Relationships among recent models for insect population dynamics with variable rates of development

A classification scheme for those population models which allow variation in development rates is proposed, based on two ways of modifying standard age-structured models. The resulting classes of models are termed development index models and sojourn time models. General formulations for the two classes of models are developed from two basic balance equations, and numerous specific models from the literature are shown to fit into the scheme. Concepts from competing risks theory are shown to be important in understanding the interplay between mortality and maturation. Relationships among the classes are investigated both for the most general forms of the models and for the simpler forms often used. The scheme can provide guidance in developing appropriate insect population models for specific modelling situations.Contribution 3878871     

A threshold result for an epidemiological model

A threshold parameter R ₀ is identified for an SIRS epidemiological model which has nonlinear incidence and a distributed delay for transfer out of the removed class. For R ₀ < 1, the disease free equilibrium is proved to be the global attractor for all solutions.Research supplied in part by NSERC A-8965     

Models for age structured populations with distributed maturation rates

In the use of age structured population models for agricultural applications such as the modeling of crop-pest interactions it is often essential that the model take into account the distribution in maturation rates present in some or all of the populations. The traditional method for incorporating distributed maturation rates into crop and pest models has been the so-called distributed delay method. In this paper we review the application of the distributed delay formalism to the McKendrick equation of an age structured population. We discuss the mathematical properties of the system of ordinary differential equations arising out of the distributed delay formalism. We then discuss an alternative method involving modification of the Leslie matrix.     

Integral equation models for endemic infectious diseases

Summary Endemic infectious diseases for which infection confers permanent immunity are described by a system of nonlinear Volterra integral equations of convolution type. These constant-parameter models include vital dynamics (births and deaths), immunization and distributed infectious period. The models are shown to be well posed, the threshold criteria are determined and the asymptotic behavior is analysed. It is concluded that distributed delays do not change the thresholds and the asymptotic behaviors of the models.This work was partially supported by NIH Grant AI 13233.     

A simple SIS epidemic model with a backward bifurcation

It is shown that an SIS epidemic model with a non-constant contact rate may have multiple stable equilibria, a backward bifurcation and hysteresis. The consequences for disease control are discussed. The model is based on a Volterra integral equation and allows for a distributed infective period. The analysis includes both local and global stability of equilibria.     

Dispersal delays, predator-prey stability, and the paradox of enrichment

It takes time for individuals to move from place to place. This travel time can be incorporated into metapopulation models via a delay in the interpatch migration term. Such a term has been shown to stabilize the positive equilibrium of the classical Lotka-Volterra predator-prey system with one species (either the predator or the prey) dispersing. We study a more realistic, Rosenzweig-MacArthur, model that includes a carrying capacity for the prey, and saturating functional response for the predator. We show that dispersal delays can stabilize the predator-prey equilibrium point despite the presence of a Type II functional response that is known to be destabilizing. We also show that dispersal delays reduce the amplitude of oscillations when the equilibrium is unstable, and therefore may help resolve the paradox of enrichment.     

NEKTAR,SPICE and Vortonics: using federated grids for large scale scientific applications

In response to a joint call from US’s NSF and UK’s EPSRC for applications that aim to utilize the combined computational resources of the US and UK, three computational science groups from UCL, Tufts and Brown Universities teamed up with a middleware team from NIU/Argonne to meet the challenge. Although the groups had three distinct codes and aims, the projects had the underlying common feature that they were comprised of large-scale distributed applications which required high-end networking and advanced middleware in order to be effectively deployed. For example, cross-site runs were found to be a very effective strategy to overcome the limitations of a single resource. The seamless federation of a grid-of-grids remains difficult. Even if interoperability at the middleware and software stack levels were to exist, it would not guarantee that the federated grids can be utilized for large scale distributed applications. There are important additional requirements for example, compatible and consistent usage policy, automated advanced reservations and most important of all co-scheduling. This paper outlines the scientific motivation and describes why distributed resources are critical for all three projects. It documents the challenges encountered in using a grid-of-grids and some of the solutions devised in response.     

A mobile agent model for fault-tolerant manipulation on distributed objects

In this paper, we discuss how to realize fault-tolerant applications on distributed objects. Servers supporting objects can be fault-tolerant by taking advantage of replication and checkpointing technologies. However, there is no discussion on how application programs being performed on clients are tolerant of clients faults. For example, servers might block in the two-phase commitment protocol due to the client fault. We newly discuss how to make application programs fault-tolerant by taking advantage of mobile agent technologies where a program can move from a computer to another computer in networks. An application program to be performed on a faulty computer can be performed on another operational computer by moving the program in the mobile agent model. In this paper, we discuss a transactional agent model where a reliable and efficient application for manipulating objects in multiple computers is realized in the mobile agent model. In the transactional agent model, only a small part of the application program named routing subagent moves around computers. A routing subagent autonomously finds a computer which to visit next. We discuss a hierarchical navigation map which computer should be visited price to another computer in a transactional agent. A routing subagent makes a decision on which computer visit for the hierarchical navigation map. Programs manipulating objects in a computer are loaded to the computer on arrival of the routing subagent in order to reduce the communication overhead. This part of the transactional agent is a manipulating subagent. The manipulation subagent still exists on the computer even after the routing subagent leaves the computer in order to hold objects until the commitment. We assume every computer may stop by fault while networks are reliable. There are kinds of faulty computers for a transactional agent; current, destination, and sibling computers where a transactional agent now exists, will move, and has visited, respectively. The types of faults are detected by neighbouring manipulation subagents by communicating with each other. If some of the manipulation subagents are faulty, the routing subagent has to be aborted. However, the routing subagent is still moving. We discuss how to efficiently deliver the abort message to the moving routing subagent. We evaluate the transactional agent model in terms of how long it takes to abort the routing subagent if some computer is faulty.

The comparative kinetic analysis of Acetocell and Lignoboost® lignin pyrolysis: the estimation of the distributed reactivity models

The non-isothermal pyrolysis kinetics of Acetocell (the organosolv) and Lignoboost? (kraft) lignins, in an inert atmosphere, have been studied by thermogravimetric analysis. Using isoconversional analysis, it was concluded that the apparent activation energy for all lignins strongly depends on conversion, showing that the pyrolysis of lignins is not a single chemical process. It was identified that the pyrolysis process of Acetocell and Lignoboost? lignin takes place over three reaction steps, which was confirmed by appearance of the corresponding isokinetic relationships (IKR). It was found that major pyrolysis stage of both lignins is characterized by stilbene pyrolysis reactions, which were subsequently followed by decomposition reactions of products derived from the stilbene pyrolytic process. It was concluded that non-isothermal pyrolysis of Acetocell and Lignoboost? lignins can be best described by n-th (n>1) reaction order kinetics, using the Weibull mixture model (as distributed reactivity model) with alternating shape parameters.