Structured population models, which account for the state of individuals given features such as age, gender, and size, are widely used in the fields of ecology and biology. In this paper, we consider an age-structured population model describing the population of adults and juveniles. The model consists of a system of ordinary and neutral delay differential equations. We present an explicit solution to the model using a generalization of the Lambert W function called the r-Lambert W function. Numerical simulations with varying parameters and initial conditions are done to illustrate the obtained solution. The proposed method is also applied to an insect population model with long larval and short adult phases.

中文翻译：

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使用r -Lambert W函数的涉及中性时滞微分方程的Lotka-Sharpe-McKendrick系统的显式解

结构化的人口模型可以解释具有特定特征（例如年龄，性别和大小）的个体状态，已广泛用于生态和生物学领域。在本文中，我们考虑了描述成年人和青少年人口的年龄结构人口模型。该模型由一个普通和中性时滞微分方程系统组成。我们使用称为r -Lambert W函数的Lambert W函数的泛化为模型提供了一个明确的解决方案。进行了具有可变参数和初始条件的数值模拟，以说明获得的解决方案。所提出的方法也适用于具有长幼虫期和短成虫期的昆虫种群模型。