Modeling individual heterogeneity in the acquisition of recurrent infections: an application to parvovirus B19

In recent years, it has been shown that individual heterogeneity in the acquisition of infectious diseases has a large impact on the estimation of important epidemiological parameters such as the (basic) reproduction number. Therefore, frailty modeling has become increasingly popular in infectious disease epidemiology. However, so far, using frailty models, it was assumed infections confer lifelong immunity after recovery, an assumption which is untenable for non-immunizing infections. Our work concentrates on refining the existing frailty models to encompass complexities of waning immunity and consequently recurrent infections while accounting for individual heterogeneity. Univariate and shared gamma frailty models, frequently used in practice, and correlated gamma frailty models that have proven to be a valuable alternative are considered. We show that incorrectly assuming lifelong immunity when applying frailty models introduces substantial bias in the estimation of both the baseline hazard and the frailty parameters, and consequently of the basic and effective reproduction number. We illustrate our work using cross-sectional serological data on parvovirus B19 (PVB19) from Belgium for which the link with varicella zoster virus is exploited.