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This paper studies the dynamic behavior of a stochastic SEIRM model of COVID-19 with a standard incidence rate. The existence of global solutions for dynamic system models is proven by integrating stochastic process theory and the concept of stopping times, together with the contradiction method. Moreover, we construct appropriate Lyapunov functions to analyze system stability and apply Dynkin’s formula and Fatou’s lemma to handle stopping times and expectations of stochastic processes. Notably, the extinction study provides mathematical proof that under the given system dynamics, the total population does not grow indefinitely but tends to stabilize over time. The properties of the diffusion matrix are harnessed to guarantee the system’s stationary distribution. Conclusively, numerical simulations confirm the model’s extinction outcomes.

In recent years, the poultry breeding industry has been converted into a large-scale, intensive, and intelligent production mode. The Internet of Things (IoT) is under rapid development, which promotes the development of precision livestock farming. In this study, we developed an intelligent service platform for a facility environment based on the IoT structure, utilizing the capabilities of Platform as a Service (PaaS). The platform consists of four layers, including an information perception layer, network layer, management service layer, and application layer. By using the cloud service model with a distributed network architecture, asynchronous data transmission, and a distributed file system, the platform can centrally manage multiple farm’s data. The intelligent service platform includes the following functions: displaying environmental data, water and electricity consumption, data analysis, and managing production data. Over a 500-day trial period in a live poultry house, the platform demonstrated high data integrity (>87%) and resilience against network disruptions and power outages. The data validity of each environmental element exceeded 94%, among which the validity of the temperature, humidity, and carbon dioxide concentration exceeded 99%. The overall accuracy of the dataset remained relatively high, providing a robust data foundation for further research. Key features included audio analysis, environmental monitoring, and production data management. The platform’s operational status was efficiently communicated via data statistics and email alerts, facilitating timely system recovery. The demonstrated modules included sound recognition, psychrometric charts for visual alerts, and financial analysis tools, offering versatile solutions for integrating PLF models and advanced analytics.

The spread of rumors in online social networks (OSNs) has caused a serious threat to the normal social order. In order to describe the rumor-spreading dynamics in OSNs during emergencies, a novel model with consideration of fans versus ordinary people is proposed in this paper. In contrast to previous studies, we consider the case that two rumors exist simultaneously. It is assumed that one is an entertainment rumor that fans care about, and the other is a common rumor. First, we derive the mean-field equations that describe the dynamics of this dual rumor propagation model and obtain the threshold parameter. Secondly, after finding the necessary and sufficient conditions for the existence of equilibriums, we examine the equilibrium’s local and global stability. Finally, simulations are used to explain how various parameters affect the process of spreading rumors.

This paper investigates the exponential stability of a class of neutral inertial neural networks with multi-proportional delays and leakage delays. By utilizing the Lyapunov stability theory, the approach of parametric variation, and the differential inequality technique, some criteria are acquired that can guarantee that all solutions of the addressed system converge exponentially to the equilibrium point. In particular, the neutral term, multi-proportional delays, and leakage delays are incorporated simultaneously, resulting in a more general model, and the findings are novel and refine the previous works. Finally, one example is provided to indicate that the dynamic behavior is consistent with the theoretical analysis.

This paper is devoted to investigating a class of neutral-type integral differential equations arising in an epidemic model. By using Mawhin’s continuation theorem and the properties of neutral-type operators, we obtain the existence conditions for positive periodic solutions of the considered neutral-type integral differential equation. Compared with previous results, the existence conditions in this paper are less restricted, thus extending the results of the existing literature. Finally, two examples are given to show the effectiveness and merits of the main results of this paper. Our results can be used to obtain the existence of a positive periodic solution to the corresponding non-neutral-type integral differential equation.

This paper studies the practical exponential stability of an impulsive stochastic food chain system with time-varying delays (ISOFCSs). By constructing an auxiliary system equivalent to the original system and comparison theorem, the existence of global positive solutions to the suggested system is discussed. Moreover, we investigate the sufficient conditions for the exponential stability and practical exponential stability of the system, which is given by Razumikhin technique and the Lyapunov method. In addition, when Razumikhin’s condition holds, the exponential stability and practical exponential stability of species are independent of time delay. Finally, numerical simulation finds the validity of the method.