Modeling avian influenza using Filippov systems to determine culling of infected birds and quarantine

Chong, Nyuk Sian; Smith, Robert J.

doi:10.1016/j.nonrwa.2015.02.007

Cited by 34 publications

(15 citation statements)

References 28 publications

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“…Wang and Wu [55] constructed a periodic systems of delay differential equations modeling the spread of avian influenza by migratory birds between the refuge ground and the summer breeding site. Chong and Smith [12] proposed two Filippov models with threshold policy to determine culling of infected birds and quarantine.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of avian influenza epidemic models

Liu

Ruan

Zhang

2017

Mathematical Biosciences

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Avian influenza is a zoonotic disease caused by the transmission of the avian influenza A virus, such as H5N1 and H7N9, from birds to humans. The avian influenza A H5N1 virus has caused more than 500 human infections worldwide with nearly a 60% death rate since it was first reported in Hong Kong in 1997. The four outbreaks of the avian influenza A H7N9 in China from March 2013 to June 2016 have resulted in 580 human cases including 202 deaths with a death rate of nearly 35%. In this paper, we construct two avian influenza bird-to-human transmission models with different growth laws of the avian population, one with logistic growth and the other with Allee effect, and analyze their dynamical behavior. We obtain a threshold value for the prevalence of avian influenza and investigate the local or global asymptotical stability of each equilibrium of these systems by using linear analysis technique or combining Liapunov function method and LaSalle's invariance principle, respectively. Moreover, we give necessary and sufficient conditions for the occurrence of periodic solutions in the avian influenza system with Allee effect of the avian population. Numerical simulations are also presented to illustrate the theoretical results.

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Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of avian influenza epidemic models

Liu

Ruan

Zhang

2017

Mathematical Biosciences

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“…Proactive culling is described through a classical ODE continuous system, while reactive culling is described through a piecewise-smooth system where the control activities are implemented when the number of infected individuals exceeds a given threshold. Models implementing sliding control have been already developed in recent years for different infections, such as West Nile Virus [48], avian influenza [17,16], and SARS [47]. Here, we find that, localized culling implemented in one of the patches may lead to an unexpected increase in the number of infected individuals in the other patch.…”

Section: Discussionmentioning

confidence: 71%

Dynamics of a metapopulation epidemic model with localized culling

Bolzoni¹,

Marca²,

Groppi³

et al. 2020

Discrete &Amp; Continuous Dynamical Systems - B

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“…Chong et al [25] considered an avian-only model considering a threshold policy. The authors chose the number of infected birds as an index, that is, once the index exceeds the threshold level I T , culling of infected birds is employed, otherwise, no action is taken.…”

Section: Introductionmentioning

confidence: 99%

Rich dynamics of a Filippov avian-only influenza model with a nonsmooth separation line

Yang

Wang

2021

Adv Differ Equ

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Depopulation of birds has been authenticated to be an effective measure in controlling avian influenza transmission. In this work, we establish a Filippov avian-only model incorporating a threshold policy control. We choose the index—the maximum between the infected threshold level $I_{T}$ I T and the product of the number of susceptible birds S and a ratio threshold value ξ—to decide on whether to trigger the control measures or not, which then leads to a discontinuous separation line and two pieces of sliding-mode domains. Meanwhile, one more sliding-mode domain gives birth to more complex dynamics. We investigate the global dynamical behavior of the Filippov model, including the real and/or virtual equilibria and the two sliding modes and their dynamics. The solutions will eventually stabilize at the real endemic equilibrium of the subsystem or the pseudoequilibria on the two sliding modes due to different threshold values. Therefore an effective and efficient threshold policy is essential to control the influenza by driving the number of infected birds below a certain level or at a previously given level.

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Modeling avian influenza using Filippov systems to determine culling of infected birds and quarantine

Cited by 34 publications

References 28 publications

Nonlinear dynamics of avian influenza epidemic models

Nonlinear dynamics of avian influenza epidemic models

Dynamics of a metapopulation epidemic model with localized culling

Rich dynamics of a Filippov avian-only influenza model with a nonsmooth separation line

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