Z. S. Boxonov
In this paper, we study a discrete-time dynamical system generated by the evolution operator of a wild mosquito population with specific rates of birth and emergence from larvae to adults. The death rates of larvae and adults are assumed to be constant. We find fixed points and under some conditions, on parameters, we show the global attractiveness of a fixed point.
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We study a discrete-time dynamical system of wild mosquito population with parameters: $β$ - the birth rate of adults; $α$ - maximum emergence rate; $μ>0$ - the death rate of adults; $γ$ - Allee effects. We prove that if $γ\geq\frac{α(β-μ)}{μ^2}$ then the mosquito population dies and if $γ<\frac{α(β-μ)}{μ^2}$ holds then extinction or survival of the mosquito population depends on their initial state.
Wolbachia invasion to wild mosquito population in stochastic environment
本文研究了受环境波动扰动的沃尔巴克氏体入侵随机蚊子种群模型，证明了其解的适正性与正性，给出了刻画种群持续与灭绝的阈值型条件，并发现随机波动能促进低初始频率下的沃尔巴克氏体入侵。
We study the discrete-time dynamical systems of a model of wild mosquito population with distinct birth (denoted by $β$) and death (denoted by $μ$) rates. The case $μ=β$ was considered in our previous work. In this paper we prove that for $β<μ$ the mosquito population will die and for $β>μ$ the population will survive, namely, the number of the larvaes goes to infinite and the number of adults has finite limit ${α\over μ}$, where $α>0$ is the maximum emergence rete.
We study the discrete-time dynamical systems associated to a stage-structured wild and sterile mosquito population. We describe all fixed points of the evolution operator (which depends on five parameters) of mosquito population and show that depending on the parameters this operator may have unique, two and infinitely many fixed points. Under some general conditions on parameters we determine type of each fixed point and give the limit points of the dynamical system. Moreover, for a special case of parameters we give full analysis of corresponding dynamical system. We give some biological int…
Description of trajectories of an evolution operator generated by mosquito population
针对蚊子种群演化算子生成的离散时间动力系统，通过寻找不变集并构造 Lyapunov 函数，证明了不动点的全局吸引性，并给出生物学解释。
Recently, continuous-time dynamical systems, based on systems of ordinary differential equations, for mosquito populations are studied. In this paper we consider discrete-time dynamical system generated by an evolution quadratic operator of mosquito population and show that this system has two fixed points, which are saddle points (under some conditions on the parameters of the system). We construct an evolution algebra taking its matrix of structural constants equal to the Jacobian of the quadratic operator at a fixed point. Idempotent and absolute nilpotent elements, simplicity properties an…
Understanding mosquitoes life cycle is of great interest presently because of the increasing impact of vector borne diseases in several countries. There is evidence of oscillations in mosquito populations independent of seasonality, still unexplained, based on observations both in laboratories and in nature. We propose a simple mathematical model of egg hatching enhancement by larvae which produces such oscillations that conveys a possible explanation. We propose both a theoretical analysis, based on slow-fast dynamics and Hopf bifurcation, and numerical investigations in order to shed some li…
Global Dynamics of a Discrete Mosquito Model with Allee Effect
本文研究带 Allee 效应的二维离散蚊子模型，分析正轨迹不变性、不动点存在性及局部与全局渐近稳定性，并用数值例子验证理论结果。
Vector control is critical to limit the circulation of vector-borne diseases like chikungunya, dengue or zika which have become important issues around the world. Among them the Sterile Insect Technique (SIT) and the Incompatible Insect Technique (IIT) recently aroused a renewed interest. In this paper we derive and study a minimalistic mathematical model designed for Aedes mosquito population elimination by SIT/IIT. Contrary to most of the previous models, it is bistable in general, allowing simultaneously for elimination of the population and for its survival. We consider dierent types of re…
Oscillatory Regimes in a Game-Theoretic Model for Mosquito Population Dynamics under Breeding Site Control
本文提出博弈论模型，研究家庭行为与蚊虫种群动态的相互作用，揭示了在繁殖地控制下的蚊虫种群振荡机制。
A note on the periodic orbits of Wolbachia spread dynamics in mosquito populations in periodic environments
本文反驳了周期环境中Wolbachia传播模型的周期轨道数量猜想，并重建证明：任意周期映射序列的非零周期轨迹数不超过两个。
We develop and analyze an ordinary differential equation model to assess the potential effectiveness of infecting mosquitoes with the Wolbachia bacteria to control the ongoing mosquito-borne epidemics, such as dengue fever, chikungunya, and Zika. Wolbachia is a natural parasitic microbe that stops the proliferation of the harmful viruses inside the mosquito and reduces disease transmission. It is difficult to sustain an infection of the maternal transmitted Wolbachia in a wild mosquito population because of the reduced fitness of the Wolbachia-infected mosquitoes and cytoplasmic incompatibilit…
