A Time-dependent SIR model for COVID-19 with Undetectable Infected Persons

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In this paper, we conduct mathematical and numerical analyses to address the following crucial questions for COVID-19: (Q1) Is it possible to contain COVID-19? (Q2) When will be the peak and the end of the epidemic? (Q3) How do the asymptomatic infections affect the spread of disease? (Q4) What is the ratio of the population that needs to be infected to achieve herd immunity? (Q5) How effective are the social distancing approaches? (Q6) What is the ratio of the population infected in the long run? For (Q1) and (Q2), we propose a time-dependent susceptible-infected-recovered (SIR) model that tracks 2 time series: (i) the transmission rate at time t and (ii) the recovering rate at time t.

• Such an approach is more adaptive than traditional static SIR models and more robust than direct estimation methods.
• Using the data provided by China, we show that the one-day prediction errors for the numbers of confirmed cases are almost in 3%, and the total number of confirmed cases is precisely predicted.
• Also, the turning point, defined as the day that the transmission rate is less than the recovering rate can be accurately predicted.