Sensitivity and control analysis of periodically forced reaction networks using the Green's function method

A general sensitivity and control analysis of periodically forced reaction networks with respect to small perturbations in arbitrary network parameters is presented. A well-known property of sensitivity coefficients for periodic processes in dynamical systems is that the coefficients generally become unbounded as time tends to infinity. To circumvent this conceptual obstacle, a relative time or phase variable is introduced so that the periodic sensitivity coefficients can be calculated. By employing the Green's function method, the sensitivity coefficients can be defined using integral control operators that relate small perturbations in the network's parameters and forcing frequency to variations in the metabolite concentrations and reaction fluxes. The properties of such operators do not depend on a particular parameter perturbation and are described by the summation and connectivity relationships within a control-matrix operator equation. The aim of this paper is to derive such a general control-matrix operator equation for periodically forced reaction networks, including metabolic pathways. To illustrate the general method, the two limiting cases of high and low forcing frequency are considered. We also discuss a practically important case where enzyme activities and forcing frequency are modulated simultaneously. We demonstrate the developed framework by calculating the sensitivity and control coefficients for a simple two reaction pathway where enzyme activities enter reaction rates linearly and specifically.     

具有脉冲和时滞的Lotka-Volterra系统的正周期解的存在性和全局渐近稳定性

主要研究具有脉冲和时滞的Lotka-Volterra系统的正周期解的存在性和全局渐近稳定性．     

On the global stability of a generalized cholera epidemiological model

In this paper, we conduct a careful global stability analysis for a generalized cholera epidemiological model originally proposed in [J. Wang and S. Liao, A generalized cholera model and epidemic/endemic analysis, J. Biol. Dyn. 6 (2012), pp. 568–589]. Cholera is a water- and food-borne infectious disease whose dynamics are complicated by the multiple interactions between the human host, the pathogen, and the environment. Using the geometric approach, we rigorously prove the endemic global stability for the cholera model in three-dimensional (when the pathogen component is a scalar) and four-dimensional (when the pathogen component is a vector) systems. This work unifies the study of global dynamics for several existing deterministic cholera models. The analytical predictions are verified by numerical simulation results.     

An Analysis of Variance of Nominal Data

This paper considers a common problem in analysis of variance where the responses to a set of treatments are nominal (i.e. are recorded in frequencies) with no underlying metric. Reasoning by analogy from standard analysis of variance of a two-way classification we develop chi-square tests for significance of treatments and interactions. Two tests are proposed for interaction and their asymptotic properties are studied.     

一类传染病模型的扩散性质

讨论了扩散对传染病模型的阈值的影响、扩散对传染病模型中染病者人数的影响以及扩散对传染病模型的平衡点的几何性质的影响．     

“How” and “what” matters: Sampling method affects biodiversity estimates of reef fishes

Understanding changes in biodiversity requires the implementation of monitoring programs encompassing different dimensions of biodiversity through varying sampling techniques. In this work, fish assemblages associated with the “outer” and “inner” sides of four marinas, two at the Canary Islands and two at southern Portugal, were investigated using three complementary sampling techniques: underwater visual censuses (UVCs), baited cameras (BCs), and fish traps (FTs). We firstly investigated the complementarity of these sampling methods to describe species composition. Then, we investigated differences in taxonomic (TD), phylogenetic (PD) and functional diversity (FD) between sides of the marinas according to each sampling method. Finally, we explored the applicability/reproducibility of each sampling technique to characterize fish assemblages according to these metrics of diversity. UVCs and BCs provided complementary information, in terms of the number and abundances of species, while FTs sampled a particular assemblage. Patterns of TD, PD, and FD between sides of the marinas varied depending on the sampling method. UVC was the most cost‐efficient technique, in terms of personnel hours, and it is recommended for local studies. However, for large‐scale studies, BCs are recommended, as it covers greater spatio‐temporal scales by a lower cost. Our study highlights the need to implement complementary sampling techniques to monitor ecological change, at various dimensions of biodiversity. The results presented here will be useful for optimizing future monitoring programs.