We investigate the elastic scattering, inelastic scattering, breakup reaction, and total fusion reactions of the $^{17}\mathrm{F}+^{208}\mathrm{Pb}$ system using an optical model approach by including the dynamical polarization potential. In particular, we focus on the breakup reaction channels, whose effects on other reactions have been argued to be small. By exploiting two different potentials composed of a surface-type Woods-Saxon potential, which were obtained by a fitting analysis, and a Love-type optical potential, the breakup reaction cross sections are explained with other elastic and quasielastic scattering cross sections. For the breakup reaction at ${E}_{\text{lab}}=170$ MeV in the forward angle region, where only exclusive reaction data are known, inclusive breakup reaction data are deduced from available theoretical and experimental $E1$ strength values. We discuss the breakup reaction effects on the other nuclear reactions related to the $^{17}\mathrm{F}$ projectile in detail.