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关键词： drug resistance   multi-strain   stability analysis  

摘要： We investigate a two-strain disease model with amplification to simulate the prevalence of drug-susceptible (s) and drug-resistant (m) disease strains. Drug resistance first emerges when drug-susceptible strains mutate and become drug-resistant, possibly as a consequence of inadequate treatment, i.e. amplification. In this case, the drug-susceptible and drug-resistant strains are coupled. We perform a dynamical analysis of the resulting system and find that the model contains three equilibrium points: a disease-free equilibrium;a mono-existent disease-endemic equilibrium at which only the drug-resistant strain persists;and a co-existent disease-endemic equilibrium where both the drug-susceptible and drug-resistant strains persist. We found two basic reproduction numbers: one associated with the drug-susceptible strain (R-0s);the other with the drug-resistant strain (R-0m), and showed that at least one of the strains can spread in a population if max[R-0s, R-0m] > 1. Furthermore, we also showed that if R-0m > max[R-0s, 1], the drug-susceptible strain dies out but the drug-resistant strain persists in the population (mono-existent equilibrium);however if R-0s > max[R-0m, 1], then both the drug-susceptible and drug-resistant strains persist in the population (co-existent equilibrium). We conducted a local stability analysis of the system equilibrium points using the Routh-Hurwitz conditions and a global stability analysis using appropriate Lyapunov functions. Sensitivity analysis was used to identify the key model parameters that drive transmission through calculation of the partial rank correlation coefficients (PRCCs). We found that the contact rate of both strains had the largest influence on prevalence. We also investigated the impact of amplification and treatment/recovery rates of both strains on the equilibrium prevalence of infection;results suggest that poor quality treatment/recovery makes coexistence more likely and increases the relative abundance of resist

关键词： Mathematical model   COVID 19   Basic reproduction number   Linearization theory   Lyapunov function   Stability analysis   Numerical simulations  

摘要： We develop a new mathematical model by including the resistive class together with quarantine class and use it to investigate the transmission dynamics of the novel corona virus disease (COVID-19). Our developed model consists of four compartments, namely the susceptible class, S(t), the healthy (resistive) class, H(t), the infected class, I(t) and the quarantine class, Q(t). We derive basic properties like, boundedness and positivity, of our proposed model in a biologically feasible region. To discuss the local as well as the global behaviour of the possible equilibria of the model, we compute the threshold quantity. The linearization and Lyapunov function theory are used to derive conditions for the stability analysis of the possible equilibrium states. We present numerical simulations to support our investigations. The simulations are compared with the available real data for Wuhan city in China, where the infection was initially originated. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： HTLV-I infection   HAM/TSP   Global stability   Lyapunov function   CTL response  

摘要： A mathematical model for the CD8+ T-cell response to Human T cell leukemia/lymphoma virus type I (HTLV-I) infection is investigated in this paper. The proposed model, which involves four coupled nonlinear ordinary differential equations, describes the interaction of uninfected CD4+T cells, latently infected CD4+T cells, actively infected CD4+T cells and HTLV-I specific cytotoxic T-lymphocytes (CTLs). Our model exhibits three biologically feasible equilibria, namely infection-free steady state, HTLV-I free steady state and an endemic steady state. Our mathematical analysis establishes that the local and global dynamics are determined by the two threshold parameters R-0 and R1, basic reproduction number for HTLV-I viral infection and for CTL response, respectively. For R-0 < 1, the infection-free steady state E-0 is globally asymptotically stable, and HTLV-I viruses are cleared. For R-1 <= 1 < R-0, the HTLV-I free singular point E-1 is globally asymptotically stable, and the HTLV-I infection becomes chronic but no CTL response can be established, and most of the HTLV-I infected individual remains as an asymptomatic carrier. Mathematical analysis shows that a unique endemic steady state E* is globally asymptotically stable for R-1 > 1 in the interior of the feasible region. We perform the sensitivity analysis to find out the key parameters of the HTLV-I infection model with respect to R-0 and R-1. Implications of our findings to the dynamics of CTL response to HTLV-I infections in vivo and pathogenesis of HTLV-I associated myelopathy/tropical spastic paraparesis (HAM/TSP) are discussed. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： crime dynamics   dynamical systems   mathematical sociology  

