Periodic and Multiperiodic Coronavirus Evolution: Phase Space Methods to Visualize Pandemic Data and Models
A novel technique to analyze and visualize pandemic data and models is presented. Based on the fact that the system evolves in a loop (or two) in phase space, the path length and phase angle in the loop are relevant measures. In analogy to a complex physical system, the phase space for a pandemic consists of the variables (cases, deaths) and their derivatives or changes (new cases, new deaths). We focus on the new cases and new deaths variables. Both of these start out low (typically zero deaths and one or a few cases), rise to maximum values, and then reduce again to zero or low numbers if the pandemic wanes in the case of a periodic evolution. In the case of a second loop, the pattern repeats either with a higher or lower maximum value. The approach is illustrated for several regions of the world (e.g. Brazil, China, Germany, Pennsylvania, New York City, and New Jersey). In each case, our lognormal model is applied for reference purposes; however the computational analysis and visualization technique is model independent. Our approach to modeling the coronavirus pandemic using a lognormal solution to the differential equa- tions plus noise and primary harmonics is seen to work very well cross the entire spectrum of infection from lowest to highest mortalities. In the multiperiodic case, the pandemic will begin a second cycle as is seen in Pennsylvania and Louisiana. In the aperiodic case, no cycle is yet ap- parent: this may be the situation for the World, Brazil, and other states or countries until a loop is evident. Government officials can use these methods of analysis and visualization in real time to guide decisions about social and economic restrictions, where and when appropriate.