  The COVID-19 epidemic has been spreading around the world for nearly three
years, and asymptomatic infections have exacerbated the spread of the epidemic.
To evaluate the role of asymptomatic infections in the spread of the epidemic,
we develop mathematical models to assess the proportion of asymptomatic
infections caused by different strains of the main covid-19 variants. The
analysis shows that when the control reproduction number is less than 1, the
disease-free equilibrium point of the model is globally asymptotically stable;
and when the control reproduction number is greater than 1, the endemic
equilibrium point exists and is unique, and is locally asymptotically stable.
We fit the epidemic data in the four time periods corresponding to the selected
614G, Alpha, Delta and Omicron variants. The fitting results show that, from
the comparison of the four time periods, the proportion of asymptomatic persons
among the infected persons gradually increased. We also predict the peak time
and peak value for the four time periods, and the results indicate that the
transmission speed and transmission intensity of the variant strains increased
to some extent. Finally, we discuss the impact of the detection ratio of
symptomatic infections on the spread of the epidemic. The results show that
with the increase of the detection ratio, the cumulative number of cases has
dropped significantly, but the decline in the proportion of asymptomatic
infections is not obvious. Therefore, in view of the hidden transmission of
asymptomatic infections, the cooperation between various epidemic prevention
and control policies is required to effectively curb the spread of the
epidemic.
