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.

Commercial Whaling, Especially for Gray Whales, Eschrichtius robustus, and Humpback Whales, Megaptera novaeangliae, at California and Baja California Shore Stations in the 19th Century (1854–1899)

Shore whaling along North America’s California and Baja California coasts during 1854–99 was ancillary to the offshore and alongshore American whale fishery, which had begun in the North Pacific in the early 1800’s and was flourishing by the 1840’s. From its inception at Monterey, Calif., in the mid 1850’s, the shore fishery, involving open boats deployed from land to catch and tow whales for processing, eventually spread from Monterey south to San Diego and Baja California and north to Crescent City near the California–Oregon border. It had declined to a relict industry by the 1880’s, although sporadic efforts continued into the early 20th century. The main target species were gray whales, Eschrichtius robustus, and humpback whales, Megaptera novaeangliae, with the valuable North Pacific right whale, Eubalaena japonica, also pursued opportunistically. Catch data are grossly incomplete for most stations; no logbooks were kept for these operations as they were for high-seas whaling voyages. Even when good information is available on catch levels, usually as number of whales landed or quantity of oil produced, it is rarely broken down by species. Therefore, we devised methods for extrapolation, interpolation, pro rationing, correction, and informed judgment to produce time series of catches. The resulting estimates of landings from 1854 to 1899 are 3,150 (SE = 112) gray whales and 1,637 (SE = 62) humpback whales. The numbers landed should be multiplied by 1.2 to account for hunting loss (i.e. whales harpooned or shot but not recovered and processed).

Rangia and Marsh Clams, Rangia cuneata, R. flexuosa, and Polymesoda caroliniana, in Eastern México: Distribution, Biology and Ecology, and Historical Fisheries

Rangia and marsh clams, Rangia cuneata, R. flexuosa, and Polymesoda caroliniana, occur in brackish waters along México’s eastern coast from the northern State of Tamaulipas to the southern State of Campeche. The clams were important to the prehispanic people in the southern part of the State of Veracruz, where they were used as food and as construction material. In modern times, they are harvested for food. The fishermen wade in shallow water and harvest the clams in soft sediments by hand. Annual landings of whole clams during a recent 5-yr period, 1998–2002, were 1,139–1,695 t. The only area with a substantial ongoing clam fishery is in the Lower Papaloapan River Basin, including Alvarado Lagoon, where as many as 450 fishermen are licensed harvesters. This fishery for the Rangia and marsh clams is the most important clam fishery along México’s Gulf Coast.