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AppliedMath
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Advanced Mathematical Modeling, Dynamics and Applications
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Advanced Mathematical Modeling, Dynamics and Applications

A special issue of AppliedMath (ISSN 2673-9909). This special issue belongs to the section "Computational and Numerical Mathematics".

Deadline for manuscript submissions: closed (30 April 2026) | Viewed by 5217

Editor

Dr. Ophir Nave

E-Mail Website
Guest Editor
1. Department of Mathematics, Faculty of Science, Jerusalem College of Technology, Jerusalem, Israel
2. Faculty of Computer Science, College of Management Academic Studies, Rishon LeZion, Israel
Interests: mathematical models of cancer; asymptotic analysis; method of integral invariant manifold; numerical

Special Issue Information

Dear Colleagues,

This Special Issue aims to focus on the application of mathematical and computational methods in the sciences, with particular emphasis on cancer modeling. We welcome studies investigating the interactions between tumors, the immune system, and therapies such as chemotherapy and immunotherapy. The submission of research addressing various cancer types—including bladder, breast, prostate, liver, brain, and cervical cancers—is encouraged.

Additionally, submissions employing advanced numerical, semi-analytical, analytical, or asymptotic techniques to analyze these models are of interest. The stability analysis of equilibrium points, offering insights into treatment efficacy and disease progression, is particularly relevant.

Furthermore, contributions exploring machine learning applications in oncology, especially in the analysis of large tumor datasets, are invited. Studies integrating machine learning with mathematical modeling to enhance predictive accuracy and optimize treatment strategies are especially welcome.

Dr. Ophir Nave
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. AppliedMath is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematical modeling
  • computational methods
  • cancer modeling
  • numerical techniques
  • semi-analytical methods
  • analytical solutions
  • asymptotic analysis
  • stability analysis

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Published Papers (6 papers)

