Exactly solvable SIR models, their extensions and their application to sensitive pandemic forecasting.
Nonlinear Dyn
; 103(3): 2955-2971, 2021.
Article
in English
| MEDLINE | ID: covidwho-1064565
ABSTRACT
The classic SIR model of epidemic dynamics is solved completely by quadratures, including a time integral transform expanded in a series of incomplete gamma functions. The model is also generalized to arbitrary time-dependent infection rates and solved explicitly when the control parameter depends on the accumulated infections at time t. Numerical results are presented by way of comparison. Autonomous and non-autonomous generalizations of SIR for interacting regions are also considered, including non-separability for two or more interacting regions. A reduction of simple SIR models to one variable leads us to a generalized logistic model, Richards model, which we use to fit Mexico's COVID-19 data up to day number 134. Forecasting scenarios resulting from various fittings are discussed. A critique to the applicability of these models to current pandemic outbreaks in terms of robustness is provided. Finally, we obtain the bifurcation diagram for a discretized version of Richards model, displaying period doubling bifurcation to chaos.
Full text:
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Collection:
International databases
Database:
MEDLINE
Language:
English
Journal:
Nonlinear Dyn
Year:
2021
Document Type:
Article
Affiliation country:
S11071-021-06248-y
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