The influence of increasing life expectancy on the dynamics of SIRS systems with immune boosting


  • Mathew P Dafilis University of Melbourne
  • Federico Frascoli University of Melbourne
  • James G Wood University of New South Wales
  • James M McCaw University of Melbourne



infectious disease, mathematical model, dynamical systems


Endemic infectious diseases constantly circulate in human populations, with prevalence fluctuating about a (theoretical and unobserved) time-independent equilibrium. For diseases for which acquired immunity is not lifelong, the classic susceptible–infectious– recovered–susceptible (SIRS) model provides a framework within which to consider temporal trends in the observed epidemiology. However, in some cases (notably pertussis), sustained multiannual fluctuations are observed, whereas the SIRS model is characterized by damped oscillatory dynamics for all biologically meaningful choices of model parameters. We show that a model that allows for “boosting†of immunity may naturally give rise to undamped oscillatory behaviour for biologically realistic parameter choices. The life expectancy of the population is critical in determining the characteristic dynamics of the system. For life expectancies up to approximately 50 years, we find that, even with boosting, damped oscillatory dynamics persist. For increasing life expectancy, the system may sustain oscillatory dynamics, or even exhibit bistable behaviour, in which both stable point attractor and limit cycle dynamics may coexist. Our results suggest that rising life expectancy may induce changes in the characteristic dynamics of infections for which immunity is not lifelong, with potential implications for disease control strategies. doi:10.1017/S1446181113000023

Author Biographies

Mathew P Dafilis, University of Melbourne

Research Fellow Melbourne School of Population Health

Federico Frascoli, University of Melbourne

Research Fellow Department of Mathematics and Statistics

James G Wood, University of New South Wales

Senior Lecturer School of Public Health and Community Medicine

James M McCaw, University of Melbourne

ARC Future Fellow Melbourne School of Population Health





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