论文标题
针对线性出生率，免疫力丧失，疫苗接种以及疾病以及疫苗接种死亡的SIR-PH流行模型的新结果和开放问题
New results and open questions for SIR-PH epidemic models with linear birth rate, loss of immunity, vaccination, and disease and vaccination fatalities
论文作者
论文摘要
我们的论文介绍了三个新的模型类别：Sir-PH，Sir-PH-FA和SIR-PH-IA，并指出了我们想解决的两个问题。回想一下，确定性的数学流行病学具有一项基本的一般法律，即“ [52，51]的R0替代性，它指出，无疾病无疾病平衡的局部稳定性条件可以表示为r0 <1，其中R0是著名的基本复制数，在分支的理论中也表明了一般法律，这是一般性的。 1。当r0> 1时，存在一个独特的固定地方性点，并且 2。当R0> 1时，地方性点在局部稳定。 人们想为大量现实的流行病模型建立这些特性（我们不包括没有人员伤亡的流行病）。我们在[7，5]中引入了一种“简单”但具有不同人口的“ SIR-PH模型”类别，其明确目的是为这些过程建立上述两个属性。由于这似乎仍然很难，我们引入了一类“ Sir-PH-FA”模型，可以将其解释为SIR-PH模型的近似值，其中包括通常在文献中研究的简单模型（具有恒定的人口，没有免疫力等）。我们论文的目的是提请人们注意上面的两个开放问题，即SIR-PH，SIR-PH-FA，以及第二个更精致的“中间近似” Sir-ph-ia。我们通过在[44，40]的SAIRS流行模型的概括中提出新结果来说明当前状态。
Our paper presents three new classes of models: SIR-PH, SIR-PH-FA, and SIR-PH-IA, and states two problems we would like to solve about them. Recall that deterministic mathematical epidemiology has one basic general law, the R0 alternative" of [52, 51], which states that the local stability condition of the disease free equilibrium may be expressed as R0 < 1, where R0 is the famous basic reproduction number, which plays also a major role in the theory of branching processes. The literature suggests that it is impossible to find general laws concerning the endemic points. However, it is quite common that 1. When R0 > 1, there exists a unique fixed endemic point, and 2. the endemic point is locally stable when R0 > 1. One would like to establish these properties for a large class of realistic epidemic models (and we do not include here epidemics without casualties). We have introduced in [7, 5] a "simple", but broad class of "SIR-PH models" with varying population, with the express purpose of establishing for these processes the two properties above. Since that seemed still hard, we have introduced a further class of "SIR-PH-FA" models, which may be interpreted as approximations for the SIR-PH models, and which includes simpler models typically studied in the literature (with constant population, without loss of immunity, etc). The goal of our paper is to draw attention to the two open problems above, for the SIR-PH, SIR-PH-FA, and also for a second, more refined "intermediate approximation" SIR-PH-IA. We illustrate the current status-quo by presenting new results on a generalization of the SAIRS epidemic model of [44, 40].
