Quantifying the contribution of asymptomatic infection to the cumulative incidence

Abstract

Many infectious diseases in humans may manifest with no or mild symptoms. While numerous studies have estimated the proportion of infectious individuals in whom symptoms are absent during the entire course of infection, the contribution of asymptomatic cases to the overall cumulative incidence is difficult to untangle. Here, with a mathematical model, we provide a simple analytical formula to quantify this contribution and highlight the potential for large errors that can arise when naively estimating it.

Keywords: Asymptomatic infection; epidemiology; mathematical modelling; public health.

Fig. 1.

The proportion (P) of cumulative incidence attributable to asymptomatic transmission as a function of the asymptomatic fraction (α), for a given r. Each curve represents this proportion P for a given relative infectivity of asymptomatic infection (r), according to the mathematical model detailed in the Supplementary Material. The shaded rectangles represent the plausible range of the asymptomatic fraction for selected infectious diseases (see Supplementary Material for the sources used to estimate these ranges). The dashed line represents the special case r = 1 where we have P = α. A value of, say, r = 0.1 means that overall–taking into account the relative contact rate, transmissibility and duration of infection–asymptomatic cases are 10 times less infectious than symptomatic ones.