The Incubation Period and the Dynamics of Infectious Disease

Studies on the 1967–68 foot and mouth disease epidemic: incubation period and herd serial interval

“…If we regard an epidemic as a network of infections, of donor-recipient pairs, the temporal length of the strand is the serial interval, and between herds or flocks the herd serial interval. The classical methods of Pickles (1939) and Sartwell (1966) can be used with some case histories, but under field conditions with a multitude of cases it is extremely difficult to determine when a donor was infective or when an infective dose of virus was acquired by the recipient. In our studies of the 1967-8 foot and mouth epidemic we were only able to identify the donorrecipient pairings in a few special cases and hence our confidence in the estimates obtained from these pairings was necessarily limited.…”

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

“…within an enclosed institution [37] such as a school, barracks or prison), then it might be more difficult to distinguish between the harmful and harmless meals. To address this problem, Sartwell [38] applied the method of quantiles to estimate the date of common exposure T in four outbreaks where the actual time of exposure was known and found that the estimates were all accurate to within 1 day. The Japanese theoretical epidemiologists Hirayama and Horiuchi also used and extended similar techniques although such approaches are somewhat sensitive to a user-defined optional value [20].…”

Estimating the date of infection from individual response times

“…If one defines the 'response time' of an individual as the interval between the earliest date on which he could have been exposed to infection (as by eating contaminated food) and the date on which he fell ill, then the distribution of individual response times is always skewed with a long tail to the right. The true distribution has often been taken as log-normal, since probit proportion of responses plotted against logarithm of time since exposure approximates to a straight line (Sartwell, 1950(Sartwell, , 1952 Meynell & Meynell, 1958;Meynell, 1963). Sartwell (1966) pointed out that, if the true distribution is indeed log-normal, an unknown date of exposure, aL, can be estimated from the dates of the individual responses by the method of quantiles (Aitchison & Brown, 1963, §6.24).…”

“…The true distribution has often been taken as log-normal, since probit proportion of responses plotted against logarithm of time since exposure approximates to a straight line (Sartwell, 1950(Sartwell, , 1952 Meynell & Meynell, 1958;Meynell, 1963). Sartwell (1966) pointed out that, if the true distribution is indeed log-normal, an unknown date of exposure, aL, can be estimated from the dates of the individual responses by the method of quantiles (Aitchison & Brown, 1963, §6.24). This is so but, owing to the actual distributions observed in practice, the earliest date of exposure can be equally well estimated by another method, and it is shown here that the two estimates necessarily disagree.…”

“…Its minimum value is 1 0, observed if all the hosts respond simultaneously, and the observed value rarely exceeds 1 5 in either epidemics (Sartwell, 1950(Sartwell, , 1952(Sartwell, , 1966Williams, 1965) or experimental infections, and is often less. Given such small values, it is apparent from Fig.…”