Abstract
The aim of this chapter is to explore non-autonomous compartment models of epidemics, like, e.g., SIR models with time-dependent transmission and recovery rates as parameters, and particularly the occurrence of rate-induced tipping phenomena. Specifically, we are interested in the question, whether there can exist parameter paths that do not cross any bifurcation points, but yet give rise to tipping if the parameters vary over time. From literature, it is known that such rate-induced tipping occurs, e.g., in two-dimensional models of ecosystems or predator–prey systems. We show in this chapter that rate-induced tipping can also occur in compartment models of epidemics. Thus, regarding the Covid-19 crisis, not only the measures established in a lockdown and the moment of the lockdown, but also the rate by which lockdown measures are implemented may have a drastic influence on the number of infectious.
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Merker, J., Kunsch, B. (2021). Rate-Induced Tipping Phenomena in Compartment Models of Epidemics. In: Agarwal, P., Nieto, J.J., Ruzhansky, M., Torres, D.F.M. (eds) Analysis of Infectious Disease Problems (Covid-19) and Their Global Impact. Infosys Science Foundation Series(). Springer, Singapore. https://doi.org/10.1007/978-981-16-2450-6_14
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