  Increasing number in global COVID-19 cases demands for mathematical model to
analyze the interaction between the virus dynamics and the response of innate
and adaptive immunity. Here, based on the assumption of a weak and delayed
response of the innate and adaptive immunity in SARS-CoV-2 infection, we
constructed a mathematical model to describe the dynamic processes of immune
system. Integrating theoretical results with clinical COVID-19 patients' data,
we classified the COVID-19 development processes into three typical modes of
immune responses, correlated with the clinical classification of mild &
moderate, severe and critical patients. We found that the immune efficacy (the
ability of host to clear virus and kill infected cells) and the lymphocyte
supply (the abundance and pool of na\"ive T and B cell) play important roles in
the dynamic process and determine the clinical outcome, especially for the
severe and critical patients. Furthermore, we put forward possible treatment
strategies for the three typical modes of immune response. We hope our results
can help to understand the dynamical mechanism of the immune response against
SARS-CoV-2 infection, and to be useful for the treatment strategies and vaccine
design.
