Dynamics of a Two Subpopulations System Including Immigration

Abstract

Abstract. The phenomenon of replacement migration into declining population prompts development of multicomponent models in population dynamics. We propose a simple model of population including resident and migrant components with migration flow as an external input. The main assumption is that offspring that are born to migrants will have the same vital rates as the resident population. The proposed model is based on partial differential equation to take into account the age structure of the population. The formulae for exact solutions are derived. We focus on the case when native population declines in the absence of migration. Assuming a sufficiently large constant growth rate of migration we obtain asymptotic solutions as t → ∞. Using the asymptotic solutions, we have calculated "critical" value of growth rate of migrant inflow that is the value that provides, as time tends to infinity, the equal number of residents and migrants in the population. We provide numerical illustrations using demographic data for Germany in 2010.

Incorporating Migration Into an Age-Structured Population Model With Variable Mortality Rate

“…Here, the authors fit smooth curves to the birth, death, and migration data in order to make predictions about future population estimates. In a recent study, the authors consider immigration by modifying the McKendrick-von Foerster model into two separate equations, one for the resident population and the second for migrant population [18]. Another approach extends the McKendrick-von Foerster model in an environment divided into patches, allowing for migration between patches [17].…”

“…Instead of the McKendrick-von Foerster model, one approach was to add a non-negative age-dependent migration function to the similar Lotka-von Foerster system [11]. All of these models involve adding a term to the original model, and our approach is similar to that of [14,18,27]. We consider our base model to be the McKendrick-von Foerster model, since it is a first-order partial differential equation and can be solved using analytical methods.…”

Epidemiology and Ecoepidemiology: Introduction to the Special Issue

“…An age-structured demographic model is considered by A. Zincenko and S. Petrovskii [7] to explore the dynamics of a system consisting of two subpopulations and including immigrations. The latter describe the resident as well as the immigrating individuals.…”