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Analysis of a reaction–diffusion SVIR model with a fixed latent period and non-local infections
Applicable Analysis ( IF 1.1 ) Pub Date : 2020-04-08 , DOI: 10.1080/00036811.2020.1750601
Jianguo Gao 1 , Chao Zhang 1 , Jinliang Wang 2
Affiliation  

This paper concerns with a reaction–diffusion susceptible-vaccinated-infectious-recovered model with a fixed latent period. The model is formulated as a non-local and time-delayed reaction–diffusion model due to the fact that an individual infected by the disease in one place may not stay at the same space in the domain due to the movement of human during the incubation period. We then derive the basic reproduction number 0 as the spectral radius of the next infection operator and show that it serves as a threshold role in predicting whether the disease will spread. Further, the explicit formula of basic reproduction number is obtained when all model parameters to be positive constants and the domain to the one-dimensional case. Moreover, we demonstrate the differences in the form of basic reproduction number between the standard incidence and bilinear incidence rate.



中文翻译:

具有固定潜伏期和非局部感染的反应扩散SVIR模型分析

本文关注具有固定潜伏期的反应-扩散易感-接种-感染-恢复模型。该模型被制定为非局部和时间延迟的反应-扩散模型,因为在一个地方感染该疾病的个体可能不会由于人类在孵化期间的移动而留在域中的同一空间时期。然后我们得出基本再生数0作为下一个感染算子的光谱半径,并表明它在预测疾病是否会传播方面起到了阈值作用。进一步,当所有模型参数为正常数且定义域为一维情况时,得到基本再生数的显式公式。此外,我们证明了标准发病率和双线性发病率之间基本再生数形式的差异。

更新日期:2020-04-08
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