The growth of micro-organismsin vivowith particular reference to the relation between dose and latent period

Abstract

The growth of Salmonella typhimurium in mice was studied by performing viable counts on pooled viscera and, in the case of fatally infected mice, by determining the relation between size of dose and mean death time. The results suggested that this system conformed to a general model which postulates (a) that the organisms causing the response (death in the present experiments) increase in vivo at a rate which is constant for all doses, and (b) that the response is certain to occur when their number reaches a constant figure. It follows that logarithm of dose (for doses > 1 ED50) should be linearly related to mean latent period (the interval between inoculation and response). A search of the literature showed that this relation was observed in many reported infective systems.The interpretation of the observations on partially resistant mice (LD50 = 102.5−106 organisms) was not straightforward for the hypothesis of independent action (Meynell & Stocker, 1957) states that only a random fraction of the inoculum usually initiates each response. Multiplication of this fraction is considered to cause a reduction in host resistance so that other organisms surviving in vivo began to increase in numbers and to contribute to the fatal infection. The observations showed that this could well occur as (i) the counts on all mice, whether fatally infected or not, increased exponentially for 2–3 days after inoculation; (ii) the growth curves of fatally infected mice showed exponential increase of the whole inoculum as postulated; and (iii) the length of the death time was found to be determined by the growth of the whole inoculum and not by the predicted random fraction. The viable count per fatally infected mouse at the time of death was approximately constant at 108.75 organisms. There was no evidence that the course of the infection was influenced by organisms which may have been killed in vivo as the requirements of the model were satisfied by the observed behaviour of the viable organisms alone. The rate of increase of organisms in a fatally infected animal was found to be less, the greater the LD50 of the host; which suggested that the degree of host resistance was determined by successive random events occurring after inoculation.The latent period/log dose curve provides a new test of the hypothesis of independent action, since this predicts that most responses to doses equal to or less than 1 ED50 are each initiated by only one inoculated organism. Hence, the latent period should become approximately constant at such doses. This was found to be so in the present experiments.The authors are grateful to the Medical Research Council for meeting part of the expenses of this work by a grant to G. G. M. They also wish to acknowledge the help of Dr W. R. Bryan, Dr B. Mandel, Dr D. B. W. Reid and Dr G. T. Stewart who provided unpublished data.

Observations on the growth of trachoma and inclusion blennorrhoea viruses in embryonate eggs

“…Furthermore, with strains killing embryos slowly there is greater variation about the mean survival time for embryos receiving the same dose and, for all strains, the less virus inoculated the greater is the scatter of embryo deaths. Our dose-response curves conform to the model proposed by Meynell & Meynell (1958) for the production of a response by the multiplication of micro-organisms for which average latent period is linearly related to logarithm of dose. The model postulates that the organisms causing the response increase in vivo at a constant rate so that their number rises exponentially and that the response (in this case death of the embryo) occurs when their total number reaches or exceeds a critical figure.…”

“…However, this method is valid only if the linear portion of the dose-response curve is used and if virus strains do not change their growth characteristics. Our results and those of Meynell & Meynell (1958) show that the linear relationship does not hold for doses < 1 LD 50 or for very large doses ( > 105 LD 50); in addition three of our strains altered their growth characteristics during passage. Furthermore, with strains killing embryos slowly there is greater variation about the mean survival time for embryos receiving the same dose and, for all strains, the less virus inoculated the greater is the scatter of embryo deaths.…”

“…Titrations of G221 and G 1 gave points fitting the curve drawn for G 17 and BOUR; for clarity they are omitted from the figure. In many infections caused by either bacteria or viruses, log dosage, within limits, is inversely proportional to mean death time (see review by Meynell & Meynell (1958), who discuss the general characteristics of such curves). This is also true of trachoma virus Watkins, 1961) and we have observed it for all the strains tested.…”

A dynamic dose–response model to account for exposure patterns in risk assessment: a case study in inhalation anthrax

“…However, a distribution that weights faster lag periods more (such as the exponential with mean of about 2 days) resulted in MLE a values between 0.9 and 1. While lag periods may be less variable and slower for doses under the ID 50 [9], such as in this dataset, future anthrax modelling for larger doses may require careful distribution selection consistent with experiments done with higher dose levels [8].…”

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).…”