Early efforts in modeling the incubation period of infectious diseases with an acute course of illness

Abstract

The incubation period of infectious diseases, the time from infection with a microorganism to onset of disease, is directly relevant to prevention and control. Since explicit models of the incubation period enhance our understanding of the spread of disease, previous classic studies were revisited, focusing on the modeling methods employed and paying particular attention to relatively unknown historical efforts. The earliest study on the incubation period of pandemic influenza was published in 1919, providing estimates of the incubation period of Spanish flu using the daily incidence on ships departing from several ports in Australia. Although the study explicitly dealt with an unknown time of exposure, the assumed periods of exposure, which had an equal probability of infection, were too long, and thus, likely resulted in slight underestimates of the incubation period.After the suggestion that the incubation period follows lognormal distribution, Japanese epidemiologists extended this assumption to estimates of the time of exposure during a point source outbreak. Although the reason why the incubation period of acute infectious diseases tends to reveal a right-skewed distribution has been explored several times, the validity of the lognormal assumption is yet to be fully clarified. At present, various different distributions are assumed, and the lack of validity in assuming lognormal distribution is particularly apparent in the case of slowly progressing diseases. The present paper indicates that (1) analysis using well-defined short periods of exposure with appropriate statistical methods is critical when the exact time of exposure is unknown, and (2) when assuming a specific distribution for the incubation period, comparisons using different distributions are needed in addition to estimations using different datasets, analyses of the determinants of incubation period, and an understanding of the underlying disease mechanisms.

Evolutionary dynamics of incubation periods

“…As shown in Extended Data Table 1, the distributions generated by highly fit pathogens and mutants are predicted to have dispersion factors (also known as geometric standard deviations) of about 1.1 − 1.4, close to the actual values of 1.1 − 1.5 observed for various diseases 8,9,11 . The model also helps to explain why so few diseases yield dispersion factors greater than 1.5.…”

“…Historically, the distribution of incubation periods has been ascribed to heterogeneity 8,11,21 in the strength and dose of the pathogen, and in the immune response of the host. To see how these potential sources of heterogeneity could account for the skewed and approximately lognormal distribution of incubation periods, consider a pathogen growing exponentially with rate r from an initial population N 0 , so that its population at time t is given by N(t) = N 0 e rt .…”

“…Likewise, but in a more qualitative sense, a normal distribution of pathogen growth rates r will also produce a skewed distribution that resembles a lognormal 11 . However, if there is no randomness in any of those sources, this model predicts a single deterministic value of T for the incubation period.…”

“…Previous explanations rest on the presumed heterogeneity of the host, the pathogen, or the dose 8,11,21 . To see how this works, return to the typhoid outbreak at the Hanford church dinner 2 .…”

A review of back-calculation techniques and their potential to inform mitigation strategies with application to non-transmissible acute infectious diseases

“…The incubation period is defined as the time from pathogen exposure to the onset of symptoms [16,20]. Owing to factors such as host susceptibility, size of inoculum, strain virulence and chance, infected persons can experience different incubation periods.…”