On a strain-structured epidemic model

Àngel Calsina, József Z. Farkas

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6 Citations (Scopus)


© 2016 Elsevier Ltd. All rights reserved. We introduce and investigate an SIS-type model for the spread of an infectious disease, where the infected population is structured with respect to the different strain of the virus/bacteria they are carrying. Our aim is to capture the interesting scenario when individuals infected with different strains cause secondary (new) infections at different rates. Therefore, we consider a nonlinear infection process, which generalises the bilinear process arising from the classic mass-action assumption. Our main motivation is to study competition between different strains of a virus/bacteria. From the mathematical point of view, we are interested whether the nonlinear infection process leads to a well-posed model. We use a semilinear formulation to show global existence and positivity of solutions up to a critical value of the exponent in the nonlinearity. Furthermore, we establish the existence of the endemic steady state for particular classes of nonlinearities.
Original languageEnglish
Pages (from-to)325-342
JournalNonlinear Analysis: Real World Applications
Publication statusPublished - 1 Oct 2016


  • Epidemiology
  • Global existence
  • Positive operators
  • Steady states
  • Structured populations
  • Super-spreaders


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