The Epidemic Curve with No Accession of Susceptibles

Abstract

The finite difference equation log x(T + l) =x(T)[long dash]k for the number of susceptibles at a time T and at a time T + 1, one incubation period later, is established as the exact integral for Soper''s fundamental equation regulating the course of an epidemic, the susceptibles x being measured as fractions of their number near the peak of the epidemic and k being a constant. This solution is compared with the approx. continuous solution obtained in the previous paper to prove that the approximation is actually extremely accurate. It is further proved that this exact solution is actually equivalent to the solution found in 1928 by W. H. Frost, using general and approximate methods of analysis.