Mathematical analysis on an age-structured SIS epidemic model with nonlocal diffusion

Hao Kang, Shigui Ruan

Research output: Contribution to journalArticlepeer-review


In this paper we propose an age-structured susceptible-infectious-susceptible epidemic model with nonlocal (convolution) diffusion to describe the geographic spread of infectious diseases via long-distance travel. We analyze the well-posedness of the model, investigate the existence and uniqueness of the nontrivial steady state corresponding to an endemic state, and study the local and global stability of this nontrivial steady state. Moreover, we discuss the asymptotic properties of the principal eigenvalue and nontrivial steady state with respect to the nonlocal diffusion rate. The analysis is carried out by using the theory of semigroups and the method of monotone and positive operators. The spectral radius of a positive linear operator associated to the solution flow of the model is identified as a threshold.

Original languageEnglish (US)
Pages (from-to)5
Number of pages1
JournalJournal of Mathematical Biology
Issue number1
StatePublished - Jun 26 2021


  • Age-structure
  • Global dynamics
  • Monotone and positive operators
  • Nonlocal diffusion
  • Principal eigenvalue
  • Semigroup theory
  • SIS model

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


Dive into the research topics of 'Mathematical analysis on an age-structured SIS epidemic model with nonlocal diffusion'. Together they form a unique fingerprint.

Cite this