Asymptotic expansions are presented for stationary and conditional quasi-stationary distributions of nonlinearly perturbed birth-death-type semi-Markov models, as well as algorithms for computing the coefficients of these expansions. Three types of applications are discussed in detail. The first is a model of population growth, where either an isolated population is perturbed by immigration, or a sink population with immigration is perturbed by internal births. The second application is epidemic spread of disease, in which a closed population is perturbed by infected individuals from outside. The third model captures the time dynamics of the genetic composition of a population with genetic drift and selection, that is perturbed by various mutation scenarios.
CITATION STYLE
Silvestrov, D., Petersson, M., & Hössjer, O. (2018). Nonlinearly perturbed birth-death-type models. In Springer Proceedings in Mathematics and Statistics (Vol. 271, pp. 189–244). Springer New York LLC. https://doi.org/10.1007/978-3-030-02825-1_11
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