Norman R, Begon M & Bowers R (1994) The population dynamics of microparasites and vertebrate hosts: the importance of immunity and recovery. Theoretical Population Biology, 46 (1), pp. 96-119. https://doi.org/10.1006/tpbi.1994.1021
The models of Anderson and May on the dynamics of vertebrate (1979, Nature 280, 361-367) and invertebrate (1981, Philos, Trans. R. Soc. 291, 451-524) populations and their microparasites have been extended and elaborated. Hence, in a series of models the effects of a range of biological factors have been considered. These models taken together clarify in particular the effects of recovery from the disease back to a state of susceptibility and the additional effects of recovery to a state of immunity. In general recovery increases both the threshold density and the equilibrium density but does not alter the prevalence of infection or the region in parameter space in which the host is regulated. Immunity causes a further increase in the equilibrium density, does not alter either the prevalence of infection or the threshold density, but reduces the region in which there is regulation. In both cases exceptions tend to occur when there is density dependence.
Theoretical Population Biology: Volume 46, Issue 1