The unbeatable ESS level of virulence
We will now look at the problem in a slightly different manner, from the perspective of invasions. Recall that the dynamics of the infected Figure 5.7. Marginal value construction used to find the optimal level of virulence. Figure 5.7. Marginal value construction used to find the optimal level of virulence. individuals are dl dt blS (v + m)1 from which we conclude that the steady state level of susceptibles is S(m) (v + m) b(m). Now let us consider an invader, which is rare and which uses an...
Diffusion and logistic population growth invasions the Fisher equation and traveling waves
We conclude this chapter with a short introduction to a complicated topic, and one that comes the closest to pure mathematics yet - we are going to show that a solution to a question exists, but we are not going to actually find the solution. By way of motivation, we begin with the empirical phenomenon. In Figure 2.21a, I show the spatial distribution of the variegated leafhopper (VLH, Erythronewra varzabz' zs) which is a pest of grapes in California (Settle and Wilson 1990), during an invasion...
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The overcapacity ratio, defined as the actual capacity of the fishery divided by the estimated long-run sustainable capacity, of various historical fisheries data from Clark 1990 and of the USA as a whole in 2002 D. Fluharty, personal communication . on Bayesian methods in stock assessment and fishery management. Good starting points include Thompson 1992 , McAllister et a . 1994 , Ellison 1996 , Kinas 1996 , McAllister 1996 , McAllister and lanelli 1997 , McAllister and Kirkwood...
Vectorbased diseases malaria
Diseases that are transmitted from one host to another via vectors rather than direct contact are common and important. For example Spielman and D'Antonio 2001 , mosquitoes transmit malaria Anopheles spp. , dengue and yellow fever Aedes spp. , West Nile Virus and filariasis, the worm that causes elephantitis Culex spp. Figure 5.10 . In this section, we will focus on malaria, which continues to be a deadly disease, killing more than one million people per year and being widespread and endemic in...
