An SIS model is investigated in which the infective individuals are assumed to have an infection-age structure. The model is formulated as an abstract non-densely defined Cauchy problem. We study some dynamical properties of the model by using the theory of integrated semigroups, the Hopf bifurcation theory and the normal form theory for semilinear equations with non-dense domain. Qualitative analysis indicates that there exist some parameter values such that this SIS model has a non-trivial periodic solution which bifurcates from the positive equilibrium. Furthermore, the explicit formulae are given to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions. Numerical simulations are also carried out to support our theoretical results.

中文翻译：

---

具有感染年龄结构的易感染模型的Hopf分叉

研究了SIS模型，其中假定感染个体具有感染年龄结构。该模型被公式化为抽象的非密集定义的柯西问题。我们使用积分半群理论，Hopf分叉理论和非稠密半线性方程组的范式理论研究模型的一些动力学性质。定性分析表明，存在一些参数值，使得该SIS模型具有一个非平凡的周期解，该周期解与正平衡分叉。此外，给出了明确的公式来确定Hopf分支的方向和分支周期解的稳定性。还进行了数值模拟以支持我们的理论结果。