Contributions to the mathematical theory of epidemics IV. Analysis of experimental epidemics of the virus disease mouse ectromelia

Abstract

1. The experimental data obtained by Greenwood et al. (1936) relating to epidemics of the virus disease ectromelia in mice have been examined in the light of mathematical theory. Attention has been directed in particular to the life tables calculated from the observed data, which give the chance of survival and death after various periods of cage life.2. The life table relating to ectromelia 1 during the steady state phase from 1. iii. 32 to 31. viii. 32 shows very close agreement over the range 0–550 days with that predicted by the theoretical equation which involves only four arbitrary constants. A slight discrepancy over the first few days is evidently due to the fact that representation of the death-rate and the recovery rate by constant coefficients does not accommodate an incubation period. The values of the constants obtained from the data give a measure of the essential characteristics of the epidemic.3. General agreement, though not so complete, is also found when the theory is applied to ectromelia 2 during the priod 1. xi. 31–30. iv. 32. During this phase however, although conditions were otherwise apparently uniform, a steady state had not actually been attained. On the other hand the equations do not apply so satisfactorily to the obviously inhomogeneous period 1. v. 32–20. x. 32.4. In the present analysis the assumption of constant rates gives a satisfactory account of the progress of an infection in a susceptible community. This result suggests that for many purposes the assumption of constant rates may be adequate.5. The short period fluctuations observed in the ectromelia epidemic were probably random in character and have no relationship to periodic fluctuations such, for example, as those detected by Brownlee in the case of measles.