Interpreting airborne pandemics spreading using fractal kinetics’ principles

Introduction The reaction between susceptible and infected subjects has been studied under the well-mixed hypothesis for almost a century. Here, we present a consistent analysis for a not well-mixed system using fractal kinetics’ principles. Methods We analyzed COVID-19 data to get insights on the disease spreading in absence/presence of preventive measures. We derived a three-parameter model and show that the “fractal” exponent h of time larger than unity can capture the impact of preventive measures affecting population mobility. Results The h=1 case, which is a power of time model, accurately describes the situation without such measures in line with a herd immunity policy. The pandemic spread in four model countries (France, Greece, Italy and Spain) for the first 10 months has gone through four stages: stages 1 and 3 with limited to no measures, stages 2 and 4 with varying lockdown conditions. For each stage and country two or three model parameters have been determined using appropriate fitting procedures. The fractal kinetics model was found to be more akin to real life. Conclusion Model predictions and their implications lead to the conclusion that the fractal kinetics model can be used as a prototype for the analysis of all contagious airborne pandemics.

SIMULATION OF KINETIC CURVES OF THERMO-OXIDATIVE DESTRUCTION OF PROLIMERS USING DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER

In the paper it is proposed to consider fractal kinetics equations for process of thermo-oxidative destruction of melt polymers in the form of differential equations of fractional order, equaling to fraction of reactant groups of polymer, which are not subjected to destruction, with order of reaction n > 1. Small νd characterize the autoslowed-down type of reaction, and at big νd <1 - the autoaccelerated thermooxidation type with an decreasing speed of oxidation reaction, respectively much more smaller and close to an integer derivative on time of the first order. Comparative analysis of calculation results with corresponding results obtained by differential equations of integer order and degree of their matching with experimental data is given. Keywords: Fractal analysis, thermo-oxidative destruction, auto-slow and auto-accelerated type of thermal oxidation, differential equations of type and fractional orders.

Demystifying the spreading of pandemics I: The fractal kinetics SI model quantifies the dynamics of COVID-19

The COVID-19 pandemic has created a public health crisis. The recently developed fractal kinetics susceptible-infected model was used for the analysis of the first COVID-19 wave data. The model was found to be in excellent agreement with the data. The “fractal” exponent of time is critical for the kinetics of the disease spreading since it captures the impact of the spatial related factors e.g. lockdowns, masks on the virus transmission. Estimates of the model parameters were derived from the epidemiological data of France, Greece, Italy and Spain. A universal law was established between the “fractal” exponent and the “apparent transmissibility constant” of the model. 173 countries were classified according to the fractal exponent and the asymptotic limit of the cumulative fraction of infected individuals.

A Fractal kinetics SI model can explain the dynamics of COVID-19 epidemics

The COVID-19 pandemic has already had a shocking impact on the lives of everybody on the planet. Here, we present a modification of the classical SI model, the Fractal Kinetics SI model which is in excellent agreement with the disease outbreak data available from the World Health Organization. The fractal kinetic approach that we propose here originates from chemical kinetics and has successfully been used in the past to describe reaction dynamics when imperfect mixing and segregation of the reactants is important and affects the dynamics of the reaction. The model introduces a novel epidemiological parameter, the “fractal” exponent h which is introduced in order to account for the self-organization of the societies against the pandemic through social distancing, lockdowns and flight restrictions.