Stability Criteria for SIS Epidemiological Models under Switching Policies

New results on the asymptotic behavior of an SIS epidemiological model with quarantine strategy, stochastic transmission, and Lévy disturbance

The spread of infectious diseases is a major challenge in our contemporary world, especially after the recent outbreak of Coronavirus disease 2019 (COVID-19). The quarantine strategy is one of the important intervention measures to control the spread of an epidemic by greatly minimizing the likelihood of contact between infected and susceptible individuals. In this study, we analyze the impact of various stochastic disturbances on the epidemic dynamics during the quarantine period. For this purpose, we present an SIQS epidemic model that incorporates the stochastic transmission and the Lévy no…

演化流行病学网络的临界点：机器学习辅助的数据驱动有效建模

Tipping Points of Evolving Epidemiological Networks: Machine Learning-Assisted, Data-Driven Effective Modeling

本研究利用机器学习辅助的数据驱动方法，为自适应SIS流行病学网络识别有效随机微分方程，揭示其亚临界Hopf分岔导致的临界点集体振荡行为，并验证了方法的通用性。

A Low-Dimensional Network Model for an SIS Epidemic: Analysis of the Super Compact Pairwise Model

Network-based models of epidemic spread have become increasingly popular in recent decades. Despite a rich foundation of such models, few low-dimensional systems for modeling SIS-type diseases have been proposed that manage to capture the complex dynamics induced by the network structure. We analyze one recently introduced model and derive important epidemiological quantities for the system. We derive the epidemic threshold and analyze the bifurcation that occurs, and we use asymptotic techniques to derive an approximation for the endemic equilibrium when it exists. We consider the sensitivity…

多菌株SIS动态在宿主种群结构下考虑共感染

Multi-strain SIS dynamics with coinfection under host population structure

本文提出了一种基于宿主种群结构的多菌株SIS模型，通过分析共感染动态，推导出全局复制方程以预测菌株共存与侵袭行为。

Study of a Discretized Fractional-order eco-epidemiological model with prey infection

In this paper, an attempt is made to understand the dynamics of a three-dimensional discrete fractional-order eco-epidemiological model with Holling type II functional response. We first discretize a fractional-order predator-prey-parasite system with piecewise constant arguments and then explore the system dynamics. Analytical conditions for the local stability of different fixed points have been determined using the Jury criterion. Several examples are given to substantiate the analytical results. Our analysis shows that stability of the discrete fractional order system strongly depends on t…

SIS流行病模型的数学研究：全局渐近稳定性分析与非标准数值格式的构造

A Mathematical Study of an SIS Epidemic Model: Global Asymptotic Stability Analysis and Construction of Nonstandard Numerical Schemes

本研究对具有饱和接触率的SIS模型进行严格数学分析，通过Lyapunov函数和Poincaré–Bendixson定理证明全局渐近稳定性，并构造保持正性和稳定性的非标准有限差分格式，数值实验验证了理论结果。