Strong biological correlations as a cause of autonomous oscillations in epidemics

We consider the impact of strong biological correlations on the epidemic process. The biological correlations mean the influence of the environment on the individual state of immunity of the infected person. Accounting for the correlations turns the traditional SIRS model into the 3D Lotka-Volterra model, the parameters of which are uniquely determined by the parameters of the original SIRS model. The measure of the biological correlations in the epidemic is the correlation strength parameter K = 1/(4 pi(T omega T)-T-2/(sigma)), where T-omega and T-sigma are the duration of the infectious period of the disease and the duration of immunity, respectively, both measured in years. If the epidemic is highly correlated (K > 1), then after the first epidemic outbreak, subsequent oscillations occur, the period T of which is less than one year. The example is the COVID-19 pandemic. If the epidemic is weakly correlated (K < 1), the period T of the oscillations is more than one year. Then in the presence of regular annual outbreaks the oscillations do not have time to manifest themselves. The examples are the ordinary flu annual epidemics. In the absence of the annual epidemic factor, the oscillations can exist and persist regardless of the K value. The examples are the measles epidemics. The 3D Lotka-Volterra model makes it possible to predict the period T of the future oscillations based on two known clinical parameters-T-omega and T-sigma. This period turns out to be equal to 2 pi multiplied by the geometric mean of the duration of the infectious period of the disease T-omega and the duration of immunity T-sigma. The adequacy of the 3D Lotka-Volterra model is supported by examples of the

Automated summary

This article discusses the impact of strong biological correlations on the epidemic process, converting the traditional SIRS model into a 3D Lotka-Volterra model and introducing the correlation strength parameter K. Highly correlated epidemics exhibit oscillations with a period of less than one year, as seen in the COVID-19 pandemic. Weakly correlated epidemics have oscillation periods longer than a year, and may not manifest in the presence of regular annual outbreaks, such as ordinary flu. The 3D Lotka-Volterra model enables the prediction of future oscillation periods based on known clinical parameters T-omega and T-sigma.