Vol. 32 No. 4 (2025)

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

Articles

Article ID: 3720

Global stability of antibody–based and CTL–based PDE models for secondary dengue infection

by Ebtehal Almohaimeed, Ahmed Elaiw, Reem Aldubiban, Aatef Hobiny

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

Infections caused by Flavivirus species, such as dengue virus (DENV), remain a significant public health concern. Because DENV has four antigenically distinct serotypes, a person can be reinfected after a first exposure. Existing within–host models, mostly based on ODEs, describe viral behavior during primary and secondary DENV infection but generally assume uniform mixing and ignore the spatial motion of cells and virions. The present work introduces two PDE models for secondary DENV infection. One captures antibody action against free virus, while the other represents cytotoxic T lymphocyte (CTL) destruction of infected cells. Immune cell production combines an intrinsic source term with a predator–prey–type activation mechanism. The study begins by verifying well-posedness through proofs of global existence and uniform bounds on all solutions. Equilibria are then determined, and the basic reproduction number is calculated to characterize the threshold separating clearance from persistence of infection. Lyapunov techniques, together with LaSalle’s invariance principle, show that the infection–free equilibrium is globally asymptotically stable for R0 ≤ 1, while the endemic state attracts all trajectories for R0 >1.Numerical tests confirm the analytical results. A sensitivity investigation highlights the parameters with the greatest impact on secondary DENV dynamics.

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.

(This article belongs to the Special Issue Mathematical Analysis Advances in System Fault Analysis, Prediction and Control (Close))

Open Access

Article

Article ID: 3441

Carbon emission prediction and intelligent regulation modeling for traffic systems using vision AI

by Yiran Zhu

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

Urban congestion poses a significant environmental challenge, particularly in developing countries, due to ineffective traffic management leading to elevated vehicle emissions from prolonged idling. This paper introduces a machine learning-based intelligent traffic signal system to cut vehicle idle time and emissions. Using YOLOv8, it detects real-time traffic from four directions. A dynamic phase algorithm replaces fixed signals, counting vehicles and adjusting green lights via capacity ratios. Self-learning, it adapts to scenarios without thresholds. The results showcased notable improvements in traffic efficiency and environmental outcomes, with reductions in delay times ranging from 9% to 65%, particularly a substantial enhancement of 1.94 vehicles per second for the westbound approach. Environmental analysis revealed a 32% reduction in carbon emissions, equivalent to 1502 kg CO₂ saved daily, translating to approximately 548 tons of annual CO₂ reduction. Based on standard carbon market valuations of $15 per metric ton CO₂, this generates 1.5 carbon credits daily with an annual economic value of $8225. The research provides empirical evidence that intelligent traffic management systems can deliver measurable environmental benefits while improving urban mobility. Government authorities validated these findings through official environmental impact assessment procedures. This implementation establishes a scalable framework for smart city initiatives, demonstrating how artificial intelligence applications can address urban environmental challenges through practical, data-driven solutions.

Open Access

Article

Article ID: 3589

Exact solutions of the (2+1)-dimensional BLMP equation via neural network based symbolic computation

by Jiang-Long Shen, Run-Fa Zhang, Jing-Wen Huang, Yu Gao, Jing-Bin Liang

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

This paper introduces a neural network-based symbolic computation framework for deriving exact analytical solutions to nonlinear partial differential equations (NLPDEs). By integrating the expressive capability of neural networks with the interpretability of symbolic methods, the approach offers a flexible, generalizable, and computationally efficient alternative to traditional techniques. Its architecture is straightforward, requiring minimal prior assumptions about the equation structure, thus enabling broad applicability across mathematical physics. As a case study, we investigate the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli (BLMP) equation, a fundamental model describing wave propagation in fluid dynamics, nonlinear optics, and plasma physics. By systematically varying hidden-layer configurations and activation functions, we construct six distinct neural network models—comprising both single- and double-hidden-layer designs. These yield multiple novel exact analytical solutions, revealing diverse dynamic behaviors such as localized wave structures, periodic oscillations, and energy-localized modes. The physical characteristics of the obtained solutions are visualized through three-dimensional surface plots, contour maps, density distributions, and temporal evolution graphs. These illustrations elucidate key features including waveform stability, soliton localization, and nonlinear interactions. Unlike conventional methods such as the Hirota bilinear transformation or inverse scattering, the proposed framework avoids complex algebraic manipulations and does not rely on specialized transformations. Compared to physics-informed neural networks, it achieves higher interpretability and reduced computational dependency. This work expands the solution space of the (2+1)-dimensional BLMP equation and highlights the potential of neural-symbolic computation for discovering exact solutions in complex nonlinear systems.

Open Access

Article

Article ID: 3739

Innovative bio-inspired lung-pattern channel design for vanadium-based redox flow energy storage

by Jacer Hamrouni, Leila Abdelgader, Chafaa Hamrouni, Abdennaceur Kachouri, Mounir Baccar

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

The all-vanadium redox flow battery (VRFB) is recognized as a leading option for large-capacity energy storage, owing to its eco-friendly nature, operational safety, and structural adaptability. Key determinants of its effectiveness include the configuration of the electrolyte channels and the transport dynamics within the porous electrodes. In this work, a novel bio-inspired lung-patterned flow architecture is proposed and assessed against a traditional serpentine layout using computational simulations. Findings reveal a reduction of approximately 5.34% in charging voltage at a state of charge (SOC) of 0.9 and an enhancement of about 9.77% in discharge voltage at SOC = 0.1, relative to the benchmark design. These performance gains originate from enhanced reactant distribution and transport efficiency. Specifically, at a low SOC of 0.1, the new configuration achieves a 35.6% higher flow uniformity, which effectively minimizes concentration polarization effects. Moreover, it raises the average active ion concentration by roughly 18%, supporting more effective electrochemical conversion. This innovative flow strategy offers meaningful progress toward optimizing VRFB systems for real-world deployment.