Global stability of models of humoral immunity against multiple viral strains

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We analyse, from a mathematical point of view, the global stability of equilibria for models describing the interaction between infectious agents and humoral immunity. We consider the models that contain the variables of pathogens explicitly. The first model considers the situation where only a single strain exists. For the single strain model, the disease steady state is globally asymptotically stable if the basic reproductive ratio is greater than one. The other models consider the situations where multiple strains exist. For the multi-strain models, the disease steady state is globally asymptotically stable. In the model that does not explicitly contain an immune variable, only one strain with the maximum basic reproductive ratio can survive at the steady state. However, in our models explicitly involving the immune system, multiple strains coexist at the steady state.

Original languageEnglish
Pages (from-to)282-295
Number of pages14
JournalJournal of Biological Dynamics
Issue number3
Publication statusPublished - May 2010



  • Global stability
  • Humoral immunity
  • Lasalle's invariance principle
  • Lyapunov function
  • Multiple strains

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Ecology

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