We consider the pandemic spread of COVID-19 in selected countries after the outbreak of the SARS-CoV-2 coronavirus in Wuhan City, China. We estimated the infection rate and the initial individuals infected with COVID-19 by using officially reported data from the early stages of the epidemic for a model of susceptible (S), infectible (I), quarantined (Q), and officially confirmed recovered (R k) populations (the so-called SIQR k model). In the officially reported data, we know the number of quarantined cases and the officially reported number of recovered cases. We cannot know about recovered cases from asymptomatic patients. In the SIQR k model, we can estimate the parameters and the initial infections (confirmed cases + asymptomatic cases) from fitted values. We obtained an infection rate in the range β = 0.233 ∼ 0.462, a basic reproduction number of R o = 1.8 ∼ 3.5, and the initial number of infected individuals, I (0) = 10 ∼ 8409, for selected countries. By using fitting parameters, we estimated that the maximum time span of the infection was around 50 days in Germany when the government invoked the quarantine policy. The disease is expected to subside about 6 months after the first patients are found.

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