Asymptotic solutions of the SIR and SEIR models well above the epidemic threshold
Ima Journal of Applied Mathematics
; : 16, 2022.
Article
in English
| Web of Science | ID: covidwho-1978230
ABSTRACT
A simple and explicit expression of the solution of the SIR epidemiological model of Kermack and McKendrick is constructed in the asymptotic limit of large basic reproduction numbers R-0. The proposed formula yields good qualitative agreement already when R-0 >= 3 and rapidly becomes quantitatively accurate as larger values of R-0 are assumed. The derivation is based on the method of matched asymptotic expansions, which exploits the fact that the exponential growing phase and the eventual recession of the outbreak occur on distinct time scales. From the newly derived solution, an analytical estimate of the time separating the first inflexion point of the epidemic curve from the peak of infections is given. Finally, we use the same method on the SEIR model and find that the inclusion of the 'exposed' population in the model can dramatically alter the time scales of the outbreak.
Full text:
Available
Collection:
Databases of international organizations
Database:
Web of Science
Language:
English
Journal:
Ima Journal of Applied Mathematics
Year:
2022
Document Type:
Article
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