Volume 1, Issue 2
Dynamical Analysis of Transmission Model of the Cattle Foot-and-Mouth Disease

Feng Li, Zhen Jin, Juan Zhang, Michael Y. Li & Youming Wang

CSIAM Trans. Appl. Math., 1 (2020), pp. 277-295.

Published online: 2020-07

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  • Abstract

The epidemic of foot-and-mouth disease (FMD) in cattle remains particular concern in many countries or areas. The epidemic can spread by direct contact with the carrier and symptomatic animals, as well as indirect contact with the contaminated environment. The outbreak of FMD indicates that the infection initially spreads through the farm before spreading between farms. In this paper, considering the cattle population, we establish a dynamical model of FMD with two patches: within-farm and outside-farm, and give the formulae of the basic reproduction number $R$0. By constructing the Lyapunov function, we prove the disease-free equilibrium is globally asymptotically stable when $R$0<1, and that of the unique endemic equilibrium when $R$0>1. By numerical simulations, we confirm the global stability of equilibria. In addition, by carrying out the sensitivity analysis of the basic reproduction number on some parameters, we reach the conclusion that vaccination, quarantining or removing of the carrier and disinfection are the useful control measures for FMD at the large-scale cattle farm.

  • Keywords

Foot and mouth disease, carriers, dynamical model, environment transmission, Lyapunov function.

  • AMS Subject Headings

34D05,34D20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CSIAM-AM-1-277, author = {Feng Li , and Zhen Jin , and Juan Zhang , and Michael Y. Li , and Youming Wang , }, title = {Dynamical Analysis of Transmission Model of the Cattle Foot-and-Mouth Disease}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2020}, volume = {1}, number = {2}, pages = {277--295}, abstract = {

The epidemic of foot-and-mouth disease (FMD) in cattle remains particular concern in many countries or areas. The epidemic can spread by direct contact with the carrier and symptomatic animals, as well as indirect contact with the contaminated environment. The outbreak of FMD indicates that the infection initially spreads through the farm before spreading between farms. In this paper, considering the cattle population, we establish a dynamical model of FMD with two patches: within-farm and outside-farm, and give the formulae of the basic reproduction number $R$0. By constructing the Lyapunov function, we prove the disease-free equilibrium is globally asymptotically stable when $R$0<1, and that of the unique endemic equilibrium when $R$0>1. By numerical simulations, we confirm the global stability of equilibria. In addition, by carrying out the sensitivity analysis of the basic reproduction number on some parameters, we reach the conclusion that vaccination, quarantining or removing of the carrier and disinfection are the useful control measures for FMD at the large-scale cattle farm.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.2020-0011}, url = {http://global-sci.org/intro/article_detail/csiam-am/17178.html} }
TY - JOUR T1 - Dynamical Analysis of Transmission Model of the Cattle Foot-and-Mouth Disease AU - Feng Li , AU - Zhen Jin , AU - Juan Zhang , AU - Michael Y. Li , AU - Youming Wang , JO - CSIAM Transactions on Applied Mathematics VL - 2 SP - 277 EP - 295 PY - 2020 DA - 2020/07 SN - 1 DO - http://doi.org/10.4208/csiam-am.2020-0011 UR - https://global-sci.org/intro/article_detail/csiam-am/17178.html KW - Foot and mouth disease, carriers, dynamical model, environment transmission, Lyapunov function. AB -

The epidemic of foot-and-mouth disease (FMD) in cattle remains particular concern in many countries or areas. The epidemic can spread by direct contact with the carrier and symptomatic animals, as well as indirect contact with the contaminated environment. The outbreak of FMD indicates that the infection initially spreads through the farm before spreading between farms. In this paper, considering the cattle population, we establish a dynamical model of FMD with two patches: within-farm and outside-farm, and give the formulae of the basic reproduction number $R$0. By constructing the Lyapunov function, we prove the disease-free equilibrium is globally asymptotically stable when $R$0<1, and that of the unique endemic equilibrium when $R$0>1. By numerical simulations, we confirm the global stability of equilibria. In addition, by carrying out the sensitivity analysis of the basic reproduction number on some parameters, we reach the conclusion that vaccination, quarantining or removing of the carrier and disinfection are the useful control measures for FMD at the large-scale cattle farm.

Feng Li, Zhen Jin, Juan Zhang, Michael Y. Li & Youming Wang. (2020). Dynamical Analysis of Transmission Model of the Cattle Foot-and-Mouth Disease. CSIAM Transactions on Applied Mathematics. 1 (2). 277-295. doi:10.4208/csiam-am.2020-0011
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