# Complex multiannual cycles of Mycoplasma pneumoniae: Persistence and the role of stochasticity

## TL;DR

This paper explains the complex outbreak cycles of Mycoplasma pneumoniae using mathematical models and shows how randomness in host behavior helps sustain these cycles.

## Contribution

The study introduces a novel explanation for M. pneumoniae's multiannual cycles using quasicycles and stochasticity.

## Key findings

- Mycoplasma pneumoniae's 5-year cycle is explained by quasicycles and loss of immunity.
- Environmental stochasticity stabilizes multiannual cycles in smaller populations.
- Cycles can be disrupted by large perturbations like NPIs from the COVID-19 pandemic.

## Abstract

The bacterium Mycoplasma pneumoniae causes respiratory illness worldwide and is known for its complex and poorly understood multiannual outbreak cycles. By fitting a mechanistic mathematical model to data from Denmark spanning several decades, we find a parsimonious explanation for the persistent 5-y periodicity, in the form of quasicycles. A deterministic model explains the periodicity and shape of the cycles, while environmental randomness—such as variability in host contact patterns—is needed to sustain them. The work has practical implications for predicting the epidemiological dynamics of M. pneumoniae across diverse settings and suggests that noise-induced dynamics should be considered as a potential driver of complex cycles in other endemic pathogens.

The epidemiological dynamics of Mycoplasma pneumoniae is characterized by poorly understood complex multiannual cycles. The origins of these cycles have long been debated, and multiple explanations of varying complexity have been suggested. Using Bayesian methods, we fit a dynamical model to half a century of M. pneumoniae surveillance data from Denmark (1958 to 1995, 2010 to 2025) and uncover a parsimonious explanation for the persistent cycles, based on the theory of quasicycles. The period of the multiannual cycle (approx. 5 y in Denmark) is explained by susceptible replenishment due, primarily, to loss of immunity. While an excellent fit to shorter time series (a few decades), the deterministic model eventually settles into an annual cycle, unable to reproduce the persistent cycles. We find that environmental stochasticity (e.g., varying contact rates) stabilizes the multiannual cycles and so does demographic noise, at least in smaller or incompletely mixing populations. The temporary disappearance of cycles during 1979 to 1985 is explained as a consequence of stochastic mode-hopping. The circulation of M. pneumoniae was recently disrupted by COVID-19 nonpharmaceutical interventions (NPIs), providing a natural experiment on the effects of large perturbations. Consequently, the effects of NPIs are included in the model and medium-term predictions are explored. Our findings highlight the intrinsic sensitivity of M. pneumoniae dynamics to perturbations and interventions, underscoring the limitations for long-term prediction. More generally, our findings provide further evidence for the role of stochasticity as a driver of complex cycles across endemic and recurring pathogens.