Vaccine coverage The project on page 479 explores an epidemiological model of vaccine

Chapter 10, Problem 10

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Vaccine coverage The project on page 479 explores an epidemiological model of vaccine coverage. For certain values of the constants the system of differential equations is dN dt 2s1 2 pdN 1 2s1 2 pdV 2 N dV dt 2pV 1 2pN 2 3V where N and V are the numbers of nonvaccinated and vaccinated infected people, respectively, and p is the fraction of the population that is vaccinated. (a) Classify the equilibrium at the origin for all values of the vaccination coverage p. (b) What is the critical vaccination coverage above which the infection dies out? (c) What is the general solution? (d) What is the solution to the initial-value problem where Ns0d k and Vs0d 0?

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