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Correspondence

In their article (Goffman, W., and Warren, K. S., 1970. An application of the Kermack-McKendrick theory to the epidemiology of schistosomiasis. Am. J. Trop. Med. & Hyg., 19: 278–283) the authors conclude (p. 281) that the modeled "process converges to an endemic state when the number of infective individuals is twice (my emphasis) that at the peak point in both definitive and intermediate-host populations." At first sight, this conclusion seems at variance with the corresponding deterministic one-host model with influx of new susceptibles, where the process, building up from zero infectives, converges through damping oscillations to an endemic state when the number of infectives is about half that at the first peak point (Bailey, N. T. J., 1957. The Mathematical Theory of Epidemics. Charles Griffin, London, p. 137). This difference in outcomes will be explored below in two comments.