We thank LetPub (www.letpub.com) for its linguistic assistance during the preparation of this manuscript. Author contributions Conceptualization, G.X., H.L., and L.Z.; methodology, J.Z., X.Z., L.H., and Y.L.; formal analysis, X.Z. and L.Z.; investigation, J.Z., Y.L., ...
Let pu be the fraction of the unvaccinated who got infected (among these a fraction k are symptomatic), and pv be the fraction among the vaccinated who got infected (and a fraction ψk among them become symptomatic). (5)1−pu=exp−r0(1−v)pu((1−k)m+k)+vpvϕ((1−ψk...