5.30. Diseases with carriers. Formulate a model for an infectious disease where there is immunity for only some of those who recover; others 'recover' to become permanent carriers, who can still cause infections. Thus susceptibles, S(t), may be infected by either infectious individuals, I(t), or carriers, C(t). A carrier can infect others at a reduced rate compared to infectious individuals but shows no symptoms.

(a) Assume there is a fixed proportion q of those recovering from the infection become carriers. Assume transmission rates B1 for normal infectives and B2 for carriers and assume that individuals remain infective for a mean time q-1. Give equations for the number of susceptible S(t), the number of infectives I (t), the number of carriers C(t), and the number of recovered who are immune R(t)

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