The simple deterministic epidemic model is extended to the situation where the initial population of susceptibles may be divided into two groups having very different infection rates. It is shown how this model may be solved exactly. Moreover there is derived a useful approximation to the solution which permits simple estimates of the infection rates. The approximate method is applied to an epidemic of yaws (Gait and deVries [1966]) for which the approximation is found to be quite adequate.
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John J. Gart (1968) studied this question.
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