At the beginning of 2020 the world has seen the initial outbreak of COVID-19, a disease caused by SARS-CoV2 virus in China. The World Health Organization (WHO) declared this disease as a pandemic on March 11 2020. As the disease spread globally, it becomes difficult to tract the transmission dynamics of this disease in all countries, as they may differ in geographical, demographic and strategical aspects. In this short note, the author proposes the utilization of a type of neural network to generate a global topological map for these dynamics, in which countries that share similar dynamics are mapped adjacently, while countries with significantly different dynamics are mapped far from each other. The author believes that this kind of topological map can be useful for further analyzing and comparing the correlation between the diseases dynamics with strategies to mitigate this global crisis in an intuitive manner. Some initial experiments with with time series of patients numbers in more than 240 countries are explained in this note.