Modeling local coronavirus outbreaks

•A probabilistic approach to modeling local coronavirus outbreaks is presented.•The model generalizes the well-known SIR and SEIR models.•The model enables new insights regarding the timing and meaning of herd immunity.•The model enables parameter estimation from observed lagged indicators of infection.•The model extends naturally to testing- and isolation-based interventions. This article presents an overview of methods developed for the modeling and control of local coronavirus outbreaks. The article reviews early transmission dynamics featuring exponential growth in infections, and links this to a renewal epidemic model where the current incidence of infection depends upon the expected value of incidence randomly lagged into the past. This leads directly to simple formulas for the fraction of the population infected in an unmitigated outbreak, and reveals herd immunity as the solution to an optimization problem. The model also leads to direct and easy-to-understand formulas for aligning observable epidemic indicators such as cases, hospitalizations and deaths with the unobservable incidence of infection, and as a byproduct leads to a simple first-order approach for estimating the effective reproduction number Rt. The model also leads naturally to direct assessments of the effectiveness of isolation in preventing the spread of infection. This is illustrated with application to repeat asymptomatic screening programs of the sort utilized by universities, sports teams and businesses to prevent the spread of infection.