Explicit solution of the SVIR (Susceptible-Vaccinated-Infectious-Recovered) epidemic model
Yoshida, N.
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An explicit solution of an initial value problem for the Susceptible-Vaccinated-Infectious-Recovered (SVIR) epidemic model is obtained, and various properties of the explicit solution are investigated. It is shown that the parametric form of the explicit solution satisfies some linear differential system including a positive solution of an integral equation. In this paper integral equations play an important role in establishing the explicit solution of the SVIR epidemic model, in particular, the number of infected individuals can be represented in a simple form by using a positive solution of an integral equation. Uniqueness of positive solutions of the SVIR epidemic model is also investigated, and it is shown that the explicit solution is a unique solution in the class of positive solutions.
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