Regression Polynomial Analysis of the COVID-19 Epidemics: An Alternative Infection Modeling

Abstract

The Vector Infection Model (VIM) assuming that infected people (vector) transmit high loads of COVID-19 to health persons by both close or near contact, is the predominant if not the only accepted pandemic modeling. Because the virus is assumed to have a very high R0, each person infects a high number of healthy people, quarantine is proposed as the way to control the epidemics. After 8 months, contagious data did not support this assumption, showing that the virus tends to spread quiescently because infected people remains asymptomatic and carrying a low virus load. Here, an alternative modeling is proposed: the Collector Infection Model (CIM) involving two not well distinguished actors: the provider releasing a virus load to others or into the environment, and the collector picking the virus from others or the environment. Virus load is low for asymptomatic and high for symptomatic individuals. Virus delivering and collecting are fundamentally governed by social rules; personal and collective behavior, as well as habits. Transition from collectors into providers is gradual depending on the available virus load and the local, duration and frequency of collecting. They take place within social networks organized as Scale free and Smallword networks. Health conditions (and consequently age) are the most important variable determining this transition. The present paper uses Polynomial and Linear Regression Analyses to study epidemic data from 8 different countries; 130 regions of these countries, and 117 Brazilian cities. Results shown a synchronized epidemic onset in the European Union countries and a progressive virus spread at various distinct rates in all other studied countries, regions and cities. The quiescent period between the first case report and epidemics onset is quite variable, being short as few weeks to long as 4 months. In addition, the virus was identified in the Florianópolis human sewage by November, 19, but the first cases in this state were reported by March 12, 2020 and epidemics broke up by June 6. Polynomial Regression Analysis shows that the epidemic dynamics has specific signatures for the different studied regions independent of the level (national; state or province; city or their neighborhoods) of the analysis, pointing to a strong influence of human social organization upon the epidemic evolution. The regional total number of cases decreases following a logarithm law at the level of cities and a power law for the other upper level regions. It is proposed, here, that local (cities and their neighborhoods) epidemics spread occurs inside Smallworld social networks, whereas at the other regional upper level it occurs inside Scale free social networks.