Global stability of an SIS epidemic model with a finite infectious period

Assuming a general distribution for the sojourn time in the in- fectious class, we consider an SIS type epidemic model formulated as a scalar integral equation. We prove that the endemic equilibrium of the model is globally asymptotically stable whenever it exists, solving the conjecture of Hethcote and van den Driessche (1995) for the case of nonfatal diseases

Dynamics of an SIS Model on Homogeneous Networks with Delayed Reduction of Contact Numbers

During infectious disease outbreaks, people may modify their contact patterns after realizing the risk of infection. In this paper, we assume that individuals make the decision of reducing a fraction of their links when the density of infected individuals exceeds some threshold, but the decision is made with some delay. Under such assumption, we study the dynamics of a delayed SIS epidemic model on homogenous networks. By theoretical analysis and simulations, we conclude that the density of infected individuals periodically oscillate for some range of the basic reproduction number. Our results indicate that information delays can have important effects on the dynamics of infectious diseases

Emergent Semiclassical Time in Quantum Gravity. I. Mechanical Models

Strategies intended to resolve the problem of time in quantum gravity by means of emergent or hidden timefunctions are considered in the arena of relational particle toy models. In situations with `heavy' and `light' degrees of freedom, two notions of emergent semiclassical WKB time emerge; these are furthermore equivalent to two notions of emergent classical `Leibniz--Mach--Barbour' time. I futhermore study the semiclassical approach, in a geometric phase formalism, extended to include linear constraints, and with particular care to make explicit those approximations and assumptions used. I propose a new iterative scheme for this in the cosmologically-motivated case with one heavy degree of freedom. I find that the usual semiclassical quantum cosmology emergence of time comes hand in hand with the emergence of other qualitatively significant terms, including back-reactions on the heavy subsystem and second time derivatives. I illustrate my analysis by taking it further for relational particle models with linearly-coupled harmonic oscillator potentials. As these examples are exactly soluble by means outside the semiclassical approach, they are additionally useful for testing the justifiability of some of the approximations and assumptions habitually made in the semiclassical approach to quantum cosmology. Finally, I contrast the emergent semiclassical timefunction with its hidden dilational Euler time counterpart.Comment: References Update

Relational Particle Models. II. Use as toy models for quantum geometrodynamics

Relational particle models are employed as toy models for the study of the Problem of Time in quantum geometrodynamics. These models' analogue of the thin sandwich is resolved. It is argued that the relative configuration space and shape space of these models are close analogues from various perspectives of superspace and conformal superspace respectively. The geometry of these spaces and quantization thereupon is presented. A quantity that is frozen in the scale invariant relational particle model is demonstrated to be an internal time in a certain portion of the relational particle reformulation of Newtonian mechanics. The semiclassical approach for these models is studied as an emergent time resolution for these models, as are consistent records approaches.Comment: Replaced with published version. Minor changes only; 1 reference correcte