An epidemiological forecast model and software assessing interventions on COVID-19 epidemic in China

Peter X Song; Lili Wang; Yiwang Zhou; Jie He; Bin Zhu; Fei Wang; Lu Tang; Marisa Eisenberg

The basic epidemiological model with both constant transmission and removal rates in SIR model (4) does not reflect the reality in China, where all levels of quarantines have been enforced. Many forms of human interventions that are altering the transmission rate over time include (i) individuallevel protective measures such as wearing masks and safety glasses, using hygiene, and taking inhome isolation, and (ii) community-level quarantines such as hospitalization for infected cases, city blockade, traffic control and restricted social activities, and so on. In addition, the virus itself may mutate to evolve, so to increase the potential rate of false negative in the disease diagnosis. As a result, some individual virus carriers are not contained. Thus, the transmission rate β indeed varies over time, which should be accounted in the modeling. One extension to the above basic epidemiological model is to allow a time-varying probability that a susceptible person meets an infected person or vice versa. Suppose at a time t, q S ptq P r0, 1s is the chance of an at-risk person being in-home isolation, and q I ptq P r0, 1s is the chance of an infected person being in-hospital quarantine. Thus, the chance of disease transmission when an at-risk person meets an infected person is modified as: βt1´q S ptquθ S t t1´q I ptquθ I t :" βπptqθ S t θ I t , with πptq :" t1´q S ptqut1´q I ptqu P r0, 1s. In effect, this πptq modifies the chance of a susceptible person meeting with an infected person or vice versa, which is termed as a transmission modifier due to quarantine in this paper. Obviously, with no quarantine in place, πptq " 1 for all time. See Figure 2 . This results in a new SIR model with a time-varying transmission rate modifier: