具有不完全接种的反应扩散禽流感模型

doi:10.6040/j.issn.1671-9352.0.2022.666

摘要/Abstract

摘要：

考虑鸟类流动性和环境异质性, 建立具有不完全接种的反应扩散禽流感模型, 研究鸟类中禽流感的传播动态。首先证明模型解的全局存在性, 其次利用下一代算子的谱半径方法计算模型的基本再生数, 分析模型的阈值动力学。此外, 考虑疫苗对鸟类起到100%预防作用的情况, 给出基本再生数和主特征值的显式表达式, 研究了病毒的灭绝和持续性。最后进行数值模拟, 分析禽流感的传播动力学并研究禽流感爆发的有效控制策略。结果表明, 提高鸟类接种疫苗的覆盖率, 及时对环境进行消毒, 清除环境中的禽流感病毒, 减少鸟类流动性对控制禽流感的传播是非常有效的。

关键词: 禽流感, 反应扩散模型, 基本再生数, 持久性

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

中图分类号:

O175.2

韩梦洁,刘俊利. 具有不完全接种的反应扩散禽流感模型[J]. 《山东大学学报(理学版)》, 2023, 58(10): 106-121.

Mengjie HAN,Junli LIU. A reaction-diffusion model of avian influenza with imperfect vaccination[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(10): 106-121.

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参考文献 28

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参数	Λ	β	θ₁	θ₂	β_W	?	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

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