Branching Process Modelling of COVID-19 Pandemic Including Immunity and Vaccination
-
Dimitar Atanasov
,
Vessela Stoimenova
Abstract
We propose modeling COVID-19 infection dynamics using a class of two-type branching processes. These models require only observations on daily statistics to estimate the average number of secondary infections caused by a host and to predict the mean number of the non-observed infected individuals. The development of the epidemic process depends on the reproduction rate as well as on additional facets as immigration, adaptive immunity, and vaccination. Usually, in the existing deterministic and stochastic models, the officially reported and publicly available data are not sufficient for estimating model parameters. An important advantage of the proposed model, in addition to its simplicity, is the possibility of direct computation of its parameters estimates from the daily available data. We illustrate the proposed model and the corresponding data analysis with data from Bulgaria, however they are not limited to Bulgaria and can be applied to other countries subject to data availability.
Funding statement: The research was partially supported by the National Scientific Foundation of Bulgaria at the Ministry of Education and Science, Grant No KP-6-H22/3 and by the financial funds allocated to the Sofia University “St. Kliment Ohridski”, Grant No. 80-10-87/2021.
Acknowledgements
The authors are very grateful to the referee for the careful reading of the paper and for the useful remarks.
References
[1] S. Asmussen and H. Hering, Branching Processes, Progr. Probab. Stat. 3, Birkhäuser, Boston, 1983. 10.1007/978-1-4615-8155-0Suche in Google Scholar
[2] D. Atanasov and V. Stoimenova, Matlab-bp-engine, GitHub, retrieved October 26, 2020, https://github.com/amitko/matlab-bp-engine/releases/tag/1.0. Suche in Google Scholar
[3] D. Atanasov, V. Stoimenova and N. Yanev, Estimators in branching processes with immigration, Pliska Stud. Math. Bulgar. 18 (2007), 19–40. Suche in Google Scholar
[4] K. B. Athreya and P. E. Ney, Branching Processes, Grundlehren Math. Wiss. 196, Springer, Berlin, 1972. 10.1007/978-3-642-65371-1Suche in Google Scholar
[5] M. Gonzalez, I. M. del Puerto and G. P. Yanev, Controlled Branching Processes, Wiley, London, 2018. 10.1002/9781119452973Suche in Google Scholar
[6] P. Guttorp, Statistical Inference for Branching Processes, John Wiley & Sons, New York, 1991. Suche in Google Scholar
[7] P. Haccou, P. Jagers and V. A. Vatutin, Branching Processes: Variation, Growth, and Extinction of Populations, Cambridge Stud. Adapt. Dynam. 5, Cambridge University Press, Cambridge, 2007. Suche in Google Scholar
[8] T. E. Harris, The Theory of Branching Processes, Grundlehren Math. Wiss. 119, Springer, Berlin, 1963. 10.1007/978-3-642-51866-9Suche in Google Scholar
[9] P. Jagers, Branching processes with biological applications, Wiley-Interscience, London, 1975. Suche in Google Scholar
[10] M. Kimmel and D. E. Axelrod, Branching Processes in Biology, 2nd ed., Interdiscip. Appl. Math. 19, Springer, New York, 2015. 10.1007/978-1-4939-1559-0_2Suche in Google Scholar
[11] C. J. Mode, Multitype Branching Processes, Elsevier, New York, 1971. Suche in Google Scholar
[12] B. A. Sevastyanov, Branching Processes (in Russian), “Nauka”, Moscow, 1971. Suche in Google Scholar
[13] M. Stehlík, J. Kiseľák, M. Alejandro Dinamarca, Y. Li and Y. Ying, On COVID-19 outbreaks predictions: Issues on stability, parameter sensitivity, and precision, Stoch. Anal. Appl. 39 (2021), no. 3, 383–404. 10.1080/07362994.2020.1802291Suche in Google Scholar
[14] V. Stoimenova, D. Atanasov and N. Yanev, Robust estimation and simulation of branching processes, C. R. Acad. Bulgare Sci. 57 (2004), no. 5, 19–22. Suche in Google Scholar
[15] A. Y. Yakovlev, V. K. Stoimenova and N. M. Yanev, Branching processes as models of progenitor cell populations and estimation of the offspring distributions, J. Amer. Statist. Assoc. 103 (2008), no. 484, 1357–1366. 10.1198/016214508000000913Suche in Google Scholar
[16] A. Y. Yakovlev and N. M. Yanev, Transient Processes in Cell Proliferation Kinetics, Lecture Notes in Biomath. 82, Springer, Berlin, 1989. 10.1007/978-3-642-48702-6Suche in Google Scholar
[17] N. M. Yanev, Statistical inference for branching processes, Records and Branching Processes, Nova Science Publishers, New York (2008), 143–168. Suche in Google Scholar
[18] N. M. Yanev, V. K. Stoimenova and D. V. Atanasov, Branching stochastic processes as models of COVID-19 epidemic development, preprint (2020), https://arxiv.org/abs/2004.14838v2. 10.7546/CRABS.2020.11.02Suche in Google Scholar
[19] N. M. Yanev, V. K. Stoimenova and D. V. Atanasov, Stochastic modeling and estimation of COVID-19 population dynamics, preprint (2020), https://arxiv.org/abs/2004.00941. 10.7546/CRABS.2020.04.02Suche in Google Scholar
[20] European Centre for Disease Prevention and Control. Suche in Google Scholar
[21] Open Data Portal, Bulgarian government, https://data.egov.bg/. Suche in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- 5th International Workshop on Branching Processes and Their Applications (IWBPA 2021)
- Critical Galton–Watson Processes with Overlapping Generations
- Linear Fractional Galton–Watson Processes in Random Environment and Perpetuities
- Limit Theorems for a Strongly Supercritical Branching Process with Immigration in Random Environment
- Asymptotic Properties of a Supercritical Branching Process with Immigration in a Random Environment
- Branching Process Modelling of COVID-19 Pandemic Including Immunity and Vaccination
- Homogeneous Branching Processes with Non-Homogeneous Immigration
Artikel in diesem Heft
- Frontmatter
- 5th International Workshop on Branching Processes and Their Applications (IWBPA 2021)
- Critical Galton–Watson Processes with Overlapping Generations
- Linear Fractional Galton–Watson Processes in Random Environment and Perpetuities
- Limit Theorems for a Strongly Supercritical Branching Process with Immigration in Random Environment
- Asymptotic Properties of a Supercritical Branching Process with Immigration in a Random Environment
- Branching Process Modelling of COVID-19 Pandemic Including Immunity and Vaccination
- Homogeneous Branching Processes with Non-Homogeneous Immigration
