With the spread of the new coronavirus around the world, governments of various countries have begun to use the mathematical modeling method to construct some virus transmission models assessing the risks of spatial spread of the new coronavirus COVID-19, while carrying out epidemic prevention work, and then calculate the inflection point for better prevention and control of epidemic transmission. This work analyzes the spread of the new coronavirus in China, Italy, Germany, Spain, and France, and explores the quantitative relationship between the growth rate of the number of new coronavirus infections and time. In investigating the dynamics of a disease such as COVID-19, its mathematical representation can be constructed at many levels of details, guided by the questions the model tries to help answer. Mathematical sophistication may have to yield to a more pragmatic approach closer to the ability to make predictions that inform public health policies. Background In December 2019 , the first Chinese patients with pneumonia of unknown cause is China admitted to hospital in Wuhan, Hubei Jinyintan , since then, COVID-19 in the rapid expansion of China Wuhan, Hubei, in a few months time, COVID-19 is Soon it spread to a total of 34 provincial-level administrative regions in China and neighboring countries, and Hubei Province immediately became the hardest hit by the new coronavirus. In an emergency situation, we strive to establish an accurate infectious disease retardation growth model to predict the development and propagation of COVID-19, and on this basis, make some short-term effective predictions. The construction of this model has Relevant departments are helpful for the prevention and monitoring of the new coronavirus, and also strive for more time for the clinical trials of Chinese researchers and the research on vaccines against the virus to eliminate the new corona virus as soon as possible. Methods According to the original data change law, Establish a Logistic growth model, we collect and compare and integrate the spread of COVID-19 in China, Italy, France, Spain and Germany, record the virus transmission trend among people in each country and the protest measures of relevant government departments. Findings Based on the analysis results of the Logistic model model, the Logistic model has a good fitting effect on the actual cumulative number of confirmed cases, which can bring a better effect to the prediction of the epidemic situation and the prevention and control of the epidemic situation. Interpretation In the early stage of the epidemic, due to inadequate anti-epidemic measures in various countries, the epidemic situation in various countries spread rapidly. However, with the gradual understanding of COVI D -19, the epidemic situation began to be gradually controlled, thereby retarding growth