What determines the number of parasites within a host? What determines the total number of parasites in a host population?

We are interested in

Density-dependent vs. density-independent effects

You can't have population regulation without some kind of density-dependent control; otherwise the population is on a random walk to infinity or zero (eventually zero). However, the population density in a given place and time is determined by both density-independent and density-dependent factors. As a simple example, if
dN/dt = (b-d-aN)N
(constant birth rate, linearly increasing death rate with population density) then the equilibrium population density is (b-d)/a = r/a; it depends both on density-independent (r) and density-dependent (a) factors.

Density-dependent regulation can happen only occasionally (e.g. in bad years, or at particular times of year), or in only one place in a (complex) host life cycle. Thus, it can be difficult to detect density dependence. It is rarely appropriate to look at low or fluctuating population densities and conclude that density-dependent controls "are not important".

However, we can ask whether the difference between population densities in two places/times arises because of differences in density-independent or density-dependent factors. [ex: Bothriocephalus (cestodes) in Gambusia (mosquito fish): seasonal variation in numbers, but not in biomass, because size of individuals changes as they mature. Furthermore, discharges from power plants (changing water temperature and/or adding pollutants such as selenium) decreases the parasite density - possibly because the free-living stages are affected by environmental conditions. In both cases both density-dependent and density-independent factors are acting, but in the first case it is the difference in density-dependent factors that matters, while in the second case it is the difference in density-independent factors.

Density-dependent regulation affects mortality (survivorship), establishment (initial survivorship), fecundity, or size (which ultimately affects mortality/fecundity)

Why is it important? Control depends on natural regulation process. Population dynamics under control?