Endemic Oscillations for SARS-CoV-2 Omicron -- A SIRS model analysis

TL;DR

This paper analyzes a SIRS epidemiological model to explain endemic oscillations of SARS-CoV-2 Omicron, showing that vaccination alone may not eliminate infection waves, but real-world contact changes could suppress these oscillations.

Contribution

It demonstrates how the SIRS model maps to classic endemic models, providing formulas for endemic bifurcation and oscillation conditions specific to SARS-CoV-2 Omicron.

Findings

Endemic oscillations occur under certain reproduction number ranges.

Continuous vaccination alone may not prevent infection waves.

Real-world contact behavior likely suppresses predicted oscillations.

Abstract

The SIRS model with constant vaccination and immunity waning rates is well known to show a transition from a disease-free to an endemic equilibrium as the basic reproduction number $r_0$ is raised above threshold. It is shown that this model maps to Hethcote's classic endemic model originally published in 1973. In this way one obtains unifying formulas for a whole class of models showing endemic bifurcation. In particular, if the vaccination rate is smaller than the recovery rate and $r_- < r_0 < r_+$ for certain upper and lower bounds $r_\pm$, then trajectories spiral into the endemic equilibrium via damped infection waves. Latest data of the SARS-CoV-2 Omicron variant suggest that according to this simplified model continuous vaccination programs will not be capable to escape the oscillating endemic phase. However, in view of the strong damping factors predicted by the model, in reality these oscillations will certainly be overruled by time-dependent contact behaviors.