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

Mathew P Dafilis, Federico Frascoli, James G Wood, James M McCaw

Abstract


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

Keywords


infectious disease, mathematical model, dynamical systems



DOI: http://dx.doi.org/10.21914/anziamj.v54i0.5886



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.