12,232 research outputs found
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
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
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
Masculinity at work: The experiences of men in female dominated occupations
This paper presents the findings of a research project on the implications of men's non-traditional career choices for their experiences within the organization and for gender identity. The research is based on 40 in-depth interviews with male workers from four occupational groups: librarian-ship, cabin crew, nurses and primary school teachers. Results suggest a typology of male workers in female dominated occupations: seekers (who actively seek the career), finders (who find the occupation in the process of making general career decisions) and settlers (who settle into the career after periods of time in mainly male dominated occupations). Men benefit from their minority status through assumptions of enhanced leadership (the assumed authority effect), by being given differential treatment (the special consideration effect) and being associated with a more careerist attitude to work (the career effect). At the same time, they feel comfortable working with women (the zone of comfort effect). Despite this comfort, men adopt a variety of strategies to re-establish a masculinity that has been undermined by the 'feminine' nature of their work. These include re-labeling, status enhancement and distancing from the feminine. The dynamics of maintaining and reproducing masculinities within the non-traditional work setting are discussed in the light of recent theorising around gender, masculinity and work
Equivalent embeddings of the dynamics on an invariant manifold
AbstractA dynamical system admitting an invariant manifold can be interpreted as a single element of an infinite class of dynamical systems that all exhibit the same behaviour on the invariant manifold. This observation is used in the context of autonomous ordinary differential equations to generalize a global stability result of Li and Muldowney. The new result is demonstrated on an epidemiological model
An Analysis of the Monostable Cathode-Coupled Multivibrator
II. PURPOSE OF THESIS
The foregoing comments pointed out the facts that: 1) little has been done to show the similarity between the multivibrator and the RC amplifier with degenerative feedback; 2) the existing treatment of the conditions under which a linear relationship between pulse duration and applied grid voltage will exist does not give results which are in very good agreement with the values used in a practical circuit.
It is the purpose of this study to fill in these gaps by showing that the equations resulting from an analysis of the cathode-coupled multivibrator are, in general, those of the degenerative amplifier multiplied by an additional factor which compensates for the heavily biased operation, and that the conditions for a nearly linear relation between pulse duration and applied grid voltage depend upon a rather complicated function of the circuit parameters which does not allow a general solution, but which does allow values to be computed for any particular case
COVID-19 Impacts on Cancer Treatment—Nosocomial Infection, Therapy Disruption, and Research Application
No abstract available
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