摘要： Recently, there have been many attempts to develop a mathematical model that captures the nature of crime. One of the successful models has been based on diffusion-type differential equations that describe how criminals spread in a specific area. Here, we propose a dynamic model that focuses on the effect of interactions between distinct types of criminals. The accumulated criminal records show that serious and minor crimes differ in many measures and are related in a complex way. While some of those who have committed minor crime spontaneously evolve into serious criminals, the transition from minor crime to major crime involves many social factors and has not been fully understood yet. In this work, we present a mathematical model to describe how minor criminals turn into major criminals inside and outside of prisons. The model assumes that a population can be divided into a set of compartments, according to the level of crime and whether arrested or not, and individuals have equal probability to change compartment. The model is design to implement two social effects which respectively have been conceptualized in popular terms "broken windows effect" and "prison as a crime school." Analysis of the system shows how the crime-related parameters such as the arrest rate, the period of imprisonment, and the in-prison contact rate affect the criminal distribution at equilibrium. Without proper control of contact between prisoners, the longer imprisonment rather increases occurrence of serious crimes in society. An optimal allocation of the police resources to suppress crimes is also discussed.

关键词： Mathematical modeling   Simulation   Micro-disk biosensor   Enzyme electrode   Non-linear equation   Michaelis-Menten kinetics  

摘要： In this study, a mathematical model of immobilized enzyme system, which follows the Michaelis-Menten kinetics for micro-disk biosensor is discussed. It is based on substrate and hydrogen peroxide profile with enzyme reaction within the biosensor under steady state condition. Accordingly, simple and compact analytical expression for substrate as well as hydrogen peroxide concentrations and electrode current for micro-disk biosensor are obtained. In addition, it acquired as a function of reaction diffusion parameter and saturated parameter using hyperbolic function method. Therefore, this hyperbolic function analysis of the proposed model is an efficient tool to predict the Michaelis-Menten constant. Furthermore, to confirm the validity and accuracy of the proposed method, the results are compared with those obtained by using well-established Homotopy analysis method and Modified Adomian decomposition method. The numerical results obtained are provided by the highly reputed program pdex2 and pdex4 in MATLAB. Tabular compilations of concentrations and current are also explored for typical values of the governing parameters.

关键词： 在线教学   数学分析   钉钉   签到   互动  

摘要： 《数学分析》是数学专业核心课程,对学生专业发展起着非常重要的作用。高校数学教师非常关注其在线教学。《数学分析》的在线教学环节包括预习活动、课前3~5 min互动、签到、作业答疑、讲新课、小组讨论、布置任务等。在一个学期的在线教学实践过程中体现了在线教学的多个优点,主要有:学生可以看回放学习;文件、案例分享就很方便;提高大学生在线学习体验。

关键词： 高中数学   分析思想   解题   应用策略  

摘要： 高中数学解题过程中最常运用的是分析思想。分析思想对于高中数学而言至关重要,教师在进行教学实践的过程中应当引导学生运用分析思想,遇到各类数学题目的时候首先不是去动笔解题,而是应当冷静地去分析问题,缕清解题思路。本篇文章将主要探讨数学分析思想在高中数学解题中的应用。

关键词： 数学分析方法   智能时代   计算机科学   经典物理学   计量经济学   数理经济学   数学语言   广义相对论  

摘要： 数学作为一门科学的语言和工具,广泛应用于各个领域。在自然科学领域,哈雷、哥白尼等人经过复杂的观测数据计算,做出了彗星回归、日心说等著名的论断;牛顿用数学语言论证了著名的经典物理学公式,包括万有引力和力学第二定律;爱因斯坦的广义相对论是以非欧几何理论为基础的。可以说,数学是自然科学发展的核心力量。在社会科学领域,定量分析研究所获得的成就也在逐渐增加,尤其是经济学已将数理经济学和计量经济学作为基础知识和必修课程,同时,定量分析和定性分析相结合成为社会科学研究发展的必要途径。

关键词： 数学分析   数学思维   数学思想   数列极限   函数极限  

摘要： 结合数学分析教学,探讨如何启发式教学才能使学生快速地适应数学分析的学习,更容易掌握重要的知识点。以数列和函数极限的关系为例,进一步探索如何培养学生的数学思维习惯,帮助学生更容易理解整个数学分析的知识体系。

关键词： 数学分析   微课   翻转课堂  

摘要： 本文剖析高师数学分析课程教学存在的问题,研究微课与翻转课堂机理,提出基于微课与翻转课堂的教学模式,以深化课程改革,提高教学质量,促进数学分析与中学微积分的有效衔接.