Threshold dynamics of an infective disease model with a fixed latent period and non-local infections

被引:94
作者
Guo, Zhiming [2 ]
Wang, Feng-Bin [1 ]
Zou, Xingfu [1 ]
机构
[1] Univ Western Ontario, Dept Appl Math, London, ON N6A 5B7, Canada
[2] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Guangdong, Peoples R China
基金
加拿大自然科学与工程研究理事会;
关键词
Infectious disease model; Reaction-diffusion equation; Non-local infection; Delay; Principal eigenvalue; Basic reproduction number; DIFFERENTIAL-EQUATIONS; SYSTEMS; TRANSMISSION; POPULATION;
D O I
10.1007/s00285-011-0500-y
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
In this paper, we derive and analyze an infectious disease model containing a fixed latency and non-local infection caused by the mobility of the latent individuals in a continuous bounded domain. The model is given by a spatially non-local reaction-diffusion system carrying a discrete delay associated with the zero-flux condition on the boundary. By applying some existing abstract results in dynamical systems theory, we prove the existence of a global attractor for the model system. By appealing to the theory of monotone dynamical systems and uniform persistence, we show that the model has the global threshold dynamics which can be described either by the principal eigenvalue of a linear non-local scalar reaction diffusion equation or equivalently by the basic reproduction number R-0 for the model. Such threshold dynamics predicts whether the disease will die out or persist. We identify the next generation operator, the spectral radius of which defines basic reproduction number. When all model parameters are constants, we are able to find explicitly the principal eigenvalue and R-0. In addition to computing the spectral radius of the next generation operator, we also discuss an alternative way to compute R-0.
引用
收藏
页码:1387 / 1410
页数:24
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