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.
Keywords: Lotka-Sharpe-McKendrick system; age-structured population model; explicit solution; insect population model; neutral delay differential equation; r-Lambert W function.