Stability analysis and observer design for discrete-time SEIR epidemic models

This paper applies Micken's discretization method to obtain a discrete-time SEIR epidemic model. The positivity of the model along with the existence and stability of equilibrium points is discussed for the discrete-time case. Afterwards, the design of a state observer for this discrete-time SEIR epidemic model is tackled. The analysis of the model along with the observer design is faced in an implicit way instead of obtaining first an explicit formulation of the system which is the novelty of the presented approach. Moreover, some sufficient conditions to ensure the asymptotic stability of the observer are provided in terms of a matrix inequality that can be cast in the form of a LMI. The feasibility of the matrix inequality is proved, while some simulation examples show the operation and usefulness of the observer.

Estimating the maximum sustainable yield of bonito (Sarda chiliensis, Scombridae) of northern Chile from monthly catch data

Monthly catch data of bonito Sarda chiliensis from northern Chile, from 1976 to 1989, were used to obtain a series of estimates of the Z-G parameter (i.e., total mortality minus the growth coefficient in weight). This series was then used to estimate a maximum sustainable yield of 4,500 t/year through a modified version of the surplus production model of J. Csirke and J. Caddy. The status of the fishery is discussed.

Maximum likelihood estimation of mortality and growth with individual variability from multiple length-frequency data

We consider estimation of mortality rates and growth parameters from length-frequency data of a fish stock and derive the underlying length distribution of the population and the catch when there is individual variability in the von Bertalanffy growth parameter L∞. The model is flexible enough to accommodate 1) any recruitment pattern as a function of both time and length, 2) length-specific selectivity, and 3) varying fishing effort over time. The maximum likelihood method gives consistent estimates, provided the underlying distribution for individual variation in growth is correctly specified. Simulation results indicate that our method is reasonably robust to violations in the assumptions. The method is applied to tiger prawn data (Penaeus semisulcatus) to obtain estimates of natural and fishing mortality.

The Northern Rockfish, Sebastes polyspinis, in Alaska: Commercial Fishery, Distribution, and Biology

The northern rockfish, Sebastes polyspinis, is the second most abundant rockfish in Alaska, and it supports a valuable trawl fishery. Little information is available, however, on either the biology of this species or its commercial fishery. To provide a synopsis of information on northern rockfish in Alaska, this study examined data for this species from commercial fishery observations in 1990–98 and from fishery-independent trawl surveys in 1980–99. Nearly all the commercial catch came from bottom trawling, mostly by large factory-trawlers, although smaller shore-based trawlers in recent years took an increasing portion of the catch in the Gulf of Alaska. Most of the northern rockfish catch in the Gulf of Alaska was taken by a directed fishery, whereas that of the Aleutian Islands predominantly came as discarded bycatch in the Atka mackerel fishery. In both regions, most of the catch was taken from a number of relatively small and discrete fishing grounds at depths of 75–150 m in the Gulf of Alaska and 75–175 m in the Aleutian Islands. These grounds, especially in the Gulf of Alaska, are on shallow rises or banks located on the outer continental shelf, and often are surrounded by deeper water. Five fishing grounds were identified in the Gulf of Alaska, and eleven in the Aleutian Islands. One fishing ground in the Gulf of Alaska, the “Snakehead” south of Kodiak Island, accounted for 46% of the total northern rockfish catch in this region. Analysis of the survey data generally revealed similar patterns of geographic distribution as those seen in the fishery, although some of the commercial fishing grounds did not stand out as areas of special abundance in the surveys. The surveys also found two areas of abundance that were not evident in the fishery data. Relatively few juvenile northern rockfish were caught in any of the surveys, but those taken in the Gulf of Alaska tended to occur more inshore and at shallower depths than adults. Individual size of northern rockfish was substantially larger in the Gulf of Alaska than in the Aleutian Islands according to both fishery and survey data. Analysis of age data from each region supports this, as Gulf of Alaska fish were found to grow significantly faster and reach a larger maximum length than those in the Aleutian Islands. Sex ratio in the Gulf of Alaska was nearly 50:50, but females predominated in the Aleutian Islands by a ratio of 57:43. In both regions, size of females was significantly larger than males.