Lyapunov Stability Analysis of a Delayed Foot-and-Mouth Disease Model with Animal Vaccination

Foot-and-mouth disease virus remains one of the most important livestock diseases in sub-Saharan Africa and several Southeast Asian countries. Vaccination of livestock has been recognized as an important tool for the control of foot-and-mouth disease virus. However, this intervention strategy has so...

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Main Authors: Tinashe B. Gashirai, Senelani D. Hove-Musekwa, Steady Mushayabasa
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2020/3891057
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spelling doaj-cacaf42f0c44446e929f404f812ac1d02020-11-25T03:57:05ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/38910573891057Lyapunov Stability Analysis of a Delayed Foot-and-Mouth Disease Model with Animal VaccinationTinashe B. Gashirai0Senelani D. Hove-Musekwa1Steady Mushayabasa2Department of Applied Mathematics, National University of Science and Technology, P.O. Box 939, Ascot, Bulawayo, ZimbabweDepartment of Applied Mathematics, National University of Science and Technology, P.O. Box 939, Ascot, Bulawayo, ZimbabweDepartment of Mathematics, University of Zimbabwe, P.O. Box MP 167, Harare, ZimbabweFoot-and-mouth disease virus remains one of the most important livestock diseases in sub-Saharan Africa and several Southeast Asian countries. Vaccination of livestock has been recognized as an important tool for the control of foot-and-mouth disease virus. However, this intervention strategy has some limitations. Generally, vaccine production is a complex multistep process which involves development, manufacturing, and delivery processes, and through this extensive process, some challenges such as poor vaccine storage often arise. More often, these challenges alter the validity of the vaccination. Foot-and-mouth disease virus epidemic dynamics have been extensively explored, but understanding the role of vaccination validity on virus endemicity is lacking. We present a time-delayed foot-and-mouth disease model that incorporates relevant biological and ecological factors, vaccination effects, and disease carriers. We determined the basic reproduction number and demonstrated that it is an important metric for persistence and extinction of the disease in the community. Numerical illustrations were utilised to support some of the analytical results.http://dx.doi.org/10.1155/2020/3891057
collection DOAJ
language English
format Article
sources DOAJ
author Tinashe B. Gashirai
Senelani D. Hove-Musekwa
Steady Mushayabasa
spellingShingle Tinashe B. Gashirai
Senelani D. Hove-Musekwa
Steady Mushayabasa
Lyapunov Stability Analysis of a Delayed Foot-and-Mouth Disease Model with Animal Vaccination
Discrete Dynamics in Nature and Society
author_facet Tinashe B. Gashirai
Senelani D. Hove-Musekwa
Steady Mushayabasa
author_sort Tinashe B. Gashirai
title Lyapunov Stability Analysis of a Delayed Foot-and-Mouth Disease Model with Animal Vaccination
title_short Lyapunov Stability Analysis of a Delayed Foot-and-Mouth Disease Model with Animal Vaccination
title_full Lyapunov Stability Analysis of a Delayed Foot-and-Mouth Disease Model with Animal Vaccination
title_fullStr Lyapunov Stability Analysis of a Delayed Foot-and-Mouth Disease Model with Animal Vaccination
title_full_unstemmed Lyapunov Stability Analysis of a Delayed Foot-and-Mouth Disease Model with Animal Vaccination
title_sort lyapunov stability analysis of a delayed foot-and-mouth disease model with animal vaccination
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2020-01-01
description Foot-and-mouth disease virus remains one of the most important livestock diseases in sub-Saharan Africa and several Southeast Asian countries. Vaccination of livestock has been recognized as an important tool for the control of foot-and-mouth disease virus. However, this intervention strategy has some limitations. Generally, vaccine production is a complex multistep process which involves development, manufacturing, and delivery processes, and through this extensive process, some challenges such as poor vaccine storage often arise. More often, these challenges alter the validity of the vaccination. Foot-and-mouth disease virus epidemic dynamics have been extensively explored, but understanding the role of vaccination validity on virus endemicity is lacking. We present a time-delayed foot-and-mouth disease model that incorporates relevant biological and ecological factors, vaccination effects, and disease carriers. We determined the basic reproduction number and demonstrated that it is an important metric for persistence and extinction of the disease in the community. Numerical illustrations were utilised to support some of the analytical results.
url http://dx.doi.org/10.1155/2020/3891057
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