Exactly solvable SIR models, their extensions and their application to sensitive pandemic forecasting

2020/10/06 by Sadurní, E., Luna-Acosta, G.
#34H05 #92D30 #Chaotic Dynamics (nlin.CD) #FOS: Biological sciences #FOS: Physical sciences #Physics and Society (physics.soc-ph) #Populations and Evolution (q-bio.PE)

paper · doi:10.48550/arxiv.2010.02897

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.

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