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.

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.