This paper deals with the global dynamics for a SLIS epidemic model with infection age. In our model, we also consider the time delay in the progression from the latent individuals to becoming infectious individuals. We verify the well posedness of the model by changing it into an abstract nondensely defined Cauchy problem and find conditions for the existence of disease free equilibrium and endemic equilibrium. The theoretic analysis shows that the disease-free equilibrium is globally asymptotically stable as the basic reproduction number $R_{0}$ is less than unity and that the endemic equilibrium is locally asymptotically stable and the system is uniformly persistent as $R_{0}$ is greater than unity. The numerical simulations illustrate that the endemic equilibrium may be asymptotically stable as $R_{0}>1$.

中文翻译：

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具有时滞的年龄结构SLIS模型的全局动力学

本文讨论了具有感染年龄的SLIS流行病模型的全局动力学。在我们的模型中，我们还考虑了从潜在个体到成为传染性个体的时间延迟。我们通过将模型更改为抽象的非密集定义的柯西问题来验证模型的适定性，并找到无病均衡和地方均衡存在的条件。理论分析表明，无病平衡在全局渐近稳定，因为基本繁殖数$ R_ {0} $小于1，地方病平衡在局部渐近稳定，并且系统统一持久性为$ R_ {0} $大于1。数值模拟表明，当$ R_ {0}> 1 $时，地方均衡可以渐近稳定。