Nonlinearly Perturbed Birth-Death-Type Models

  • Dmitrii Silvestrov
  • Mikael Petersson
  • Ola Hössjer
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 271)


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.


Semi-Markov birth-death process Quasi-stationary distribution Nonlinear perturbation Population dynamics model Population genetics model Epidemic model 


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Dmitrii Silvestrov
    • 1
  • Mikael Petersson
    • 2
  • Ola Hössjer
    • 1
  1. 1.Department of MathematicsStockholm UniversityStockholmSweden
  2. 2.Statistics SwedenStockholmSweden

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