The Malthus growth model is the most widely used law to model dynamic processes. In this work, we use the Malthusian theory to estimate the growth rate of new daily cases of COVID-19 infection and two periods of time in which this type of growth occurred, the first of 41 days and the second of 101 days. In the first one, the growth rate was 10 times greater than in the second one. From the results, it is concluded that the United States, Spain, France, Italy, Germany and the United Kingdom were the countries that had the greatest impact on exponential growth during the first period, while the Americas, Russia and India were the ones that contributed the most in the second one.