Global stability of an SIR epidemic model with time delays

An SIR disease transmission model is formulated under the assumption that the force of infection at the present time depends on the number of infectives at the past. It is shown that a disease free equilibrium point is globally stable if no endemic equilibrium point exists. Further the endemic point (if it exists) is globally stable with respect to the whole state space except the neighborhood of the disease free state.Research partly supported by the Ministry of Education, Science and Culture, Japan, Grant 05640256     

Proliferation of pulmonary endothelial cells: Time-lapse cinematography of growth to confluence and restitution of monolayer after wounding

A fundamental characteristic of vascular endothelium is that it exists as a monolayer, a condition that must be met in both vascular growth and repair. Maintenance of the monolayer is important both for the exchange of nutrients and for interactions between blood solutes and endothelial enzymes and transport systems. We have used time-lapse cinematography to compare proliferative behavior of bovine pulmonary endothelial cells in (1) establisment of a monolayer from a low-density seed (7.5 × 10⁴ cells in a 60 mm dish) and (2) restitution of a confluent monolayer (approx. 2.9 × 10⁶ cells in a 60 mm dish) following a mechanical wound (removal of cells from an area 5 × 15 mm by scraping). Culture 2 was not refed after wounding. In culture 2, approx. 30% of the cells accounted for repopulation (confluence in 40 hr). In culture I, all cells entered into division. Participating cells of culture 2 began division immediately (69 divisions/filmed area in 10 hr, vs. four divisions in culture I). Interdivision times (IDT) were longer and relatively constant in culture I until near confluence; none were < 10 h, whereas in 2, 24% of the IDT's were ≤ 10 hr. Remarkably, IDTs of culture 2 decreased steadily until confluence was re-established. Cell migration in culture 1 was multidirectional while direction of migration in culture 2 was always into the wound area. Mean migration rate (MIG) in culture 2 was related to the site of origin of the cells, those dividing farthest from the unwounded area had fastest MIGs. Neither culture formed more than a single layer of cells. Although the cell kinetics of cultures 1 and 2 differed, the same goal, confluence, was achieved in either case.     

Succession,diversité et amplitude de niche dans les påturages du centre de la péninsule ibérique

Some diversity and niche amplitude parameters were applied to rangeland pastures of the Central Iberian Peninsula and to their succession stages after the periodical ploughing typical of the traditional management of these areas. Four different slopes within a large area of undulating terrain were selected for the monitoring of succession as they contained the characteristical geomorphological pattern of the area (denudation, transport and accumulation sectors).If we consider the total entropy theorem, H (E.P.)=H(E)+H(P/E), the total entropy of the slope H(E.P) and the entropy of species H(E) increase as succession progresses. As the value of the entropy of the sampling plots conditioned by the species H(P/E) is affected by the number of plots utilized, we employed the expression A=H(P/E)/log₂ number of plots, similar to Pielou's index for niche amplitude, W=H(P/E)/H(P).This values decreases with succession, indicating that plant species tend to occupy more definite sectors along the slope. The number of low entropy species H(P/E) _i or specialist species, confined to narrow sectors also increases. When computed separately within the different sectors niche amplitude results in small values for the low slope regions (accumulation sector). This effect becomes more pronounced when succession advances.

Nous remercions le Conseil d'Administration de La Paranza, propriétaire du Castillo de Vañuelas, et particulièrement Mrs. C. Hernandez-Ros et J. A. Léon-Vrquijò, pour les faeilités qu'ils ont données à cette équipe durant la réalisation de ce travail.     

Genetic architecture of yield and components of yield in mustard (Brassica juncea (L.) Czern & Coss.)

Summary The relative ability of cross- and self-pollen to achieve fertilisation in Brassica was studied by making double pollinations using cross-pollen carrying a dominant seedling marker gene. With simultaneous self- and crosspollination 12–40% self-seed was set, but when cross-pollen was applied to the stigma four hours before self-pollen, only 2–4% self-seed was obtained. In two plants to which cross-pollen was applied at various time intervals after self-pollen there was a tendency for the percentage of self-seed to increase as the time interval increased. In a third plant this trend was not apparent, probably because of a greater degree of self-incompatibility. The competitive advantage of the first pollen to arrive on the stigma is discussed in relation to the strength of the self-incompatibility and the sib problem in F₁ hybrid brassicas.     

Alternative risk-taking styles: The case of time-budgeting strategies of terrestrial gastropods

The terrestrial slugs Arion ater, Limax maximus and Ariolimax columbianus have similar morphological designs but differ remarkably in their life history tactics and behavioural time budgets. The adaptive value of particular risk-taking styles was investigated using a comprehensive computer simulation model. The model allowed each species' success (growth rates, food acquisition) and costs (distance travelled, hydration deficits, injury from aggressive encounters) to be evaluated in various types of weather (benign, harsh and surprise). This was interpreted in terms of the species' life history design. In addition, each species was simulated with the behavioural strategy of the other two species substituted for its natural programming. The simulation experiments demonstrated how variations in a few simple rules could lead to divergent cost-benefit consequences. The model also illustrated that coarsely-tuned sensitivity to the environment may be better than finely-tuned responses, depending on the animal's ability to respond quickly and the degree of risk. The simulations suggested that competition has shaped the time-budgeting tactics of A. ater and L. maximus. Each species actually performed better in harsh weather, using the behavioural program of the other. L. maximus is an aggressive species with a narrow, nocturnal activity period. The concentrated activity of L. maximus may allow it to displace competitors more effectively, whereas the broader time span of A. ater's activity may be necessary to avoid L. maximus.     

The derivation and use of biosynthetic incorporation and dilution values

Mathematical expressions governing incorporation and dilution values in a simple, three component biosynthetic system are established and used to track the influence of pathway structure and sampling time on the numerical value of these parameters. A more productive manner of using the incorporation concept is suggested.