Contributions to the mathematical theory of epidemics--III. Further studies of the problem of endemicity. 1933.

(1) The mathematical investigation of the progress of an infectious disease in a community of susceptible individuals has been extended to include the case where members of the community are removed as the result of some general cause of death acting according to constant non-specific death rates, as well as by death from the disease itself. Under the more general conditions here dealt with the main conclusions arrived at in the previous paper remain qualitatively unaltered. The limitations which remain are that the susceptibility and the infective power of the individual are supposed to be independent of his age, and further that specific individual immunity does not exist in the sense that the part of the population which escapes infection is assumed to be just as susceptible as the whole population would have been if it had not been infected.

Contributions to the mathematical theory of epidemics--II. The problem of endemicity.1932.

(1) A mathematical investigation has been made of the prevalence of a disease in a population from which certain individuals are being removed as the result of the disease, whilst fresh individuals are being introduced as the result of birth or immigration. Allowance is made for the effects of the immunity produced as the result of an attack of the disease, but the effect of deaths from other causes is not taken into account, and the action of the disease is supposed to be independent of the age of the individual. (2) As a special case of the above, results have been obtained for a closed population in which no deaths occur and to which no fresh individuals are added, but in which the individuals after being infected acquire immunity, and then may be again infected.

Contributions to the mathematical theory of epidemics--I. 1927.

(1) A mathematical investigation has been made of the progress of an epidemic in a homogeneous population. It has been assumed that complete immunity is conferred by a single attack, and that an individual is not infective at the moment at which he receives infection. With these reservations the problem has been investigated in its most general aspects, and the following conclusions have been arrived at.