The basic reproduction number for linear semigroups in R^n with an invariant cone

Abstract: We consider linear ODEs dx/dt=Ax on R^n and first characterize the class of operators A that have the property that e^{tA}(K) is contained in K for all non-negative t. These turn out to be the so-called cross-positive operators on K, or equivalently, the class of resolvent-positive operators (with respect to K). We then introduce the notion of a basic reproduction number R0 and discuss the trichotomy which says that R0-1 and the spectral abscissa s(A) of A always have the same sign (positive, negative or zero). Basic reproduction numbers are often easier to calculate than the spectral abscissa, which is why they are so popular in epidemiology and ecology. We shall illustrate these concepts and results on a simple model of an infectious disease, and if time permits, show that controlling R0 one way may have an opposite effect on the spectral abscissa. This suggests that one should be (more) careful when lowering R0 in order to control an infectious disease.

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

( video )

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Seminar on the Mathematics of Reaction Networks

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This seminar series focuses on progress in mathematical theory for the study of reaction networks, mainly in biology and chemistry. The scope is broad and accommodates works arising from dynamical systems, stochastics, algebra, topology and beyond.

We aim at providing a common forum for sharing knowledge and encouraging discussion across subfields. In particular we aim at facilitating interactions between junior and established researchers. These considerations will be represented in the choice of invited speakers and we will strive to create an excellent, exciting and diverse schedule.

The seminar runs twice a month, typically on the 2nd and 4th Thursday of the month, at 17:00 Brussels time (observe that this webpage shows the schedule in your current time zone). Each session consists of two 25-minute talks followed by 5-minute questions. After the two talks, longer discussions will take place for those interested. To this end, we will use breakout rooms. For this to work well, you need to have the latest version of Zoom installed (version 5.3.0 or higher), and use the desktop client or mobile app (not supported on ChromeOS).

We look forward hearing about new work and meeting many of you over zoom!

The organizers.

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