Epidemiological model with anomalous kinetics - The Covid-19 pandemics

Abstract

We generalize the phenomenological, law of mass action-like, SIR and SEIR epidemiological models to situations with anomalous kinetics. Specifically, the contagion and removal terms, normally linear in the fraction $I$ of infecteds, are taken to depend on $I^{\,q_{up}}$ and $I^{\,q_{down}}$, respectively. These dependencies can be understood as highly reduced effective descriptions of contagion via anomalous diffusion of susceptibles and infecteds in fractal geometries, and removal (i.e., recovery or death) via complex mechanisms leading to slowly decaying removal-time distributions. We obtain rather convincing fits to time series for both active cases and mortality with the same values of $(q_{up},q_{down})$ for a given country, suggesting that such aspects may in fact be present in the evolution of the Covid-19 pandemic. We also obtain approximate values for the effective population $N_{eff}$, which turns out to be a small percentage of the entire population $N$ for each country.

A novel methodology for epidemic risk assessment of COVID-19 outbreak

“…Despite all this, the large amount of official data published in the last months, and updated daily 4 , 5 , has nourished the development of several mathematical models, which are fundamental to understand the possible evolution of an epidemic and to plan effective control strategies 6 – 15 . However, due to the incompleteness of the data and to the intrinsic complexity of our globalized world, predicting the evolution, the peak or the end of the pandemic is a very difficult challenge 16 , 17 .…”

Connecting complex networks to nonadditive entropies

“…This form, more precisely , optimizes the entropy under appropriate canonical constraints, being the site energy and the inverse temperature; the BG weight is recovered at the limit. This thermostatistical approach has been successfully applied in a wide diversity of areas, such as long-range-interacting Hamiltonian systems 23 , vortices in type II supercondutors 24 , cold atoms 25 , granular matter 26 , high-energy physics experiments on Earth 27 and observations in the outer space 28 , 29 , civil engineering 30 , and for predicting COVID-19 peaks around the world 31 , 32 .…”

Standard and anomalous waves of COVID-19: A multiple-wave growth model for epidemics

“…Furthermore, we follow Refs. 33, 34 and replace the term I ( t ) on the right-hand side of all equations above by [ I ( t )] p , to obtain Although this model is still not general enough to accommodate all the phenomenology of the intervention biased dynamics of the COVID-19 epidemics, it does nonetheless exhibit subexponential behaviour for both short and large time scales in all compartments. In order to show this, we define y ( t ) = S ( t ) + I ( t ) and divide (11) by (10) to obtain where R 0 = β/ ( γ 1 + γ 2 ).…”