Monotonicity of the number of passages in linear chains and of the basic reproduction number in epidemic models

J. Müller, K. P. Hadeler

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

In models for infectious diseases, the basic reproduction number is the crucial parameter which determines the possibility of an outbreak. In simple situations it depends in a monotone way on the infectivity. Non-monotone behavior may occur in diseases where infectivity depends on time since infection and where transmission depends on social structure, as is shown by an example. A typical application is the HIV infection where transmission rates depend on existing pair bonds and infectivity changes drastically over time. For a class of epidemic models with pair formation models and infectivity depending on time since infection it is shown that the basic reproduction number is a monotone function of infectivity. This observation is a consequence of a general result on a class of cyclic linear reaction chains with tridiagonal structure for which it is shown that the number of passages depends in a monotone way on the rates.

Original languageEnglish
Pages (from-to)61-75
Number of pages15
JournalZeitschrift fur Analysis und ihre Anwendung
Volume19
Issue number1
StatePublished - 2000
Externally publishedYes

Keywords

  • Basic reproduction number
  • Epidemiology
  • Linear chain
  • Markov chain

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