CAIMS Code of Conduct
“All participants are expected to comply with the CAIMS-SCMAI Code of Conduct”
Recurrent and chaotic outbreaks in SIR model with variable infection rate
We consider the SIR model under the natural assumption that the immunity loss happens on a much longer timescale (e.g. years) compared to the timescale of the outbreak (e.g. days or weeks). In this regime, the standard SIR model exhibits decaying oscillations towards an endemic equilibrium. Therefore the basic model is insufficient to understand recurring disease outbreaks. We propose several extensions of the basic model which are able to capture such recurrent outbreaks. These include: slow periodic modulations of model parameters (e.g. due to seasonal variability); random drift, and state-dependent parameters (e.g. due to health measures imposed during the outbreaks, and relaxed afterwards). For the case of a periodic modulations, we derive instability thresholds leading to recurrent outbreaks, as well as an asymptotic return map which predicts the timing of the outbreaks. Period-doubling and chaotic behaviour is observed.