Mathematical Biology and Ecology Seminar
Wednesday, April 23, 2014 - 11:00
1 hour (actually 50 minutes)
We will introduce a PDE model to investigate how epidemic metrics, such as the basic reproductive ratio R_0 and infection prevalence, depend on a pathogen's virulence. We define virulence as all harm inflicted on the host by the pathogen, so it includes direct virulence (increased host mortality and decreased fecundity) and indirect virulence (increased predation on infected hosts). To study these effects we use a Daphnia-parasite disease system. Daphnia are freshwater crustaceans that get infected while feeding, by consuming free-living parasite spores. These spores after they are ingested, they start reproducing within the host and the host eventually dies. Dead hosts decay releasing the spores they contain back in the water column. Visual predators, such as fish, can detect infected hosts easier because they become opaque, hence they prey preferentially on them. Our model includes two host classes (susceptible and infected), the free-living propagules, and the food resource (algae). Using experimental data, we obtain the qualitative curves for the dependence of disease-induced mortality and fecundity reduction on the age of infection. Among other things, we will show that in order the predator to keep the host population healthy, it needs to (i) detect the infected hosts very soon after they become infected and (ii) show very high preference on consuming them in comparison to the uninfected hosts. In order to address questions about the evolution of virulence, we will also discuss how we defined the invasion fitness for this compartmental model. We will finish with some pairwise invasibility plots, that show when a mutant strain can invade the resident strain in this disease system.