Global Properties of Infectious Disease Models with Nonlinear Incidence

We consider global properties for the classical SIR, SIRS and SEIR models of infectious diseases, including the models with the vertical transmission, assuming that the horizontal transmission is governed by an unspecified function f(S,I). We construct Lyapunov functions which enable us to find biologically realistic conditions sufficient to ensure existence and uniqueness of a globally asymptotically stable equilibrium state. This state can be either endemic, or infection-free, depending on the value of the basic reproduction number.     

Mathematical Model of BCG Immunotherapy in Superficial Bladder Cancer

Immunotherapy with Bacillus Calmette–Guérin (BCG)—an attenuated strain of Mycobacterium bovis (M. bovis) used for anti tuberculosis immunization—is a clinically established procedure for the treatment of superficial bladder cancer. However, the mode of action has not yet been fully elucidated, despite much extensive biological experience. The purpose of this paper is to develop a first mathematical model that describes tumor-immune interactions in the bladder as a result of BCG therapy. A mathematical analysis of the ODE model identifies multiple equilibrium points, their stability properties, and bifurcation points. Intriguing regimes of bistability are identified in which treatment has potential to result in a tumor-free equilibrium or a full-blown tumor depending only on initial conditions. Attention is given to estimating parameters and validating the model using published data taken from in vitro, mouse and human studies. The model makes clear that intensity of immunotherapy must be kept in limited bounds. While small treatment levels may fail to clear the tumor, a treatment that is too large can lead to an over-stimulated immune system having dangerous side effects for the patient.     

Global analysis of an epidemic model with nonmonotone incidence rate

In this paper we study an epidemic model with nonmonotonic incidence rate, which describes the psychological effect of certain serious diseases on the community when the number of infectives is getting larger. By carrying out a global analysis of the model and studying the stability of the disease-free equilibrium and the endemic equilibrium, we show that either the number of infective individuals tends to zero as time evolves or the disease persists.     

Ultrasound and matter--physical interactions

The basic physical characteristics of ultrasound waves are reviewed in terms of the typical displacements, velocities, accelerations and pressures generated in various fluid media as a function of frequency. The effects on wave propagation of interfaces are considered, and the way in which waves are reflected, transmitted and mode converted at interfaces introduced. Then the nonlinear propagation of high amplitude ultrasound is explained, and its consequences, including the generation of harmonic frequencies and enhanced attenuation, considered. The absorption of ultrasonic waves and the resulting heat deposition in absorbing media are described together with factors determining the resulting temperature rises obtained. In the case of tissue these include conduction and perfusion. The characteristics of cavitation in fluid media are also briefly covered. Finally, secondary nonlinear physical effects are described. These include radiation forces on interfaces and streaming in fluids.     

A prolegomenon to nonlinear empiricism in the human behavioral sciences

We propose a general framework for integrating theory and empiricism in human evolutionary ecology. We specifically emphasize the joint use of stochastic nonlinear dynamics and information theory. To illustrate critical ideas associated with historical contingency and complex dynamics, we review recent research on social preferences and social learning from behavioral economics. We additionally examine recent work on ecological approaches in history, the modeling of chaotic populations, and statistical application of information theory.     

Nonlinear time series analysis of food intake in the dab and the rainbow trout

Evidence suggests that dab and rainbow trout are able to quickly adjust their food intake to an appropriate level when offered novel diets. In addition day-to-day and meal-to-meal food intake varies greatly and meal timing is plastic. Why this is the case is not clear: Food intake in fish is influenced by many factors, however the hierarchy and mechanisms by which these interact is not yet fully understood. A model of food intake may be helpful to understand these phenomena; to determine model type it is necessary to understand the qualitative nature of food intake. Food intake can be regarded as an autoregressive (AR) time series, as the amount of food eaten at time t will be influenced by previous meals, and this allows food intake to be considered using time series analyses. Here, time series data were analysed using nonlinear techniques to obtain qualitative information from which evidence for the hierarchy of mechanisms controlling food intake may be drawn. Time series were obtained for a group of dab and individuals and a group of rainbow trout for analysis. Surrogate data sets were generated to test several null hypotheses describing linear processes and all proved significantly different to the real data, suggesting nonlinear dynamics. Examination of topography and recurrence diagrams suggested that all series were deterministic and non-stationary. The point correlation dimension (PD2i) suggested low-dimensional dynamics. Our findings suggest therefore that any model of appetite should create output that is deterministic, non-stationary, low-dimensional and having nonlinear dynamics.     

非线性种群反应扩散系统奇摄动ROBIN问题

研究了一类具有非线性种群反应扩散系统奇摄动Robin初始边值问题.在适当的条件下,利用微分不等式理论,讨论了问题解的存在性和渐近性态.     

非线性拟双曲方程的交替方向变网格有限元方法

研究在神经传播过程中的一类非线性拟双曲方程的初边值问题,提出了一种三维交替方向变网格有限元格式,应用微分方程先验估计的理论和技巧,得到了最佳阶的L^2模误差估计结果。并作了数值实验。指明方法是高效可行的．     

A moss “canopy” – Small-scale differences in microclimate and physiological traits in Tortula ruralis

We studied vertical changes in light regime and water content (WC) in combination with vertical gradients in several physiological response variables, i.e. net CO₂ uptake, chlorophyll content and nitrogen content in the moss species, Tortula ruralis. The rate of light attenuation within the moss turf, which was determined with a custom-made optical microprobe system, was strongly dependent on plant WC. Curling movements of the upper leaves associated with the beginning desiccation of the uppermost parts of a turf allowed increased penetration of light to greater depth with decreasing WC. The capacity to fix carbon declined steeply with depth: below ca. 9 mm no net CO₂ uptake occurred, even when removing the shading parts above. The potential rates of photosynthesis in different depths were highly correlated with chlorophyll content, but not nitrogen content.