Extinction times in the subcritical stochastic SIS logistic epidemic

Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights into the near-critical regime by considering the stochastic SIS logistic epidemic, a well-known birth-and-death chain used to model the spread of an epidemic within a population of a given size $N$. We study the behaviour of the process as the population size $N$ tends to infinity. Our results cover the entire subcritical regime, including the "barely subcritical" regime, where the recovery rate exceeds the infection rate by an amount that tends to 0 as $N \to \infty$ but more slowly than $N^{-1/2}$. We derive precise asymptotics for the distribution of the extinction time and the total number of cases throughout the subcritical regime, give a detailed description of the course of the epidemic, and compare to numerical results for a range of parameter values. We hypothesise that features of the course of the epidemic will be seen in a wide class of other epidemic models, and we use real data to provide some tentative and preliminary support for this theory.Comment: Revised; 34 pages; 6 figure

Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle dies with instantaneous rate $\mu_n$. Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make explicit an important derivation connecting transition probabilities and continued fractions. We then develop an efficient algorithm for computing these probabilities that analyzes the error associated with approximations in the method. We demonstrate that this error-controlled method agrees with known solutions and outperforms previous approaches to computing these probabilities. Finally, we apply our novel method to several important problems in ecology, evolution, and genetics

Isotopic and molecular distributions of biochemicals from fresh and buried Rhizophora mangle leaves†

Rhizophora mangle L. (red mangrove) is the dominant species of mangrove in the Americas. At Twin Cays, Belize (BZ) red mangroves are present in a variety of stand structures (tall >5 m in height, transition ~2–4 m and dwarf ~1–1.5 m). These height differences are coupled with very different stable carbon and nitrogen isotopic values[1] (mean tall δ(13)C = -28.3‰, δ(15)N = 0‰; mean tall δ(13)C = -25.3‰, δ(15)N = -10‰). To determine the utility of using these distinct isotopic compositions as 'biomarkers' for paleoenvironmental reconstruction of mangrove ecosystems and nutrient availability, we investigated the distribution and isotopic (δ(13)C and δ(15)N) composition of different biochemical fractions (water soluble compounds, free lipids, acid hydrolysable compounds, individual amino acids, and the residual un-extractable compounds) in fresh and preserved red mangrove leaves from dwarf and tall trees. The distribution of biochemicals are similar in dwarf and tall red mangrove leaves, suggesting that, regardless of stand structure, red mangroves use nutrients for biosynthesis and metabolism in a similar manner. However, the δ(13)C and δ(15)N of the bulk leaf, the biochemical fractions, and seven amino acids can be used to distinguish dwarf and tall trees at Twin Cays, BZ. The data support the theory that the fractionation of carbon and nitrogen occurs prior to or during uptake in dwarf and tall red mangrove trees. Stable carbon and nitrogen isotopes could, therefore, be powerful tools for predicting levels of nutrient limitation at Twin Cays. The δ(13)C and δ(15)N of biochemical fractions within preserved leaves, reflect sedimentary cycling and nitrogen immobilization. The δ(15)N of the immobilized fraction reveals the overlying stand structure at the time of leaf deposition. The isotopic composition of preserved mangrove leaves could yield significant information about changes in ecosystem dynamics, nutrient limitation and past stand structure in mangrove paleoecosystems

Calcium-Dependent Increases in Protein Kinase-A Activity in Mouse Retinal Ganglion Cells Are Mediated by Multiple Adenylate Cyclases

Neurons undergo long term, activity dependent changes that are mediated by activation of second messenger cascades. In particular, calcium-dependent activation of the cyclic-AMP/Protein kinase A signaling cascade has been implicated in several developmental processes including cell survival, axonal outgrowth, and axonal refinement. The biochemical link between calcium influx and the activation of the cAMP/PKA pathway is primarily mediated through adenylate cyclases. Here, dual imaging of intracellular calcium concentration and PKA activity was used to assay the role of different classes of calcium-dependent adenylate cyclases (ACs) in the activation of the cAMP/PKA pathway in retinal ganglion cells (RGCs). Surprisingly, depolarization-induced calcium-dependent PKA transients persist in barrelless mice lacking AC1, the predominant calcium-dependent adenylate cyclase in RGCs, as well as in double knockout mice lacking both AC1 and AC8. Furthermore, in a subset of RGCs, depolarization-induced PKA transients persist during the inhibition of all transmembrane adenylate cyclases. These results are consistent with the existence of a soluble adenylate cyclase that plays a role in calcium-dependent activation of the cAMP/PKA cascade in neurons

Protective efficiacy of taurine against pulmonary edema progression: experimental study

Re-expansion pulmonary edema (RPE) is an acute, rare and potentially lethal complication [1,2]. Its beginning is sudden and dramatic. The mechanism is not yet fully understood [1]. Some authors suggest that it may occur after rapid re-inflation of a collapsed lung [1]. It was reported by other authors that it may relate to surfactant depletion or may result from hypoxic capillary damage, leading to increased capillary permeability [1,3]. In RPE, unilateral lung injury is initiated by cytotoxic oxygen metabolites and temporally associated with an influx of polymorphonuclear neutrophils [1]. These toxic oxygen products are the results of re-oxygenation of a collapsed lung. Treatment of re-expansion pulmonary edema is basically preventive [4]

Protective efficiacy of taurine against pulmonary edema progression: experimental study

Re-expansion pulmonary edema (RPE) is an acute, rare and potentially lethal complication [1,2]. Its beginning is sudden and dramatic. The mechanism is not yet fully understood [1]. Some authors suggest that it may occur after rapid re-inflation of a collapsed lung [1]. It was reported by other authors that it may relate to surfactant depletion or may result from hypoxic capillary damage, leading to increased capillary permeability [1,3]. In RPE, unilateral lung injury is initiated by cytotoxic oxygen metabolites and temporally associated with an influx of polymorphonuclear neutrophils [1]. These toxic oxygen products are the results of re-oxygenation of a collapsed lung. Treatment of re-expansion pulmonary edema is basically preventive [4]

A unified treatment of single component replacement models

In this paper we discuss a general framework for single component replacement models. This framework is based on the regenerative structure of these models and by using results from renewal theory a unified presentation of the discounted and average finite and infinite horizon cost models is given. Finally, some well-known replacement models are discussed, and making use of the previous results an easy derivation of their cost functions is presented