Open Access

Articles

Article ID: 3703

A Delay Mathematical Model to Examine Control Strategies of the Coronavirus Pandemic with an Efficient Approach

by Awais Ahmad, Muhammad Uzair Awan, Shah Zeb, Baboucarr Ceesay, Muhammad Rafiq, Ayesha Kamran, Awais Shaukat

Advances in Differential Equations and Control Processes, Vol.32, No.4, 2025;

Most of the countries all over the world are affected by the COVID-19 disease, with many deaths and infected cases. Coronavirus is a viral disease causing a symptoms such as Fever or chills, Dry cough, Shortness of breath, Loss of taste or smell and Headache. Since these variables have a significant impact on the spread of this infection, a delayed pandemic model of coronavirus disease is developed in this work by taking vaccination into account. Further described the positivity and boundedness of the delayed pandemic model. The fixed-point theory result also describes the model’s existence and uniqueness. The Routh-Hurwitz criterion result, the Jacobian matrix, and the Lyapunov functions are used to explain the system’s local and global stability at both disease-free and endemic sites. The next-generation matrix approach, which defined whether or not the disease continues in the population, was used to determine the basic reproductive number. We employ the non-standard finite difference approach, RK-4, and Euler in our numerical analysis. We have shown the consistency of analysis and positivity of the model.The NSFD scheme is more reliable and sufficient as compare to Forward Euler and  scheme.The results of the given model are directly applicable to the health sector, since they allow predicting the outbreak pattern and evaluating the efficiency of interventions. Knowing and planning the impact of delay factors and vaccination strategies on the disease dynamics, health authorities may incorporate specific interventions, minimise the infection peaks, and utilise the resources available in the health system without overloading it.

Open Access

Article

Article ID: 3659

Optimal periodic switching strategy for self-cycling bioprocesses: Fliess series-based parameter design and ethanol fermentation case

by Wenliang Li, Chi Zhai

Advances in Differential Equations and Control Processes, Vol.32, No.4, 2025;

This study proposes a framework for optimizing cyclic discharge-reload operations in successive batch bioreactors under integral input constraints (e.g., total substrate consumption, cumulative energy use). Prior research has shown that candidates for optimal fed-batch and periodic on/off operation, formulated in an input-affine system, can be derived from bang-bang form. However, the practical application of these results to successive batch configurations requires a prior knowledge of operational periodicity, which limits flexibility and adaptability to variability. To address this limitation, we reformulate the switching strategy into an algebraic form using the Fliess series expansion. This expansion explicitly embeds periodicity constraints, enabling direct computation of switching parameters from predefined boundary conditions. The overall performance, defined as the over-yield relative to steady-state operations, is quantified via integrated integrals. For practical implementation, we leverage self-cycling fermentation as a foundational framework to determine required periodicity, and design optimal trajectories. Analytical results are derived to clarify the quantitative relationship between boundary conditions and switching parameters for any arbitrary anchor point (i.e., reference state for cycle initialization). The proposed framework is validated using an experimentally calibrated ethanol fermentation model. Simulation results demonstrate that the optimized cyclic strategy achieve a 25.58% relative increase in ethanol yield compared to traditional batch operations. This method enables the seamless integration of on/off operation with optimal periodicity, addressing critical gaps between theoretical periodic switching strategy and industrial bioprocess implementation.

Open Access

Article

Article ID: 3511

A ROI-based medical image encryption scheme using improved Lorenz chaotic system, hybrid pixel-bit permutation, and SHA-256 hashing

by Huiqing Wu, Xiaohong Wang

Advances in Differential Equations and Control Processes, Vol.32, No.4, 2025;

Medical images contain highly sensitive diagnostic and personal information that requires robust protection during storage and transmission. To address this, we propose a region-of-interest (ROI)-based hybrid encryption algorithm that combines pixel-level and bit-level permutation with bit-wise diffusion driven by an improved Lorenz chaotic system. The scheme first employs a robust ROI perception mechanism to accurately identify diagnostically important areas while avoiding unnecessary processing of non-critical regions, thereby enhancing computational efficiency and security. Image-dependent SHA-256 hashing is integrated to generate keystreams tightly bound to image content, improving key sensitivity and resisting plaintext attacks. Dual-layer chaotic scrambling ensures both global confusion and local diffusion, while a dedicated bit-wise diffusion stage further randomizes the ciphertext, strengthening resistance against differential, statistical, and noise-based attacks. Experimental evaluations demonstrate that the proposed method achieves high security and robustness: the average information entropy of encrypted images reaches 7.9992, and NPCR and UACI values are 99.63% and 33.47%, respectively. Compared with existing encryption techniques, the proposed algorithm exhibits higher randomness, stronger differential attack resistance, and better protection of sensitive medical data, without embedding ROI location metadata into non-interest regions. The results indicate that this approach provides an efficient and secure framework for safeguarding medical images in telemedicine, healthcare information systems, and other critical applications.

