A model to predict COVID-19 epidemics with applications to South Korea, Italy, and Spain

Glenn F Webb; Pierre Magal; Zhihua Liu; Ousmane Seydi

Here t ≥ t 0 is time in days, t 0 is the beginning date of the epidemic, S(t) is the number of individuals susceptible to infection at time t, E(t) is the number of asymptomatic noninfectious (exposed or latent infected) individuals at time t, I(t) is the number of asymptomatic but infectious individuals at time t, R(t) is the number of reported symptomatic infectious individuals at time t, and U (t) is the number of unreported symptomatic infectious individuals at time t. The time-dependent transmission rate parameter is τ (t). Newly infected noninfectious asymptomatic individuals E(t) are incubating an average period of 1/α days. Asymptomatic infectious individuals I(t) are infectious for an average period of 1/ν days. Reported symptomatic infectious individuals R(t) are infectious for an average period of 1/η days, as are unreported symptomatic infectious individuals U (t). We assume that reported symptomatic infectious individuals R(t) are reported and isolated immediately, and cause no further infections. The asymptomatic individuals I(t) can also be viewed as having a lowlevel symptomatic state. All infections are acquired from either I(t) or U (t) infectious individuals. The fraction f of asymptomatic infectious become reported symptomatic infectious, and the fraction 1 − f become unreported symptomatic infectious. The rate at which asymptomatic infectious become reported symptomatic is ν 1 = f ν, the rate at which asymptomatic infectious become unreported symptomatic is