Extending frailty models applied to infectious disease epidemiology

Abstract

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 modelling 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 infection processes with reinfections and waning immunity. Shared gamma frailty models, which are frequently used in practice, and correlated gamma frailty models that have proven to be a valuable alternative are considered. We show that naively assuming lifelong immunity in frailty models introduces substantial bias in the estimation of the basic and effective reproduction number. We illustrate our work using Belgian cross-sectional serological data on parvovirus B19 (PVB19) and varicella zoster virus (VZV). Whereas it is typically assumed that lifelong immunity holds for VZV, more recently, empirical evidence for PVB19 indicates waning of immunity after infection, leading to potential reinfections with the virus.