The protection zone for biological population in random environment

A biomathematical model is described by stochastic differential equations with Markovian switching. The long‐time dynamical properties are studied both theoretically and numerically. Results show that both the persistence and extinction have close relationship with environmental noises (white and color noises). These results are of important biological significance for biological conservation. Copyright © 2012 John Wiley & Sons, Ltd.     

具有迁移效应和隔离措施的COVID-19传播模型分析

基于COVID-19传播过程中人口流动的必然性、无症状感染者的普遍性和隔离策略的有效性,该文提出了一类具有迁移效应、无症状感染者、自我防护意识和隔离策略的COVID-19传播动力学模型,利用下一代矩阵方法给出了各类子系统和全系统基本再生数的精确表达式.进一步地,通过采用线性近似理论,构造Lyapunov函数、比较原理等方法,得到了无病平衡点的全局渐近稳定性以及疾病的持久性.最后,数值模拟解释了主要的理论结果以及人口的迁移和隔离对疾病传播的影响.     

Development and analysis of a malaria transmission mathematical model with seasonal mosquito life-history traits

In this paper, we develop and analyze a malaria model with seasonality of mosquito life-history traits: periodic-mosquitoes per capita birth rate, -mosquitoes death rate, -probability of mosquito to human disease transmission, -probability of human to mosquito disease transmission, and -mosquitoes biting rate. All these parameters are assumed to be time dependent leading to a nonautonomous differential equation system. We provide a global analysis of the model depending on two threshold parameters and (with ). When , then the disease-free stationary state is locally asymptotically stable. In the presence of the human disease-induced mortality, the global stability of the disease-free stationary state is guarantied when . On the contrary, if , the disease persists in the host population in the long term and the model admits at least one positive periodic solution. Moreover, by a numerical simulation, we show that a sub-critical (backward) bifurcation is possible at . Finally, the simulation results are in accordance with the seasonal variation of the reported cases of a malaria-epidemic region in Mpumalanga province in South Africa.     

Polymer physics inspired approaches for the study of the mechanical properties of amyloid fibrils

Amyloid structures constitute a class of highly ordered nanomaterials formed by insoluble protein aggregates. These aggregates are characterized by a cross‐β structural motif in which β‐sheets are oriented perpendicular to the fibril axis and bound together by a dense hydrogen bonding network. Although they have been associated with several neurodegenerative disorders, such as Alzheimer's and Parkinson's diseases, amyloid fibrils have also been found in many physiologically beneficial roles, for instance in adhesives and hormone storage. Inspired by this natural occurrence of functional amyloid, the hierarchal self‐assembly of these structures has recently been used to develop artificial biomaterials for applications in medicine and nanotechnology. In order to realize the full potential of amyloids as functional materials, it is important to understand their fundamental mechanical properties. This review explores a range of experimental strategies to determine the mechanical properties of amyloid fibrils and discusses the results in the context of polymer physics concepts. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 281–292     

A conjecture by G. Ladas

In this paper, a sufficient condition for boundedness and persistence of the solu1 /of the following delay difference equation is obtained. A conjecture by G. Ladas is proved here xn-1=A/x^pn B/x^qn-1, n=0,1,...where A, B, p, q, x-1, xo∈(0,∞).     

成都市典型重度灰霾期间NO_2演化长期持续性特征的空间稳定性

应用消除趋势波动分析方法,研究了成都市一次典型重度灰霾期间,城区6个监测站点大气NO2小时平均浓度序列的时空演化尺度特征.研究表明,尽管在灰霾期间成都市各站点NO2浓度波动在空间上差异很大,但NO2演化动态在5 d的宏观时间尺度上表现出很强的长期持续特征,且各站点的差异性不大,在空间上具有稳定性.该特征表明,成都市灰霾期间某一时刻所排放的NO2将持续地对未来5 d的NO2浓度带来影响,成都市灰霾期间NO2的波动演化在动力学上主要是由NO2的长期持续性特征主导控制.研究结果有助于进一步加强对灰霾期间大气NO2污染演化复杂规律的认识.     

一类具有非单调型功能反应的捕食-食饵扩散系统的持久性和全局吸引性

利用微分方程的比较原理和重合度理论中的延拓定理,及Lyapunov函数和Barbalat引理,研究了一类具有双密度制约和非单调型功能性反应的捕食-食饵扩散系统的持久性和全局吸引性,获得了周期系统存在唯一全局渐近稳定正周期解的充分条件.     

MODELING THE EFFECTS OF WOOD AND NON‐WOOD BASED INDUSTRIES ON FORESTRY RESOURCES

Pollution due to the wood and non‐wood based industries is one of the main reasons for the depletion of forestry resources. On the onset of industrial era, the number of industries was less but now it has increased much due to rapid pace of development. Industrialization affects forestry resources in two ways: (i) using raw materials by wood based industries and cut down by non‐wood based industries and (ii) emitting pollutants by wood and non‐wood based industries. In view of this, in this paper, we have proposed and analyzed a mathematical model to assess the effects of wood and non‐wood based industries on the depletion of forestry resources. In the modeling process, it is assumed that wood and non‐wood based industries deplete the forestry resources directly, whereas pollutants emitted by both types of industries decrease the growth rate of forestry resources indirectly. The equilibria are obtained and their stability is discussed. The model analysis reveals that forestry resources decrease due to the growth in wood based industries but the overgrowth in non‐wood based industries and pollutants emitted by them in the environment adversely affect the forestry resources. Numerical simulation is provided to support analytical findings.