Abstract
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 confirmed recovered (Rk) populations (the so-called SIQRk 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 SIQRk 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 six months after the first patients are found.
Highlights
On December 31, 2019, Chinese authorities reported pneumonia from an unknown cause to the World Health Organization (WHO) in Wuhan City, Hubei province, China
When patients are found at a location, doctors and experts from the Korean Center for Disease Control and Prevention (KCDC) checked all people who had been in contact with those patients
The number of initially infected people is very big, the World Health Organization and the KCDC performed a wide range of inspections, imposed a strong policy for quarantines, and provided information on the people contacted by the confirmed patient
Summary
On December 31, 2019, Chinese authorities reported pneumonia from an unknown cause to the World Health Organization (WHO) in Wuhan City, Hubei province, China. We consider a susceptible, infectible, quarantined, and confirmed recovered (SIQRK) model based on only known data for active cases and recovered cases. Under the homogenous mixing postulate, we consider the so-called SIQRK model as follows: dS(t) In this model, the parameter β denotes the infection rate, and α is the rate at which patients become non-infectious by recovering without showing any symptoms. We propose that the parameter included in the dynamic equations should be the initial number of infected cases, which is the sum of officially known cases and the unknown population of asymptomatic cases. In this model we don’t include the number of deaths. From this idea we can predict some parameters from the officially provided data
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