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The classic SIR model of epidemic dynamics is solved completely byquadratures, including a time integral transform expanded in a series ofincomplete gamma functions. The model is also generalized to arbitrarytime-dependent infection rates and solved explicitly when the control parameterdepends on the accumulated infections at time $t$. Numerical results arepresented by way of comparison. Autonomous and non-autonomous generalizationsof SIR for interacting regions are also considered, including non-separabilityfor two or more interacting regions. A reduction of simple SIR models to onevariable leads us to a generalized logistic model, Richards model, which we useto fit Mexico's COVID-19 data up to day number 134. Forecasting scenariosresulting from various fittings are discussed. A critique to the applicabilityof these models to current pandemic outbreaks in terms of robustness isprovided. Finally, we obtain the bifurcation diagram for a discretized versionof Richards model, displaying period doubling bifurcation to chaos.

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