Extending the Basic Reproduction Number to Biochemical Reaction Networks

Abstract: We extend the next generation matrix method for computing the basic reproduction number in mathematical epidemiology to computing an analogous number for establishing the stability of boundary faces in biochemistry. In epidemiology, the basic reproduction number indicates whether a disease can invade a population, with values below one leading to disease-free stability and values above one signaling an outbreak. In biochemistry, the number determines whether certain chemical species persist or go extinct, with values greater than one leading to persistence. The next generation matrix method approach is typically significantly more computationally tractable than standard Jacobian or Routh-Hurwitz methods for establishing stability; consequently, the method could have significant applications for understanding metabolic function.

chemical biologychemical kineticsalgebraic geometrydynamical systemsprobability

Audience: researchers in the topic

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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! Many of the talks are recorded; to see the recording, from Past Talks, open details of the listed talk for a video link.

The organizers.

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