To date, over 182 million people on infected with COVID-19. It causes more 3.9 millions deaths. This paper introduces a symptomatic-asymptomatic-recoverer-dead differential equation model (SARDDE)
To date, over 182 million people on infected with COVID-19. It causes more 3.9 millions deaths. This paper introduces a symptomatic-asymptomatic-recoverer-dead differential equation model (SARDDE). It gives the conditions of the asymptotical stability on the disease-free equilibrium of SARDDE. It proposes the necessary conditions of disease spreading for the SARDDE. Based on the reported data of the first and the second COVID-19 epidemics in Beijing and simulations, it determines the parameters of SARDDE, respectively. Numerical simulations of SARDDE describe well the outcomes of current symptomatic and asymptomatic individuals, recovered symptomatic and asymptomatic individuals, and died individuals, respectively. The numerical simulations suggest that both symptomatic and asymptomatic individuals cause lesser asymptomatic spread than symptomatic spread; the blocking rates of about 80% and 97.5% to the symptomatic individuals cannot prevent the spread of the first and second COVID19 epidemics in Beijing, respectively. Virtual simulations suggest that the strict prevention and control strategies implemented by Beijing government are not only very effective but also completely necessary. The numerical simulations suggest also that using the data from the beginning to the day after about 14 -- 17 days at the turning point can estimate well the following outcomes of the two COVID-19 academics, respectively. It is expected that the research can provide better understanding, explaining, and dominating for epidemic spreads, prevention and control measures.