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

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Dynamics

Background:

• The SIRS model with constant vaccination and immunity waning demonstrates a transition from disease-free to endemic states.
• This transition is linked to the basic reproduction number exceeding a critical threshold.

Purpose of the Study:

• To unify various endemic bifurcation models by mapping the SIRS model to Hethcote's classic endemic model.
• To analyze the conditions leading to damped infection waves and endemic equilibria.

Main Methods:

• Mathematical modeling using the SIRS framework.
• Mapping the SIRS model to Hethcote's endemic model (1973).
• Analysis of endemic bifurcation and trajectory dynamics.

Main Results:

• Unifying formulas were derived for models exhibiting endemic bifurcation.
• Specific conditions (vaccination rate < recovery rate, basic reproduction number within bounds) lead to damped infection waves spiraling into endemic equilibrium.
• The model suggests continuous vaccination may not prevent oscillating endemic phases for SARS-CoV-2 Omicron.

Conclusions:

• The SIRS model provides a unified framework for understanding endemic bifurcations.
• While simplified models predict oscillating endemic phases for SARS-CoV-2, strong damping factors suggest these will be minimal in reality.
• Time-dependent contact behaviors are likely to override predicted oscillations.