We present a deterministic SEIR model of the said form. The population in point can be considered as consisting of a local population together with a migrant subpopulation. The migrants come into the local population for a short stay. In particular, the model allows for a constant inflow of individuals into different classes and constant outflow of individuals from the R-class. The system of ordinary differential equations has positive solutions and the infected classes remain above specified threshold levels. The equilibrium points are shown to be asymptotically stable. The utility of the model is demonstrated by way of an application to measles.

中文翻译：

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带有感染移民和康复移民的 SEIR 模型

我们提出了上述形式的确定性 SEIR 模型。点上的人口可以被认为是由本地人口和移民亚人口组成。移民进入当地居民短暂停留。特别是，该模型允许个体不断流入不同的类，而个体不断地从 R 类流出。常微分方程组有正解，受感染的类别保持在指定的阈值水平以上。平衡点被证明是渐近稳定的。该模型的实用性通过对麻疹的应用得到了证明。