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

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Dafilis MP, Frascoli F, Wood JG, McCaw JM, The influence of increasing life expectancy on the dynamics of SIRS systems with immune boosting, Australian New Zealand Industrial and Applied Mathematics Journal 54:50-63 (2012). doi:10.1017/S1446181113000023.


Endemic infectious diseases constantly circulate in human populations, with prevalence fluctuating about a (theoretical and unobserved) time-independent equilibrium prevalence. 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 multi-annual fluctuations are observed, whereas the SIRS model is characterised by damped oscillatory dynamics for all biologically meaningful choices of model parameters.

Here, 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 persists. 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 life-long, with potential implications for disease control strategies.