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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Main Authors: Kenji Itao, Fumiya Omata, Yoshitaka Nishikawa, Tetsuro Oda, Toshiharu Sasaki, Cherri Zhang, John Solomon Maninang, Takayuki Yamaguchi
Format: Article
Language:English
Published: AIMS Press 2019-06-01
Series:Mathematical Biosciences and Engineering
Subjects:
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.
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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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