Avian-human influenza epidemic model with diffusion

Kim, Kwang Ik; Lin, Zhigui; Zhang, Lai

doi:10.1016/j.nonrwa.2008.11.015

Cited by 59 publications

(41 citation statements)

References 20 publications

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“…In that case, E + corresponds to an endemic state in which a part of the population remains infected. Those facts suggest that the parameter r 0 depends on the capacity of farm c, the constant ω, and the removal rate m. Stability of constant solutions of nonlinear system such as system (4) has been studied by other authors [2]. Let µ be the eigenvalue of the operator −∆ with homogeneous boundary conditions on the interval [0, l], that is,…”

Section: Mathematical Model With Spatial Virus Diffusionmentioning

confidence: 99%

“…A disease transmission model with diffusive terms to investigate spatial spread of Avian Influenza among flock and human were studied [9]. A diffusive epidemic that describes the transmission of Avian Influenza among birds and humans is investigated [2]. Mathematical models for bird flu infection process within a poultry farm were also proposed in previous study [5,6,8,10].…”

Section: Introductionmentioning

confidence: 99%

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Study on Bird Flu Infection Process within a Poultry Farm with Effects of Spatial Diffusion

Putri¹,

Watanabe²,

Nova³

2017

ujar

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We describe an ODE model and a PDE model.A nonlinear diffusion system of partial differential equations is analyzed for investigation of bird flu transmission process within a poultry farm. Effect of threshold number that gives measure of infectious intensity is investigated. It depends on three factors: removal of infected birds, vaccination, and capacity of the farm. Our analysis shows that the transmission of bird flu within a poultry farm is expressible in terms of traveling wave solutions. It also shows a spatial significance of diffusivity.

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Section: Mathematical Model With Spatial Virus Diffusionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Study on Bird Flu Infection Process within a Poultry Farm with Effects of Spatial Diffusion

Putri¹,

Watanabe²,

Nova³

2017

ujar

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“…Therefore, there exists I * 5 in the interval (18), such that F(I * 5 ) = 1. Once I * 5 is determined, the remaining values of the equilibrium can be determined as follows:…”

Section: A Solution Of the Equation F (I ) = 1 Withmentioning

confidence: 99%

“…Time dependent optimal control strategies for the prevention of avian influenza pandemic were discussed in [17]. Spatial spread of avian influenza was the focus of [16,18,21].…”

Section: Introductionmentioning

confidence: 99%

An evolutionary model of influenza A with drift and shift

Martcheva

2012

Journal of Biological Dynamics

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Influenza A virus evolves through two types of evolutionary mechanisms -drift and shift. These two evolutionary mechanisms allow the pathogen to infect us repeatedly, as well as occasionally create pandemics with large morbidity and mortality. Here we introduce a novel model that incorporates both evolutionary mechanisms. This necessitates the modelling of three types of strains -seasonal human strains, bird-to-human transmittable H5N1 strains and evolved pandemic H5N1 strain. We define reproduction and invasion reproduction numbers and use them to establish the presence of dominant and coexistence equilibria. We find that the amino acid substitution structure of human influenza can destabilize the human influenza equilibrium and sustained oscillations are possible. We find that for low levels of infection in domestic birds, these oscillations persist, inducing oscillations in the number of humans infected with the avian flu strain. The oscillations have a period of 365 days, similar to the one that can be observed in the cumulative number of human H5N1 cases reported by the World Health Organization (WHO). Furthermore, we establish some partial global results on the competition of the strains.

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“…Two similar theoretical models [53][54] have assessed the likelihood of transmission between birds and people for avian influenza and a mutant influenza, but depending on the formulation/parameterization of the models, present different conclusions regarding the effectiveness of culling infected birds and the eventual probability of a pandemic occurring. The method used is stability analysis, which can give useful, quick results on whether an epidemic will continue or die out; however, at the present time it is unlikely that accurate data would be available to populate these detailed transmission models during the first stages of an outbreak.…”

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confidence: 99%