Microparasites that infect a single host with no intervening secondary host may behave according to simple mass action principles in terms of disease development.
Those microparasites and macroparasites that require more than one species of host to complete their life cycles must be described by more complex models.
Some examples of fish pathogens that have multiple- host life cycles are listed in Table 4. Since there is more than one host involved, the models for dynamics involve essentially a multiplicative interaction of S–I–R among hosts.
For example, in Myxobolus cerebralis infections, R0 is dependent on fish density (the ratio of the vector to the fish host), contact rate, b, immunity, natural survival rate, etc., as well as on survival of the pathogen and its rate of development while in the worm host or in the environment, the latent period in the worm, and the survival rate of the worm.
Models of important human diseases, such as malaria, with complex life cycles have been developed (May 1977), and if the appropriate information on the various components is available, there is no reason why models of infection cannot eventually be constructed for fish diseases such as whirling disease and others that have complex life cycles.
Spatial considerations:
—The dynamic models described above assume homogeneity of the population with respect to both time and space, a simplistic assumption. This assumption, however, is probably valid for diseases in aquaculture, in which the densities are high and individuals tend to mix within the constraints of troughs, raceways, ponds, or sea cages.
This movement of potentially infectious individuals within a confined space over a long period will lead to spatial homogeneity. Also in aquaculture, the densities do not change markedly with time. Once a year-class has been placed into a container, they are graded at intervals and split to maintain appropriate, relatively constant densities.
On the other hand, in wild fish ecosystems, neither of these constraints is operable. For most of their life cycles, the salmonids are not particularly social and tend to occupy spatial niches separate from others of their own species and adhere assiduously to cover (Weatherly and Gill 1987).
Thus, for a given stretch of river, stream, or lake, there are pockets where the local densities are high and others where few, if any, fish reside. This patchy distribution can promote the retention of disease, which may not otherwise occur if the population were distributed homogeneously; it would also protect a proportion of the population from infection. Likewise, during the annual—and longer—spawning cycles of the salmonids, a large fluctuation in density is promulgated by the spawning process.
During spawning season, higher concentrations of fish are migrating upstream to spawn and occupying redds in close proximity to each other, thereby increasing the probability of pathogen transfer.
If spawning fish are infectious, they may consequently transfer the infectious agent directly to progeny or to susceptible fish residing nearby or downstream. As long as the parent fish is infectious, this could occur whether or not the disease is manifest at the time of spawning.
This characteristic density increase is also manifest for the embryonation period and the fry stage when young-of-the-year fish are in the gravel on the redds and during outmigration.
These types of density perturbations are also found for other wild and domesticated animals that mate only at relatively circumscribed periods, as compared with animals such as humans, which produce young at a rate unrelated to season.
Consequently, for fish in the wild, adjustments must be made in models to deal with the relatively episodic but predictable changes in densities, as compared with a constant change over time.
Author:
PAUL W. RENO
