The Law of Mass Action in Epidemiology

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Abstract
The law of mass action, which has been widely, used in the theory of the epidemic curve of a disease like measles, is usually taken as C=(S/m)C(t[long dash][tau]), meaning that the case rate C at any time is proportional jointly to the number of susceptibles, 8, and to the case rate at a time one incubation period ([tau]) earlier, 1/m being the constant factor of proportionality. The authors propose the more general law in which S/m is replaced by its pth power. They find that to the order of approximation used by Soper, the epidemic curve has the same form [image], that this solution is exact when and only when p = 2 and when the number of susceptibles initially present happens to be of just the right magnitude, that there is a simple approx. relation m/p= (total cases) 2/8 peak cases which connects the value of the ratio m/p with the observable values of the total number of cases and the number of cases at the peak of the epidemic, and the modification of this result which follows from the exact finite difference solution is given.

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