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SUMMARY:Patrick DeLeenher (Oregon State University)
DTSTART:20221201T160000Z
DTEND:20221201T163000Z
DTSTAMP:20260421T125156Z
UID:MoRN/60
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MoRN/60/">Th
 e basic reproduction number for linear semigroups in R^n with an invariant
  cone</a>\nby Patrick DeLeenher (Oregon State University) as part of Semin
 ar on the Mathematics of Reaction Networks\n\n\nAbstract\nWe consider line
 ar ODEs dx/dt=Ax on R^n and first characterize the class of operators A th
 at 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 dis
 cuss 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 reproduc
 tion numbers are often easier to calculate than the spectral abscissa\, wh
 ich is why they are so popular in epidemiology and ecology. We shall illus
 trate these concepts and results on a simple model of an infectious diseas
 e\, and if time permits\, show that controlling R0 one way may have an opp
 osite effect on the spectral abscissa. This suggests that one should be (m
 ore) careful when lowering R0 in order to control an infectious disease.\n
LOCATION:https://researchseminars.org/talk/MoRN/60/
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