Epidemiology: Gray Immunity Model Gives Qualitatively Different Predictions

Abstract

Compartmental models like the SIR model that dynamically divide the host population in categories such as susceptible, infected and immune form the mainstream of epidemiological modelling. Effectively such models treat infection and immunity as binary variables. We show here that considering immunity as a continuous variable instead of binary and incorporating factors that bring about small changes in immunity lead to qualitatively different epidemiological predictions. The small immunity effects (SIE) constitute cross immunity by other infections, small increments in immunity by sub clinical exposures and slow decay in the absence of repeated exposure. The SIE model explains many epidemiological patterns observed during the Covid-19 pandemic that are not adequately explained by conventional models. In the SIE model repeated waves are possible without the need for new variants. Peak and decline of a wave much before reaching herd immunity threshold, low level apparently stable existence of the pathogen, new surges after variable and unpredictable gaps, new surge after vaccinating majority of population are the common features of the pandemic mimicked by simulations using the SIE model. The model further shows complex interactions of different interventions that can be contextually synergistic as well as antagonistic. As a result, interventions intended to arrest the transmission are not always effective and can turn counterproductive under some conditions. Interventions that are beneficial in the short run can be potentially hazardous in the long run. In the absence of empirical estimates of many parameters, the model may not be useful to make quantitative predictions at this stage but it certainly challenges traditional wisdom and currently held beliefs behind non-pharmaceutical interventions recommended to control the epidemic. We also suggest testable predictions to differentiate between the causal logic of the SIE model against the prevalent explanations for the same observed phenomena.