of the important interventions for the outbreak of animal diseases. Simulation models using actual case scenarios conclude that early depopulation is the most efficient in preventing the spread of foot-and-mouth disease (FMD). However, the long delay in its initiation was often seen in the actual cases and the theoretical analyses of FMD epidemiology with depopulation needs further elaboration. Here, we investigated the qualitative features of epidemic models when depopulation at a fixed capacity was delayed. We built a simple deterministic model for FMD based on state-transition, the SEIIR model whose unit is a single farm. The model settings and parameters were determined using the data from the 2010 epidemic in Miyazaki, Japan. By numerical calculation, we showed the existence of the threshold phenomenon with respect to delays in the initiation of depopulation and if the initiation of full-fledged depopulation surpasses the certain critical timing, the final size of the epidemic rapidly increases leading to a "catastrophic situation". We also revealed the mechanism of the threshold phenomenon from the relationship between the depopulation capacity and the increasing rate of infection. Although it can be delayed with lower transmission coefficients, the threshold phenomenon still exists. Thus, the existence of the critical timing for depopulation appears to be a universal feature of FMD epidemiology when depopulation is used as the main treatment for disease control. |
| first_indexed | 2024-04-12T11:28:07Z |
| format | Article |
| id | doaj.art-f5aed0b01320495480985b39d1daf7f3 |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-04-12T11:28:07Z |
| publishDate | 2019-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-f5aed0b01320495480985b39d1daf7f32022-12-22T03:35:09ZengAIMS PressMathematical Biosciences and Engineering1551-00182019-06-011655931594610.3934/mbe.2019297Threshold phenomena with respect to the initiation of depopulation in a simple model of foot-and-mouth diseaseKenji Itao0Fumiya Omata 1Yoshitaka Nishikawa2Tetsuro Oda3Toshiharu Sasaki 4Cherri Zhang5John Solomon Maninang6Takayuki Yamaguchi71. Department of Basic Science, Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, Japan2. Kurihara Central Hospital 3-1-1 Miyano-Chuo Tukidate Kurihara city, Miyagi, Japan3. Department of Health Informatics, Kyoto University School of Public Health, Yoshida-honmachi, Sakyo-ku, Kyoto, Japan4. Zimmer Biomet G.K., 16F Sumitomo Fudosan Sibakoen Tower, 11-1, Shibakoen 2-chome, Minato-ku, Tokyo, Japan5. Department of Infectious Diseases, Fujita Health University School of Medicine, 1-98 Dengakugakubo, Kutsukake-cho, Toyoake, Aichi, Japan6. Department of Global Health Policy, The Faculty of Medicine, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan7. ALESS Program, Center for Global Communication Strategies, College of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, Japan8. The Center for Data Science Education and Research, Shiga University, 1-1-1, Banba, Hikone-city, Shiga, JapanDepopulation is one of the important interventions for the outbreak of animal diseases. Simulation models using actual case scenarios conclude that early depopulation is the most efficient in preventing the spread of foot-and-mouth disease (FMD). However, the long delay in its initiation was often seen in the actual cases and the theoretical analyses of FMD epidemiology with depopulation needs further elaboration. Here, we investigated the qualitative features of epidemic models when depopulation at a fixed capacity was delayed. We built a simple deterministic model for FMD based on state-transition, the SEIIR model whose unit is a single farm. The model settings and parameters were determined using the data from the 2010 epidemic in Miyazaki, Japan. By numerical calculation, we showed the existence of the threshold phenomenon with respect to delays in the initiation of depopulation and if the initiation of full-fledged depopulation surpasses the certain critical timing, the final size of the epidemic rapidly increases leading to a "catastrophic situation". We also revealed the mechanism of the threshold phenomenon from the relationship between the depopulation capacity and the increasing rate of infection. Although it can be delayed with lower transmission coefficients, the threshold phenomenon still exists. Thus, the existence of the critical timing for depopulation appears to be a universal feature of FMD epidemiology when depopulation is used as the main treatment for disease control.https://www.aimspress.com/article/doi/10.3934/mbe.2019297?viewType=HTMLfoot-and-mouth diseasedepopulationinfectious disease modellingthreshold phenomenaepidemiology of domestic animals |
| spellingShingle | Kenji Itao Fumiya Omata Yoshitaka Nishikawa Tetsuro Oda Toshiharu Sasaki Cherri Zhang John Solomon Maninang Takayuki Yamaguchi Threshold phenomena with respect to the initiation of depopulation in a simple model of foot-and-mouth disease Mathematical Biosciences and Engineering foot-and-mouth disease depopulation infectious disease modelling threshold phenomena epidemiology of domestic animals |
| title | Threshold phenomena with respect to the initiation of depopulation in a simple model of foot-and-mouth disease |
| title_full | Threshold phenomena with respect to the initiation of depopulation in a simple model of foot-and-mouth disease |
| title_fullStr | Threshold phenomena with respect to the initiation of depopulation in a simple model of foot-and-mouth disease |
| title_full_unstemmed | Threshold phenomena with respect to the initiation of depopulation in a simple model of foot-and-mouth disease |
| title_short | Threshold phenomena with respect to the initiation of depopulation in a simple model of foot-and-mouth disease |
| title_sort | threshold phenomena with respect to the initiation of depopulation in a simple model of foot and mouth disease |
| topic | foot-and-mouth disease depopulation infectious disease modelling threshold phenomena epidemiology of domestic animals |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2019297?viewType=HTML |
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