Convergence of a Discrete-Time Age-Structured Population Toward a Given Steady State Through Controlled Immigration

To explore the concept of stability in an age-structured population with migration, a Markov transition matrix model is built, where age classes can be of different length, and the time step is not necessarily equal to the length of the age class. The conditions under which a vector of the model has a steady population structure are identified, as well as those under which the age structure converges to a given steady state, through a series of decisions or controls of letting immigrants in or forbidding them entry into the country. The decisions are expressed as vectors of proportions of immigrants. In the steady state, when the increment of population is proportional to its size, the age- or stage-structure remains unchanged between transitions.