The basic reproduction number and the instability of the trivial equilibrium point of structured population models described by ODEs
Ryusuke Kon （今 隆助）
06/05/09, 13:30 at Room 3631 (6th floor of building 3 of the Faculty of Sciences)
The basic reproduction number R0 plays an important role in the study of structured population models. In many specific examples, R0>1 implies the instability of the trivial (or population free) equilibrium point. In this talk, we define the basic reproduction number for structured population models described by ordinary differential equations and give its simple algebraic formula (see Diekmann et al., 1990). Furthermore, we provide the condition under which the trivial equilibrium point is unstable (resp. stable) if and only if R0>1 (resp. R0<1). Our results can be obtained almost parallel to the results by Cushing and Yicang (1994). To illustrate the usefulness of our results, we apply them to some specific models: stage-structured and spatially structured models. |
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