JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (10): 106-121.doi: 10.6040/j.issn.1671-9352.0.2022.666

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A reaction-diffusion model of avian influenza with imperfect vaccination

Mengjie HAN(),Junli LIU*()   

  1. School of Science, Xi'an Polytechnic University, Xi'an 710048, Shaanxi, China
  • Received:2022-12-16 Online:2023-10-20 Published:2023-10-17
  • Contact: Junli LIU E-mail:hmj3040508337@163.com;jlliu2008@126.com

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Abstract:

In this paper, a model of avian influenza with imperfect vaccination reaction-diffusion is established to study the transmission dynamics of avian influenza in birds considering the mobility of birds and environmental heterogeneity. The global existence of the solution of the model is proved, then the basic reproduction number of the model is calculated using the spectral radius of the next generation operator, and the threshold dynamics of the model are analyzed. We also consider the case where the vaccine has 100% preventive effect on birds, the explicit expressions of the basic reproduction number and the principal eigenvalue are given, extinction and persistence of viruses are investigated. Finally, numerical simulations are carried out to analyze the transmission dynamics of avian influenza, effective control strategies for the outbreaks of avian influenza are also discussed. It shows that increasing the coverage of bird vaccination, disinfecting the environment, removing the avian influenza virus in the environment, and reducing the migration of birds are very effective to control the spread of avian influenza.

Key words: avian influenza, reaction-diffusion model, basic reproduction number, persistence

CLC Number: 

  • O175.2

Table 1

Parameter values of System (1.4)-(1.6)"

参数 Λ β θ1 θ2 βW ? c μ ξ γ
取值 2 10-9 0.3 0.3 3.55×10-9 0.32 1.5 $\frac{1}{365}$ 0.1 0.5
参数 ρ $\hat{c}$ δ k T0 T1 a b D
取值 0.4 1.4 $\frac{1}{7}$ 103 13 -18 -0.12 5.1 0.1

Fig.1

When R0 < 1, the time evolution of S(x, t) and I(x, t)"

Fig.2

When R0>1, the time evolution of S(x, t) and I(x, t)"

Fig.3

Basic reproduction number R0's sensitivity to the parameters"

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