On the interaction between the immune system and an exponentially replicating pathogen

Alberto D'Onofrio

Research output: Contribution to journalArticlepeer-review


In this work, we generalize the Pugliese-GandolfiModel [A. Pugliese and A. Gandolfi, Math Biosc, 214,73 (2008)] of interaction between an exponentially replicating pathogen and the immune system. After the generalization, we study the properties of boundedness and unboundedness of the solutions, and we also give a condition for the global eradication as well as for the onset of sustained oscillations. Then, we study the condition for the uniqueness of the arising limit cycle, with numerical applications to the Pugliese-Gandolfi model. By means of simulations, we also show some alternative ways to reaching the elimination of the pathogen and interesting effects linked to variations in aspecific immune response. After shortly studying some pathological cases of interest, we include in our model distributed and constant delays and we show that also delays may unstabilize the equilibria.

Original languageEnglish
Pages (from-to)579-602
Number of pages24
JournalMathematical Biosciences and Engineering
Issue number3
Publication statusPublished - Jul 2010


  • Delay Differential Equations
  • Immunology
  • Limit cycles

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Applied Mathematics
  • Computational Mathematics
  • Modelling and Simulation
  • Medicine(all)


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