Medical statistics reveal a significant dependence of hospitalized dengue patient on the patient's age. To incorporate an age-dependence into a mathematical model, we extend the classical ODE system of disease dynamics to a PDE system. The equilibrium distribution is then determined by the fixed points of resulting integro-differential equations. In this paper we use an extension of the concept of the basic reproductive number to characterize parameter regimes, where either only the disease-free or an endemic equilibrium exists. Using rather general and minimal assumptions on the population distribution and on the age-dependent transmission rate, we prove the existence of those equilibria. Furthermore, we are able to prove the convergence of an iteration scheme to compute the endemic equilibrium. To validate our model, we use existing data from the city of Semarang, Indonesia for comparison and to identify the model parameters.

中文翻译：

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登革热传播的年龄相关模型：与现场数据的分析和比较

医学统计数据显示，住院登革热患者对患者年龄的依赖性很大。为了将年龄依赖性纳入数学模型，我们将经典的疾病动力学 ODE 系统扩展到 PDE 系统。然后平衡分布由所得积分微分方程的不动点确定。在本文中，我们使用基本再生数概念的扩展来表征参数制度，其中仅存在无病平衡或地方病平衡。对人口分布和年龄相关的传播率使用相当普遍和最小的假设，我们证明了这些平衡的存在。此外，我们能够证明迭代方案的收敛性来计算地方性均衡。为了验证我们的模型，