tetano
Editor, Senior Moderator
Appl Math Model
. 2021 Feb;90:466-473.
doi: 10.1016/j.apm.2020.08.057. Epub 2020 Sep 28.
Analytical features of the SIR model and their applications to COVID-19
Nikolay A Kudryashov[SUP] 1 [/SUP], Mikhail A Chmykhov[SUP] 1 [/SUP], Michael Vigdorowitsch[SUP] 2 [/SUP]
Affiliations
Abstract
A classic two-parameter epidemiological SIR-model of the coronavirus propagation is considered. The first integrals of the system of non-linear equations are obtained. The Painlev? test shows that the system of equations is not integrable in the general case. However, the general solution is obtained in quadrature as an inverse time-function. Using the first integrals of the system of equations, analytical dependencies for the number of infected patients I(t) and that of recovered patients R(t) on the number of susceptible to infection S(t) are obtained. A particular attention is paid to interrelation of I(t) and R(t) both depending on α/β, where α is the contact rate in the community and β is the intensity of recovery/decease of patients. It is demonstrated that the data on particular morbidity waves in Hubei (China), Italy, Austria, South Korea, Moscow (Russia) as well some Australian territories are satisfactorily described by the expressions obtained for I(R). The variability of parameter N having been traditionally considered as a static population size is discussed.
Keywords: Coronavirus; First integral; Infection; Nonlinear differential equation; SIR-model; Solution.
. 2021 Feb;90:466-473.
doi: 10.1016/j.apm.2020.08.057. Epub 2020 Sep 28.
Analytical features of the SIR model and their applications to COVID-19
Nikolay A Kudryashov[SUP] 1 [/SUP], Mikhail A Chmykhov[SUP] 1 [/SUP], Michael Vigdorowitsch[SUP] 2 [/SUP]
Affiliations
- PMID: 33012957
- PMCID: PMC7521893
- DOI: 10.1016/j.apm.2020.08.057
Abstract
A classic two-parameter epidemiological SIR-model of the coronavirus propagation is considered. The first integrals of the system of non-linear equations are obtained. The Painlev? test shows that the system of equations is not integrable in the general case. However, the general solution is obtained in quadrature as an inverse time-function. Using the first integrals of the system of equations, analytical dependencies for the number of infected patients I(t) and that of recovered patients R(t) on the number of susceptible to infection S(t) are obtained. A particular attention is paid to interrelation of I(t) and R(t) both depending on α/β, where α is the contact rate in the community and β is the intensity of recovery/decease of patients. It is demonstrated that the data on particular morbidity waves in Hubei (China), Italy, Austria, South Korea, Moscow (Russia) as well some Australian territories are satisfactorily described by the expressions obtained for I(R). The variability of parameter N having been traditionally considered as a static population size is discussed.
Keywords: Coronavirus; First integral; Infection; Nonlinear differential equation; SIR-model; Solution.