Time-dependent forcing in the geosciences and in epidemiology

For many of us, the Covid-19 pandemic brought long-time scientific interest in epidemiology to the point of involvement. An important aspect of the evolution of acute respiratory epidemics is their seasonal character. Our toolkit for handling seasonal phenomena in the geosciences has increased in the last dozen years or so with the development and application of concepts and methods from the theory of nonautonomous and random dynamical systems (NDSs and RDSs). In this talk, I will briefly:

• Introduce some elements of these two closely related theories.

• Illustrate the two with an application to seasonal effects within a chaotic model of the El

  Niño–Southern Oscillation (ENSO).

• Introduce to a geoscientific audience a simple epidemiological “box” model of the

  Susceptible–Exposed–Infectious–Recovered (SEIR) type.

• Summarize NDS results for a chaotic SEIR model with seasonal effects.

• Mention the utility of data assimilation (DA) tools in the parameter identification and

  prediction of an epidemic’s evolution

  References

  - Chekroun, M D, Ghil M, Neelin J D (2018) Pullback attractor crisis in a delay differential ENSO model, in Nonlinear Advances in Geosciences, A. Tsonis (Ed.), Springer, pp. 1–33, doi: 10.1007/978-3-319-58895-7

  - Crisan D, Ghil, M (2022) Asymptotic behavior of the forecast–assimilation process with unstable dynamics, Chaos, in preparation

  - Faranda D, Castillo I P, Hulme O, Jezequel A, Lamb J S, Sato Y, Thompson E L (2020) Asymptotic estimates of SARS-CoV-2 infection counts and their sensitivity to stochastic perturbation<? Chaos, 30(5): 051107, doi: 10.1063/5.0009454

  - Ghil, M (2019) A century of nonlinearity in the geosciences. Earth & Space Science 6:1007–1042, doi:10.1029/2019EA000599

  - Kovács, T (2020) How can contemporary climate research help understand epidemic dynamics? Ensemble approach and snapshot attractors. J. Roy. Soc. Interface, 17(173):20200648, doi: 10.1098/rsif.2020.0648