The results so far obtained have raised many questions and answered few of them. The important rôle played in the spread of epidemic disease by the re-accumulation of a susceptible population is clearly indicated. It seems not unreasonable to hope that valuable information as to the effect produced by variations in the rate of such re-accumulation, and on other matters, may be obtained by the satisfying method of direct experiment. The bearing of such information on the well-known fluctuations in the incidence of epidemic diseases, and especially perhaps of those which fall most heavily on children, are too obvious to need emphasising.The following conclusions seem permissible at the present stage:(1) If susceptible mice be continuously added to an infected population the spread of infection will continue over a long period of time. There is no evidence that this period has a limit.(2) When susceptible mice are added continuously and at a constant rate to an infected population, the spread of infection, as judged by a mortality curve, is propagated in regularly recurring waves. These waves are most easily observed by noting the fluctutations in the total cage-population. It seems probable that the period of these fluctuations will be found to depend on the rate of addition of susceptible individuals, but this point has still to be determined.(3) The actual deaths may occur in large groups, with intervals during which deaths are few and far between, or they may fall in a succession of smaller groups, increasing and diminishing in size to form the larger waves. In all cases there is this tendency for the occurrence of such small groups of deaths with definite maximal points. There would seem to be two fluctuating processes, the one superimposed upon the other.(4) The average survival-time of mice added to the cage, and their chance of ultimate survival if no more susceptible mice are introduced, vary according to the phase at which they are added. If they gain entrance to the cage during the rise of a wave they are unlikely to live for long. If they are introduced during the fall of a wave their chances of survival are greatly increased, and they will usually outlive mice which are added at a later date but at a time before the commencement of the next wave.(5) The rate of extinction of a population, among which infection is actively spreading, will be far less rapid if they are kept isolated, than if further susceptible individuals continuously gain access to them. A proportion of the infected population, which would have survived indefinitely under the former circumstances, will die under the latter.(6) The ultimate survivors among such a population have not escaped infection, but have successfully resisted it. A considerable proportion of them are harbouring the causative parasite in their tissues.My sincere thanks are due to my colleagues, Dr H. B. Weir and Dr G. S. Wilson, for their constant help, and to Mrs Phyllis Worthington whose assistance in this work I have been able to obtain by the aid of the Medical Research Council.
Pattern Dynamics of Nonlocal Delay SI Epidemic Model with the Growth of the Susceptible following Logistic Mode
