论文标题
接种疫苗的爵士模型：分叉分析
SIR model with vaccination: bifurcation analysis
论文作者
论文摘要
在文献中，很少有改编的SIR模型结合了疫苗接种和逻辑生长。在本文中，我们研究了SIR模型的分叉，其中易感人群会在逻辑上生长，并经常接受疫苗接种。我们明确地证明了地方性平衡是参数空间$（\ Mathcal {r} _0，p）$中的两个奇异性，其中$ \ Mathcal {r} _0 $是基本的再现号码，$ p $是成功疫苗在出生时接种疫苗的比例。 我们明确表现出Hopf，跨批评，Belyakov，杂节和鞍形节点分叉曲线展现了奇异性。这两个参数$（\ Mathcal {r} _0，p）$以有用的方式编写，以评估消除疾病所必需的疫苗接种人的比例，并结论如何影响疫苗接种可能影响流行病的结果。我们还在疾病持续存在的参数空间中展示了该区域，并通过数值模拟说明了我们的主要结果，并强调了参数的作用。
There are few adapted SIR models in the literature that combine vaccination and logistic growth. In this article, we study bifurcations of a SIR model where the class of Susceptible individuals grows logistically and has been subject to constant vaccination. We explicitly prove that the endemic equilibrium is a codimension two singularity in the parameter space $(\mathcal{R}_0, p)$, where $\mathcal{R}_0$ is the basic reproduction number and $p$ is the proportion of Susceptible individuals successfully vaccinated at birth. We exhibit explicitly the Hopf, transcritical, Belyakov, heteroclinic and saddle-node bifurcation curves unfolding the singularity. The two parameters $(\mathcal{R}_0, p)$ are written in a useful way to evaluate the proportion of vaccinated individuals necessary to eliminate the disease and to conclude how the vaccination may affect the outcome of the epidemic. We also exhibit the region in the parameter space where the disease persists and we illustrate our main result with numerical simulations, emphasizing the role of the parameters.
