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...

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...