Novel spatiotemporal evaluative methodology of COVID-19 pandemic velocity based on differential equations

Abstract Introduction: The trajectory of disease outbreaks has been characterized through second order differential equations.Objective: To develop a universal methodology to predict the velocity of COVID-19 pandemic in the United States, Spain, Belgium, and Austria based on differential equations and ranges of the number infected.Methodology: Seven comparison ranges were established to analyze discrete values of COVID-19 total cases. Then, right-angled triangles where their base represented the number of days elapsed and their height the maximum number infected that was reached for each range were designed to then find the triangles’ areas. Given that there is a change rate between the triangles’ areas with respect to time , their velocity was found through a differential equation. Finally, these results were used to compare the propagation speed of the pandemic in these four countries.Results: The areas obtained for the right-angled triangles for all the countries varied between 2.888 and 1.056.204. The change rate between the triangles areas and the days elapsed for a range change oscillated between 3.079 and 1.264.558, while the variation of the number infected with respect to time presented values between 4.6 and 21549.7.Conclusion: An acausal generalization was developed based on differential equations that allows to simplify and facilitate the spatiotemporal evaluation of COVID-19 pandemic velocity which is useful for public health