Equilibrium Equations for Human Populations with Immigration
F. Thomas Bruss

TL;DR
This paper develops a new resource-dependent model to analyze the conditions for equilibrium in human populations with immigration, considering factors like natality, productivity, consumption, and policies, providing insights for policy-making.
Contribution
It introduces a comprehensive model based on Resource Dependent Branching Processes to study equilibrium criteria in populations with immigration, including integration and continuous immigration effects.
Findings
Equilibrium conditions are often strict and sensitive.
Control measures' feasibility and efficiency are analyzed.
Preliminary suggestions for optimal immigration policies are provided.
Abstract
The objective of this article is to create a framework to study asymptotic equilibria in human populations with a special focus on immigration. We present a new model, based on Resource Dependent Branching Processes, which is now broad enough to cope with the goal of finding equilibrium criteria under reasonable hypotheses. Our equations are expressed in terms of natality rates, mean productivity and mean consumption of the home-population and the immigrant population as well as policies of the Society to distribute resources among individuals. We also study the impact of integration of one sub-population into the other one, and in a third model, the additional influence of a continuous stream of new immigrants. Proofs of the results are based on classical limit theorems, on Borel-Cantelli type arguments, on the Theorem of envelopment of Bruss and Duerinckx (2015), on a maximum…
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Taxonomy
TopicsStochastic processes and statistical mechanics · Markov Chains and Monte Carlo Methods · Mathematical and Theoretical Epidemiology and Ecology Models
