Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (COVID-19)

Ruiyun Li; Sen Pei; Bin Chen; Yimeng Song; Tao Zhang; Wan Yang; Jeffrey Shaman

We developed a mathematical model that simulates the spatio-temporal dynamics of infections among 375 Chinese cities. The model incorporates information on human movement within the following metapopulation structure: [5] where < , < , < A , < B and < are the susceptible, exposed, documented infected, undocumented infected and total population in city i. Note that we define patients with symptoms severe enough to be confirmed as documented infected individuals; whereas other infected persons are defined as undocumented infected individuals. We specified a rate parameter, β, for the transmission rate due to documented infected individuals. The transmission rate due to undocumented individuals is reduced by a factor . In addition, is the fraction of documented infections, Z is the average latency period and D is the average duration of infection. The effective reproduction number ( 4 ) is calculated as 4 = + (1 − ) (see Supplementary Appendix for details). Spatial coupling within the model is represented by the daily number of people traveling from city j to city i ( <3 ) and a multiplicative factor, , which is greater than 1 to reflect underreporting of human movements (see below). We assume that individuals in the < A group do not move between cities. A similar metapopulation model has been used to forecast the spatial transmission of influenza in the United States 7 .