Global asymptotic properties of a delay SIR epidemic model with finite incubation times
Global asymptotic properties of a delay SIR epidemic model with finite incubation times
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DOI：
10.1016/s0362-546x(99)00138-8
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发表时间：
2000-11-01
影响因子：
1.4
通讯作者：
Beretta, E
中科院分区：
文献类型：
--
作者：
Takeuchi, Y;Ma, WB;Beretta, E
在这一节中，我们给出了由媒介（蚊子）传播的流行病（如疟疾）的方程，媒介（蚊子）有一个潜伏期，可以传染。该模型将产生一个系统的分布延迟微分方程。Cooke [6]提出了一个传染病传播模型（仅涉及易感者和感染个体），该模型通过媒介（如蚊子）在潜伏期后传播。Busenberg和Cooke [5]、Marcati和Pozio [11]和Volz [13]考虑了他的模型的扩展。Thieme [12]也考虑了Cooke的模型，通过根据蚊子叮咬的平均频率（媒介）对种群进行连续分层来扩展模型。本模型仍然可以被认为是库克模型的扩展。我们假设：（A）人口由具有生命动力学的SIR模型描述，其中人口的总规模N是常数（见[8]）。因此死亡常数率
In this section we present the equations for epidemics (eg malaria) spread by vectors (mosquitoes) which have an incubation time to become infectious. The model will give rise to a system of distributed delay differential equations. A model for the spread of an infectious disease (involving only susceptibles and infective individuals) transmitted by a vector (eg mosquitoes) after an incubation time, was proposed by Cooke [6]. Extensions of his model were considered by Busenberg and Cooke [5], Marcati and Pozio [11] and Volz [13]. Thieme [12] has also considered the model by Cooke, extending the model by continuously stratifying the population according to the average frequency of the bites by a mosquito (the vector). The present model still can be considered an extension of Cooke’s model. We assume that:(A) Human population is described by an SIR model with vital dynamics where the total size N of human population is constant (see [8]). Hence the death constant rate