  Understanding waning of vaccine-induced protection is important for both
immunology and public health. Population heterogeneities in underlying
(pre-vaccination) susceptibility and vaccine response can cause measured
vaccine effectiveness (mVE) to change over time even in the absence of pathogen
evolution and any actual waning of immune responses. We use a multi-scale
agent-based models parameterized using epidemiological and immunological data,
to investigate the effect of these heterogeneities on mVE as measured by the
hazard ratio. Based on our previous work, we consider waning of antibodies
according to a power law and link it to protection in two ways: 1) motivated by
correlates of risk data and 2) using a within-host model of stochastic viral
extinction. The effect of the heterogeneities is given by concise and
understandable formulas, one of which is essentially a generalization of
Fisher's fundamental theorem of natural selection to include higher
derivatives. Heterogeneity in underlying susceptibility accelerates apparent
waning, whereas heterogeneity in vaccine response slows down apparent waning.
Our models suggest that heterogeneity in underlying susceptibility is likely to
dominate. However, heterogeneity in vaccine response offsets <10% to >100%
(median of 29%) of this effect in our simulations. Our methodology and results
may be helpful in understanding competing heterogeneities and waning of
immunity and vaccine-induced protection. Our study suggests heterogeneity is
more likely to 'bias' mVE downwards towards faster waning of immunity but a
subtle bias in the opposite direction is also plausible.
