Quantifying the re-exposure process to an infectious agent. Measles and varicella as examples

For viral infections conferring what is usually considered as permanent immunity, re-exposure to the pathogen due to contacts with infectious individuals might be critical for immunity boosting. A major example is represented by the varicella-zoster virus (VZV) where re-exposure is thought to lead to boosting of cell mediated immunity (CMI), which plays a protective role against the development of herpes zoster (HZ). Similar concerns have recently been raised also in relation to measles. However, while the first effective exposure, i.e. infection, has been the object of many studies, both theoretical and epidemiological, there has been no corresponding investigation of the re-exposure process.

By combining basic concepts from deterministic and stochastic modelling of infection, we develop a basic model for quantifying the timing and number of re-exposures and, consequently, the potential for immune boosting at any given age. The model is then applied to measles, mumps and rubella (MMR) in the UK, and to varicella in Italy, using literature estimates of the pre-vaccination forces of infection.

We supply analytical expressions for the expected number of lifetime re-exposures and for underlying age-patterns, including the average age at which the last re-exposure occurs. Based on updated estimates of the force of VZV infection, we show that the expected number of boosting opportunities of CMI might be in the range 2-3, which is consistent with recent findings about the development of herpes zoster. We also show that the estimate of the age at which the last re-exposure to VZV occurs is highly sensitive to the underlying form of age dependence of the force of infection.

Our results contribute to the study of the potential immunity boosting effect of re-exposures to an infective agent by quantifying the re-exposure process.