Contrasting abundance and residency patterns of two sympatric populations of transient killer whales (Orcinus orca) in the northern Gulf of Alaska

Two sympatric populations of “transient” (mammal-eating) killer whales were photo-identified over 27 years (1984–2010) in Prince William Sound and Kenai Fjords, coastal waters of the northern Gulf of Alaska (GOA). A total of 88 individuals were identified during 203 encounters with “AT1” transients (22 individuals) and 91 encounters with “GOA” transients (66 individuals). The median number of individuals identified annually was similar for both populations (AT1=7; GOA=8), but mark-recapture estimates showed the AT1 whales to have much higher fidelity to the study area, whereas the GOA whales had a higher exchange of individuals. Apparent survival estimates were generally high for both populations, but there was a significant reduction in the survival of AT1 transients after the Exxon Valdez oil spill in 1989, with an abrupt decline in estimated abundance from a high of 22 in 1989 to a low of seven whales at the end of 2010. There was no detectable decline in GOA population abundance or survival over the same period, but abundance ranged from just 6 to 18 whales annually. Resighting data from adjacent coastal waters and movement tracks from satellite tags further indicated that the GOA whales are part of a larger population with a more extensive range, whereas AT1 whales are resident to the study area.

Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability

This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.

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.

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.