Mosquito population suppression models with seasonality and d-concave equations
本文通过分析d-凹标量方程，利用庞加莱映射逆的三阶导数正号条件，简化周期情形论证，从而在简单可检验条件下精确描述含季节性的蚊子种群抑制模型动力学，推广并改进了近期文献结果。
The model considers the human population, the adult mosquito population and the population of immature stages, which includes eggs, larvae and pupae. The model also considers the vertical transmission of dengue in the mosquitoes and the seasonal variation in the mosquito population. From this basic model describing the dynamics of dengue infection, we deduce thresholds for avoiding the introduction of the disease and for the elimination of the disease. In particular, we deduce a Basic Reproduction Number for dengue that includes parameters related to the immature stages of the mosquito. By neg…
Backstepping control for the sterile mosquitoes technique: stabilization of extinction equilibrium
针对蚊子种群控制问题，提出一种以不育雄蚊释放率为输入的非负反步控制律，可全局镇定系统灭绝平衡点，仿真验证其在简化和完整种群动力学模型上均有效。
In this paper, we propose a simplified bidimensional Wolbachia infestation model in a population of Aedes aegypti mosquitoes, preserving the main features associated with the biology of this species that can be found in higher-dimensional models. Namely, our model represents the maternal transmission of the Wolbachia symbiont, expresses the reproductive phenotype of cytoplasmic incompatibility, accounts for different fecundities and mortalities of infected and wild insects, and exhibits the bistable nature leading to the so-called principle of competitive exclusion. Since Wolbachia-based bioco…
Modeling Medea gene-drive population replacement: thresholds and release strategies
本研究建立埃及伊蚊中 Medea 基因驱动的连续时间模型，分析其平衡点、稳定性及双稳态释放阈值，并通过敏感性分析和分批释放模拟，为野外种群替换提供策略指导。
Modeling and control of malaria dynamics in fish farming regions
针对阿克里州鱼塘滋生蚊虫并加剧疟疾传播的问题，本文建立带清理脉冲控制的非线性常微分方程模型，刻画养殖活动影响，并给出蚊虫消亡或存续、疟疾消除或地方化的充分条件。
For some one-dimensional discrete-time autonomous population models, local stability implies global stability of the positive equilibrismo point. One of the known techniques is the enveloping method. In this paper we extend the enveloping method to one single periodic population models. We show that, under certain conditions, "individual enveloping" implies "periodic enveloping" in one-dimensional periodic population models.
Dynamical behavior and bifurcation analysis for a theoretical model of dengue fever transmission with incubation period and delayed recovery
本文构建了同时考虑内外潜伏期和恢复期时间延迟的登革热传播数学模型，通过稳定性与分岔分析揭示了恢复延迟对传播动力学的显著影响。
On the study of the limit cycles for a class of population models with time-varying factors
本文针对含时变因素的种群模型，提出离散导数公式与极限环存在判据，并应用于季节性捕捞模型（最多两个极限环）、Abel方程模型（最多三个）及蚊子抑制模型，改进已有结果。
Qualitative analysis and numerical investigations of time-fractional Zika virus model arising in population dynamics
本文研究时间分数阶寨卡病毒模型，通过稳定性分析和数值模拟探讨其在种群动力学中的应用与疾病传播预测。
A model of population growth and dispersal is considered where the spatial habitat is a lattice and reproduction occurs generationally. The resulting discrete dynamical systems exhibits velocity locking, where rational speed invasion fronts are observed to persist as parameters are varied. In this article, we construct locked fronts for a particular piecewise linear reproduction function. These fronts are shown to be linear combinations of exponentially decaying solutions to the linear system near the unstable state. Based upon these front solutions, we then derive expressions for the boundary…
The Oort-Hulst-Safronov equation, shorterned as OHS is a relevant population balance model. Its discrete form, developed by Dubovski is the main focus of our analysis. The existence and density conservation are established for the coagulation rate $V_{i,j} \leqs (i+j),$ $\forall i,j \in \mathbb{N}$. Differentiability of the solutions is investigated for the kernel $V_{i,j} \leqs i^α+j^α$ where $0 \leqs α\leqs 1$. The article finally deals with the uniqueness result that requires the boundedness of the second moment.
Host-parasitoid population dynamics is often probed using a semi-discrete/hybrid modeling framework. Here, the update functions in the discrete-time model connecting year-to-year changes in the population densities are obtained by solving ordinary differential equations that mechanistically describe interactions when hosts become vulnerable to parasitoid attacks. We use this semi-discrete formalism to study two key spatial effects: local movement (migration) of parasitoids between patches during the vulnerable period; and yearly redistribution of populations across patches outside the vulnerab…
Two-dimensional maps can model interactions between populations. Despite their simplicity, these dynamical systems can show some complex situations, as multistability or fractal boundaries between basins that lead to remarkable pictures. Some of them are shown and explained here for three different 2D discrete models.
A multiscale discrete-to-continuum framework for structured population models
本文提出一种多尺度离散到连续框架，用于系统推导结构化种群模型的连续近似，通过多重尺度方法和匹配渐近展开，识别结构空间中的合适区域并推导偏微分方程，验证了该方法在动脉粥样硬化早期脂质结构模型中的应用。
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