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adult assume assumption asymptotically stable average age average duration basic replacement ratio Beverton-Holt biomass Borel measurable boundary equilibrium bounded variation cannibalism capita birth rate capita mortality rate Chapter consider constant continuously differentiable converge convex Corollary defined denotes derivatives difference equation disease disease-free equilibrium dynamics eigenvalues endemic equilibrium epidemic expectation of remaining exponentially distributed Figure finite fixed point formula Furthermore Hence Hopf bifurcation implies infectious period infective individual initial data interior equilibrium intermediate value theorem interval juvenile Lemma Let f locally asymptotically stable Malthusian parameter mean sojourn monotone monotone nonincreasing nonincreasing nonnegative obtain periodic orbits population Proof Proposition Recall remaining sojourn reproduction satisfies Section sequence sojourn function solutions starting spectral radius stable manifold stage age stage duration step function Stieltjes integral strictly decreasing strictly positive subset susceptible Toolbox toxicant unstable vaccination value theorem variables vector Verhulst Verhulst equation
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Reinhard Bürger - 2005 - Journal of Mathematical Biology
Luís MA Bettencourt, Ariel Cintrón-Arias, David I Kaiser, Carlos Castillo-Chávez - 2006 - Physica A: Statistical Mechanics and its Applications
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