COVID-19 cases with a contact history: A modeling study of contact history-stratified data in Japan

The purpose of the present study was to develop a transmission model of COVID-19 cases with and without a contact history to understand the meaning of the proportion of infected individuals with a contact history over time. We extracted epidemiological information regarding the proportion of coronavirus disease 2019 (COVID-19) cases with a contact history and analyzed incidence data stratified by the presence of a contact history in Osaka from January 15 to June 30, 2020. To clarify the relationship between transmission dynamics and cases with a contact history, we used a bivariate renewal process model to describe transmission among cases with and without a contact history. We quantified the next-generation matrix as a function of time; thus, the instantaneous (effective) reproduction number was calculated for different periods of the epidemic wave. We objectively interpreted the estimated next-generation matrix and replicated the proportion of cases with a contact p(t) over time, and we examined the relevance to the reproduction number. We found that p(t) does not take either the maximum or minimum value at a threshold level of transmission with R(t)=1.0. With R(t) < 1 (subcritical level), p(t) was a decreasing function of R(t). Qualitatively, the minimum p(t) was seen in the domain with R(t) > 1. An important future implication for use of the proposed model is to monitor the success of ongoing contact tracing practice. A decreasing signal of p(t) reflects the increasing difficulty of contact tracing. The present study findings indicate that monitoring p(t) would be a useful addition to surveillance.