Open Access

Article

Article ID: 3693

Bifurcation and chaos analysis of a gear-shaft-bearing system considering tooth-bearing backlash nonlinearity and time-varying mesh stiffness

by Wei Liu, Ying Cui, Qiang Wang, Hanlong Cai, Weimin Ding

Advances in Differential Equations and Control Processes, Vol.32, No.4, 2025;

The bifurcation and chaos of gear-shaft-bearing system considering tooth-bearing backlash nonlinearity and time-varying mesh stiffness (TVMS) are investigated through employing shafting element method. In our previous work, the dynamic system merely considered the simple nonlinear backlash and completely ignored the case that tooth-bearing backlash were introduced simultaneously. This work primarily concentrates on the investigation of nonlinear dynamics of gear-shaft-bearing system with tooth-bearing backlash. Initially, TVMS is calculated and simulated to validate Y.Cai result. The coupling relationship for the tooth backlash, TVMS and time-varying center distance is taken into account. Accordingly, the expression of TVMS considering tooth backlash and time-varying center distance is decuced theroetically. Based on the shaft element method, the whole gear dynamic model is established mathematically with the help of the shaft element, gear mesh element and bearing element. Bifurcation diagrams of the system are investigated and compared for three cases, i.e., only tooth backlash, no coupling backlash and coupling backlash. Furthermore, time-domain responses, phase diagrams, and Poincare maps of central components with different speed conditions are analyzed. Ultimately, the illustrative parametric studies are further scrutinized to exhibit the nonlinear dynamics. The results show that chaotic motion region of gear system becomes wider while coupling the tooth-bearing backlash nonlinearity. With the speed condition increase, the gear system exhibits significant nonlinear behavior, i.e., periodic motion and chaotic motion. This work is extremely helpful for the optimization design and vibration reduction of gear system.

Open Access

Article

Article ID: 3674

Global martingale solutions to a stochastic superlinear cross-diffusion population system

by Xi Lin

Advances in Differential Equations and Control Processes, Vol.32, No.4, 2025;

In this work we try to show a martingale solution exists to a stochastic cross-diffusion population system. The transition rate is superlinear. The diffusion matrix does not satisfy the local Lipschitz property. Once the diffusion matrix does not satisfy the local Lipschitz property, we can not apply the existence and uniqueness theorem to derive approximated solutions of this stochastic population system. We have to regularize the diffusion matrix in order to apply the existence and uniqueness theorem, and this is the key idea of this work. By applying the existence and uniqueness theorem, we derive a sequence of approximated solutions. We rely on the Itob formula to estimate approximated solutions. Then we derive the tightness of the approximated sequence in a topological space, with its limit a martingale solution of a stochastic cross-diffusion system. The diffusion matrix of this stochastic cross-diffusion system is a regularization of the original diffusion matrix. The limit of this sequence of regularized diffusion matrices is the diffusion matrix of the original stochastic population system. We show that the limit of this sequence of martingale solutions is also the martingale solution of the original stochastic population system. Nonnegative property for the martingale solution is proved via a standard Stampacchia-type argument.

Open Access

Article

Article ID: 3307

Research on safety sustainability of LNG tanks based on multi-attribute decision-making-FCEM coupled modeling

by Dehong Zhou, Peihe Zhang, Jingyi Zang, Shiyu Peng

Advances in Differential Equations and Control Processes, Vol.32, No.4, 2025;

Against the backdrop of the “dual carbon goals”, China has been advancing its “coal-to-gas transition” strategy, during which LNG leakage incidents have occurred frequently. Addressing the challenge of assessing the interrelated risks of multiple factors, this study constructs an ANP-CRITIC-FCEM coupled model, establishing a micro-level risk identification system from five dimensions: “environment, equipment, process, personnel, and materials”. Considering the conflicts and mutual influences between different risk factors, the model integrates game theory to couple subjective and objective weights and combines fuzzy comprehensive evaluation to quantify safety and sustainable development capabilities. The study indicates that the safety and sustainable development capability level of a certain factory’s LNG storage tank area is Grade IV, with equipment factors dominating as the primary risk source, with a comprehensive weight of 0.5205. Among these, pipeline C22 and safety accessory C23 have a significant impact on the tank’s sustainable development capability; This model improves the accuracy of traditional AHP-FCEM identification, fully considers the influence and conflicts between various factors, visualizes the influence sensitivity between factors, and identifies process factors (25.36% weight) such as pressure regulation process (40.28% sub-weight), personnel “three violations” behavior (69.01% sub-weight), and methane concentration (64.35% sub-weight) constitute secondary key risks. Based on this, targeted improvement strategies are proposed, including equipment-level corrosion monitoring, process-level intelligent pressure regulation, and management-level behavioral analysis and early warning, providing a data-driven framework for the coordinated advancement of LNG storage tank safety management and dual carbon goals. Through comparative analysis, this model is found to be relatively accurate and effective.