论文标题
多组SAIRS流行模型的全球稳定性
Global stability of multi-group SAIRS epidemic models
论文作者
论文摘要
我们研究了具有疫苗接种的多组SAIRS型流行模型。在人口分裂的群体中，在疾病的传播模式中明确考虑了无症状和有症状的传染病的作用。这是在Ottaviano等人中研究的均质混合SAIRS模型的自然扩展。 AL（2021）到一个社区网络。我们为模型提供了全球稳定性分析。我们确定基本复制号$ \ MATHCAL {R} _0 $的值，并证明如果$ \ Mathcal {r} _0 _0 <1 $ $，则无病平衡在全球渐近稳定。对于没有疫苗接种的SAIRS模型，当$ \ Mathcal {r} _0 = 1 $时，我们也证明了无病平衡的全球渐近稳定性。此外，如果$ \ Mathcal {r} _0> 1 $，则无病平衡是不稳定的，并且存在独特的地方平衡。首先，我们研究了原始模型的两种变体，研究了地方性平衡的局部渐近稳定性及其随后的全球稳定性。最后，我们提供数值模拟，以比较不同网络拓扑上的流行病扩散。
We study a multi-group SAIRS-type epidemic model with vaccination. The role of asymptomatic and symptomatic infectious individuals is explicitly considered in the transmission pattern of the disease among the groups in which the population is divided. This is a natural extension of the homogeneous mixing SAIRS model with vaccination studied in Ottaviano et. al (2021) to a network of communities. We provide a global stability analysis for the model. We determine the value of the basic reproduction number $\mathcal{R}_0$ and prove that the disease-free equilibrium is globally asymptotically stable if $\mathcal{R}_0 < 1$. In the case of the SAIRS model without vaccination, we prove the global asymptotic stability of the disease-free equilibrium also when $\mathcal{R}_0=1$. Moreover, if $\mathcal{R}_0 > 1$, the disease-free equilibrium is unstable and a unique endemic equilibrium exists. First, we investigate the local asymptotic stability of the endemic equilibrium and subsequently its global stability, for two variations of the original model. Last, we provide numerical simulations to compare the epidemic spreading on different networks topologies.
