Nonlinear Physiologically Structured Population Models with Two Internal Variables

Hao Kang, Xi Huo, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


First-order hyperbolic partial differential equations with two internal variables have been used to model biological and epidemiological problems with two physiological structures, such as chronological age and infection age in epidemic models, age and another physiological character (maturation, size, stage) in population models, and cell-age and molecular content (cyclin content, maturity level, plasmid copies, telomere length) in cell population models. In this paper, we study nonlinear double physiologically structured population models with two internal variables by applying integrated semigroup theory and non-densely defined operators. We consider first a semilinear model and then a nonlinear model, use the method of characteristic lines to find the resolvent of the infinitesimal generator and the variation of constant formula, apply Krasnoselskii’s fixed point theorem to obtain the existence of a steady state, and study the stability of the steady state by estimating the essential growth bound of the semigroup. Finally, we generalize the techniques to investigate a nonlinear age-size structured model with size-dependent growth rate.

Original languageEnglish (US)
Pages (from-to)2847-2884
Number of pages38
JournalJournal of Nonlinear Science
Issue number6
StatePublished - Dec 1 2020


  • Cauchy problem with non-dense domain
  • Infinitesimal generator
  • Integrated semigroups
  • Physiological structure
  • Spectrum theory
  • Stability

ASJC Scopus subject areas

  • Modeling and Simulation
  • Engineering(all)
  • Applied Mathematics


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