Nonlinearly Perturbed Birth-Death-Type Models

TL;DR

This paper develops asymptotic expansions for stationary and quasi-stationary distributions in nonlinearly perturbed birth-death semi-Markov models, with applications to population dynamics, epidemics, and genetics.

Contribution

It introduces new asymptotic expansion techniques for complex birth-death models under nonlinear perturbations, extending previous linear approaches.

Findings

Derived asymptotic formulas for stationary distributions

Analyzed quasi-stationary distributions under perturbations

Applied methods to biological and epidemiological models

Abstract

Asymptotic expansions for stationary and conditional quasi-stationary distributions of nonlinearly perturbed birth-death-type semi-Markov models are presented. Applications to models of population growth, epidemic spread and population genetics are discussed.