Infection-age structured transmission model highlights the efficacy of case-finding operations

Early epidemic control often relies on case-finding operations. To assess their theoretical efficacy, we develop an infection-age structured early growth transmission model that incorporates symptom-based diagnosis, mass screening, and both forward and backward contact tracing. By deriving integral equations for the forward and backward tracing rates and coupling them with a Lotka-Euler-type equation for the early growth rate, we obtain a closed deterministic system. This system enables the computation of early growth rates and reproduction numbers under different case-finding scenarios. Using parameter values calibrated from the 2021 Yangzhou outbreak, the theoretical scenario comparisons show that diagnosis alone provides limited control of early epidemic growth, whereas the integrated case-finding scenario substantially suppresses transmission. The results further show that reducing the effective reproduction number below one requires stronger mass screening and contact tracing when infected individuals generate more secondary infections on average. Together, these findings indicate that the theoretical efficacy of case-finding operations depends jointly on intervention intensity and the effective transmission structure.