On the Stability and Equilibrium Points of Multistaged SI (n) R Epidemic Models

This paper relies on the concept of next generation matrix defined ad hoc for a new proposed extended SEIR model referred to as SI(n)R-model to study its stability. The model includes n successive stages of infectious subpopulations, each one acting at the exposed subpopulation of the next infectious stage in a cascade global disposal where each infectious population acts as the exposed subpopulation of the next infectious stage. The model also has internal delays which characterize the time intervals of the coupling of the susceptible dynamics with the infectious populations of the various cascade infectious stages. Since the susceptible subpopulation is common, and then unique, to all the infectious stages, its coupled dynamic action on each of those stages is modeled with an increasing delay as the infectious stage index increases from 1 to n. The physical interpretation of the model is that the dynamics of the disease exhibits different stages in which the infectivity and the mortality rates vary as the individual numbers go through the process of recovery, each stage with a characteristic average time.

Comparison of average larval fish vertical distributions among species exhibiting different transport pathways on the southeast United States continental shelf

Water currents are vertically structured in many marine systems and as a result, vertical movements by fish larvae and zooplankton affect horizontal transport (Power, 1984). In estuaries, the vertical movements of larvae with tidal periods can result in their retention or ingress (Fortier and Leggett, 1983; Rijnsdorp et al., 1985; Cronin and Forward, 1986; Forward et al., 1999). On the continental shelf, the vertical movements of organisms interact daily and ontogenetically with depth-varying currents to affect horizontal transport (Pillar et al., 1989; Barange and Pillar, 1992; Cowen et al., 1993, 2000; Batchelder et al., 2002).

Year-class formation in Pacific herring (Clupea pallasi) estimated from spawning-date distributions of juveniles in San Francisco Bay, California

Inter and intra-annual variation in year-class strength was analyzed for San Francisco Bay Pacific herring (Clupea pallasi) by using otoliths of juveniles. Juvenile herring were collected from March through June in 1999 and 2000 and otoliths from subsamples of these collections were aged by daily otolith increment analysis. The composition of the year classes in 1999 and 2000 were determined by back-calculating the birth date distribution for surviving juvenile herring. In 2000, 729% more juveniles were captured than in 1999, even though an estimated 12% fewer eggs were spawned in 2000. Spawning-date distributions show that survival for the 2000 year class was exceptionally good for a short (approximately 1 month) period of spawning, resulting in a large abundance of juvenile recruits. Analysis of age at size shows that growth rate increased significantly as the spawning season progressed both in 1999 and 2000. However, only in 2000 were the bulk of surviving juveniles a product of the fast growth period. In the two years examined, year-class strength was not predicted by the estimated number of eggs spawned, but rather appeared to depend on survival of eggs or larvae (or both) through the juvenile stage. Fast growth through the larval stage may have little effect on year-class strength if mortality during the egg stage is high and few larvae are available.