Branching stochastic processes as models of Covid-19 epidemic development

Paper can be found in arXiv.org
  • Nikolay M. Yanev, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
  • Vessela K. Stoimenova, Faculty of Mathematics and Informatics, Sofia University
  • Dimitar V. Atanasov, New Bulgarian University

Abstract

The aim of the paper is to describe two models of Covid-19 infection dynam- ics. For this purpose a special class of branching processes with two types of individuals is considered. These models are intended to use only the observed daily statistics to estimate the main parameter of the infection and to give a prediction of the mean value of the non-observed population of the infected in- dividuals. Similar problems are considered also in the case when the processes admit an immigration component. This is a serious advantage in comparison with other more complicated models where the officially reported data are not sufficient for estimation of the model parameters. In this way the specific de- velopment of the Covid-19 epidemics is considered also for all countries as it is given in the specially created site http://ir-statistics.net/covid-19 where the obtained results are updated daily.

Using that methodology, up-to-date reports based on the dataset provided by European Centre for Disease Prevention and Control are available HERE.

The reports are updated daily.


Stochastic modeling and estimation of COVID-19 population dynamics

  • Nikolay M. Yanev, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
  • Vessela K. Stoimenova, Faculty of Mathematics and Informatics, Sofia University
  • Dimitar V. Atanasov, New Bulgarian University

Abstract

The aim of the paper is to describe a model of the development of the Covid-19 contamination of the population of a country or a region. For this purpose a special branching process with two types of individuals is considered. This model is available to use only the observed daily statistics to estimate the main parameter of the contamination and to give a prediction of the mean value of the non-observed population of the contaminated individuals. This is a serious advantage in comparison with other more complicated models where the observed statistics are not sufficient. In this way the specific development of the Covid-19 epidemics is considered for some different countries.

Preliminary verssion of the paper can be found in arXiv.org . The paper is published in Comptes rendus de l’Acade'mie bulgare des Sciences, Vol 73, No4, pp.451-460. DOI: 10.7546/CRABS.2020.04.02


Modelling COVID-19 with a General Branching Process (GBP), also called Crump-Mode-Jagers branching process

Very interesting results are obtained using Branching Process Simulator developed by Plamen Trayanov, PhD. Recently he was able to perfor a COVID-19 models for Germany, France, Italy, Sweden, Indonesia and Bulgaria. The considered branching processes are alternative to the classical epidemics model like SEIR.

A brief description of the model (in Bulgarian) can be foun HERE.