On Using Curvature to Demonstrate Stability

A new approach for demonstrating the global stability of ordinary differential equations is given. It is shown that if the curvature of solutions is bounded on some set, then any nonconstant orbits that remain in the set, must contain points that lie some minimum distance apart from each other. This is used to establish a negative-criterion for periodic orbits. This is extended to give a method of proving an equilibrium to be globally stable. The approach can also be used to rule out the sudden appearance of large-amplitude periodic orbits

Global Stability for an SEIR Epidemiological Model with Varying Infectivity and Infinite Delay

A recent paper (Math. Biosci. and Eng. (2008) 5:389-402) presented an SEIR model using an infinite delay to account for varying infectivity. The analysis in that paper did not resolve the global dynamics for R0 \u3e 1. Here, we show that the endemic equilibrium is globally stable for R0 \u3e 1. The proof uses a Lyapunov functional that includes an integral over all previous states

Lyapunov Functions for Tuberculosis Models with Fast and Slow Progression

The spread of tuberculosis is studied through two models which include fast and slow progression to the infected class. For each model, Lyapunov functions are used to show that when the basic reproduction number is less than or equal to one, the disease-free equilibrium is globally asymptotically stable, and when it is greater than one there is an endemic equilibrium which is globally asymptotically stable

Global Stability of an SIR Epidemic Model with Delay and General Nonlinear Incidence

An SIR model with distributed delay and a general incidence function is studied. Conditions are given under which the system exhibits threshold behaviour: the disease-free equilibrium is globally asymptotically stable if R0 \u3c 1 and globally attracting if R0 = 1; if R0 \u3e 1, then the unique endemic equilibrium is globally asymptotically stable. The global stability proofs use a Lyapunov functional and do not require uniform persistence to be shown a priori. It is shown that the given conditions are satisfied by several common forms of the incidence function

Mass flow in the interacting binary TX Ursae Majoris

Twenty-two far-ultraviolet and 23 near-ultraviolet high resolution IUE spectra of the interactive Algol-type binary TX Ursae Majoris (B8 V + F-K III-IV) were analyzed in order to determine the nature of the mass flow occurring in this system. Absorption features due to high-temperature ions of Si IV, C IV, and N V are always present. The resonance lines of Al III, Fe II, Mg II and Si IV show strong phase and secular variations indicative of gas streaming and circumstellar/circumbinary material. Radial velocities as high as 500 to 600 km/sec are present. The gas flow is particularly prominent in 1985 between phases 0.7 and 0.0. The system is more active than U Sagittae and as active as U Cephei

Stability Implications of Bendixson’s Criterion

This note presents a proof that the omega limit set of a solution to a planar system satisfying the Bendixson criterion is either empty or is a single equilibrium. The proof involves elementary techniques which should be accessible to senior undergraduates and graduate students

FEDERAL GRAZING REFORM AND AVOIDABLE RISK

Recent rangeland reform attempts have increased ranchers'Â’ uncertainty of retaining grazing permits on federal land. This uncertainty is analyzed with a model of grazing on federal land. Ranchers facing this uncertainty will behave differently than if they were guaranteed the renewal of grazing permits at constant real grazing fees. It is shown that the socially optimal outcome may be achieved by adding avoidable risk through targeted rangeland reform. Rangeland reform attempts that create unavoidable risk can make both ranchers and environmental groups worse off.Agricultural and Food Policy,

An Sveir Model for Assessing Potential Impact of an Imperfect Anti-SARS Vaccine

The control of severe acute respiratory syndrome (SARS), a fatal contagious viral disease that spread to over 32 countries in 2003, was based on quarantine of latently infected individuals and isolation of individuals with clinical symptoms of SARS. Owing to the recent ongoing clinical trials of some candidate anti-SARS vaccines, this study aims to assess, via mathematical modelling, the potential impact of a SARS vaccine, assumed to be imperfect, in curtailing future outbreaks. A relatively simple deterministic model is designed for this purpose. It is shown, using Lyapunov function theory and the theory of compound matrices, that the dynamics of the model are determined by a certain threshold quantity known as the control reproduction number (Rv). If Rv ≤ 1, the disease will be eliminated from the community; whereas an epidemic occurs if Rv \u3e 1. This study further shows that an imperfect SARS vaccine with infection-blocking efficacy is always beneficial in reducing disease spread within the community, although its overall impact increases with increasing efficacy and coverage. In particular, it is shown that the fraction of individuals vaccinated at steady-state and vaccine efficacy play equal roles in reducing disease burden, and the vaccine must have efficacy of at least 75% to lead to effective control of SARS (assuming R0 = 4). Numerical simulations are used to explore the severity of outbreaks when Rv \u3e 1

From abuse to trust and back again

oai:westminsterresearch.westminster.ac.uk:w7qv

Making Digital Surveillance Unacceptable? Security, Democracy, and the Political Sociology of Disputes

Despite extensive criticisms of mass surveillance and mobilization by civil liberties and digital rights activists, surveillance has paradoxically been extended and legalized in the name of security. How do some democratic claims against surveillance appear to be normal and common-sense, whereas others are deemed unacceptable, even outlandish? Instead of starting from particular “logics” of either security or democracy, this paper proposes to develop a political sociology of disputes to trace how the relation between security and democracy is shaped by critique in practice. Disputes entail critique and demands for justification. They allow us to account for the constraints which govern whether an argument is deemed acceptable or improper; commonsensical or peculiar. We mobilize disputes in conjunction with Arjun Appadurai’s reflections on “small numbers” in democracies in order to understand how justifications of surveillance for security enact a “rise in generality,” whereas critiques of digital surveillance that mobilize democratic claims enact a “descent into singularity.” To this purpose, we analyze public mobilizations against mass surveillance and challenges brought before the European Court of Human Rights (ECtHR). We draw on interviews with a range of actors involved in the disputes, the parties’ submissions, oral hearings, judgments, and public reports