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Research

26 pages, 26402 KB  
Article
Displacement-Constrained Continuum Structure Topology Optimization Based on an Improved Movable Morphable Smooth-Boundary Method
by Jiazheng Du, Bing Lin, Hongling Ye and Zhichao Guo
AppliedMath 2026, 6(7), 110; https://doi.org/10.3390/appliedmath6070110 - 9 Jul 2026
Viewed by 168
Abstract
To address jagged boundaries in conventional fixed-mesh topology optimization and the discontinuous transfer of topology information after remeshing, this study proposes an improved Movable Morphable Smooth-Boundary (MMSB) method for displacement-constrained continuum topology optimization. A topology optimization model is established using the Independent Continuous [...] Read more.
To address jagged boundaries in conventional fixed-mesh topology optimization and the discontinuous transfer of topology information after remeshing, this study proposes an improved Movable Morphable Smooth-Boundary (MMSB) method for displacement-constrained continuum topology optimization. A topology optimization model is established using the Independent Continuous Mapping (ICM) method, with structural weight minimization as the objective and displacement as the constraint. In the proposed framework, a triangular mesh is adopted as the current analysis mesh, threshold boundary points are identified using a holographic scanning strategy, and a fixed background mesh is introduced as an intermediate carrier for topology-variable transfer before and after remeshing. Three numerical examples are used to validate the proposed method and to compare it with the original MMSB method. The results show that the proposed method produces clearer boundary representations and more distinct load-transfer paths. In Examples 1–3, the number of result analyses is reduced from 60 to 24, from 144 to 36, and from 112 to 24, respectively. The number of boundary movements is also reduced from 5 to 4, from 8 to 6, and from 7 to 4, respectively. Meanwhile, the final structural weights are 22.0 kg, 101.4 kg, and 1.64 kg, which are close to or slightly lower than those obtained by the original MMSB method. These results indicate that the proposed method improves topology-information continuity and boundary representation while maintaining structural performance. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling, Dynamics and Applications)
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19 pages, 337 KB  
Article
Hamilton–Jacobi–Bellman-Based Optimal Effort Allocation for Student Productivity Dynamics
by Wafa Louafi, Houda Tadjer and Yacine Lafifi
AppliedMath 2026, 6(6), 91; https://doi.org/10.3390/appliedmath6060091 - 9 Jun 2026
Viewed by 322
Abstract
The adaptive regulation of student productivity remains a challenging problem in technology-enhanced learning environments due to the continuous and uncertain nature of cognitive effort, attention, and behavioral fluctuations. While existing educational intervention models are predominantly based on discrete-time decision frameworks, they often provide [...] Read more.
The adaptive regulation of student productivity remains a challenging problem in technology-enhanced learning environments due to the continuous and uncertain nature of cognitive effort, attention, and behavioral fluctuations. While existing educational intervention models are predominantly based on discrete-time decision frameworks, they often provide limited support for the representation of stochastic productivity dynamics and continuous effort adaptation. This paper proposes a continuous-time stochastic optimal control framework for adaptive effort allocation in student productivity regulation. The learner productivity level is modeled as a bounded stochastic diffusion process evolving on the interval ([0, 1]), where the drift and diffusion coefficients depend on both effort allocation and learner-specific psychological characteristics. The control objective is formulated as the maximization of an expected cumulative productivity reward penalized by excessive cognitive effort over a finite study horizon. Using the Hamilton–Jacobi–Bellman (HJB) framework, we derive an optimal state-dependent feedback policy that dynamically adjusts effort allocation according to the current productivity level, the remaining study horizon, and the learner profile. We establish the well-posedness of the controlled stochastic dynamics and show that the productivity state remains invariant within the admissible interval. The resulting HJB equation is solved numerically using a semi-implicit finite-difference approximation combined with iterative feedback updates. Simulation experiments conducted on synthetic learner profiles illustrate the qualitative behavior of the proposed controller under heterogeneous psychological configurations. Compared with constant-effort and threshold-based heuristic strategies, the adaptive feedback policy produces smoother productivity trajectories and more stable effort allocation patterns under stochastic perturbations. The proposed framework provides a mathematically grounded approach for studying adaptive productivity regulation under uncertainty and establishes a foundation for future data-driven calibration and personalized intervention systems. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling, Dynamics and Applications)
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15 pages, 3088 KB  
Article
Differential System Approach to Gene Regulatory Network Modeling
by Olga Kozlovska and Felix Sadyrbaev
AppliedMath 2026, 6(6), 84; https://doi.org/10.3390/appliedmath6060084 - 28 May 2026
Viewed by 486
Abstract
The system of ordinary differential equations that arises in models of genetic networks is considered. This system has both nonlinear and linear parts. As a nonlinear part, we use a piecewise linear function. This allows us to treat systems with multiple (up to [...] Read more.
The system of ordinary differential equations that arises in models of genetic networks is considered. This system has both nonlinear and linear parts. As a nonlinear part, we use a piecewise linear function. This allows us to treat systems with multiple (up to ten) equations. Special attention is paid to the four-dimensional systems that have an attractor in the form of a periodic solution. In the final part, the 10th-dimensional system is considered, which describes a subnetwork of a larger network that arises in a practical biomedical problem. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling, Dynamics and Applications)
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31 pages, 4613 KB  
Article
An Inventory Model for Growing Items with Imperfect Quality, Deterioration, and Freshness- and Inventory Level-Dependent Demand Under Carbon Emissions
by Kapya Tshinangi, Olufemi Adetunji and Sarma Yadavalli
AppliedMath 2025, 5(4), 181; https://doi.org/10.3390/appliedmath5040181 - 12 Dec 2025
Cited by 2 | Viewed by 1274
Abstract
Inventory models have evolved to incorporate a wide range of realistic factors, including growing items, imperfect quality, deterioration, and sustainability concerns. While these areas have received significant individual attention, no model has yet integrated the complexities of growing items, imperfect quality, deterioration, and [...] Read more.
Inventory models have evolved to incorporate a wide range of realistic factors, including growing items, imperfect quality, deterioration, and sustainability concerns. While these areas have received significant individual attention, no model has yet integrated the complexities of growing items, imperfect quality, deterioration, and carbon emissions. This study addresses this gap by introducing an economic order quantity (EOQ) model for growing items that simultaneously accounts for imperfect quality, deterioration, carbon emissions, and a demand rate that is influenced by both stock levels and the freshness condition. The goal is to determine the replenishment cycle and the optimal order quantity that will maximise profit. A numerical example is presented to illustrate the model’s feasibility. A sensitivity analysis on key parameters is also conducted to provide critical managerial insights. The results reveal that the shelf life of items and the scaling parameter of demand are among the most influential factors of profit, causing up to 150% and 112% increase in profit, respectively. The findings also indicate that deterioration significantly impacts system profitability by up to −45%. Another critical insight is that profit decreases by up to 80% when the weight of the growing items increases. Furthermore, emissions can be most effectively reduced by focusing on the feeding process, which represents the most impactful factor for improving sustainability, whereas emissions from the screening process, purchasing, deterioration, and storage hold minimal financial consequence. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling, Dynamics and Applications)
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25 pages, 1007 KB  
Article
Impact of Cattaneo–Christov Fluxes on Bio-Convective Flow of a Second-Grade Hybrid Nanofluid in a Porous Medium
by Mapule Pheko, Sicelo P. Goqo, Salma Ahmedai and Letlhogonolo Moleleki
AppliedMath 2025, 5(4), 180; https://doi.org/10.3390/appliedmath5040180 - 12 Dec 2025
Viewed by 1466
Abstract
This paper investigates the flow of a second-grade hybrid nanofluid through a Darcy–Forchheimer porous medium under Cattaneo–Christov heat and mass flux models. The hybrid nanofluid, composed of alumina and copper nanoparticles in water, enhances thermal and mass transport, while the second-grade model captures [...] Read more.
This paper investigates the flow of a second-grade hybrid nanofluid through a Darcy–Forchheimer porous medium under Cattaneo–Christov heat and mass flux models. The hybrid nanofluid, composed of alumina and copper nanoparticles in water, enhances thermal and mass transport, while the second-grade model captures viscoelastic effects, and the Darcy–Forchheimer medium accounts for both linear and nonlinear drag. Using similarity transformations and the spectral quasilinearisation method, the nonlinear governing equations are solved numerically and validated against benchmark results. The results show that hybrid nanoparticles significantly boost heat and mass transfer, while Cattaneo–Christov fluxes delay thermal and concentration responses, reducing the near-wall temperature and concentration. The distributions of velocity, temperature, concentration, and microorganism density are markedly affected by porosity, the Forchheimer number, the bio-convection Peclet number, and relaxation times. The results illustrate that hybrid nanoparticles significantly increase heat and mass transfer, whereas thermal and concentration relaxation factors delay energy and species diffusion, thickening the associated boundary layers. Viscoelasticity, porous medium resistance, Forchheimer drag, and bio-convection all have an influence on flow velocity and transfer rates, highlighting the subtle link between these mechanisms. These breakthroughs may be beneficial in establishing and enhancing bioreactors, microbial fuel cells, geothermal systems, and other applications that need hybrid nanofluids and non-Fourier/non-Fickian transport. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling, Dynamics and Applications)
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24 pages, 546 KB  
Article
Stochastic Analysis of a System of Two Interconnected Inventories
by Venkata S. S. Yadavalli, Kapya Tshinangi and Olufemi Adetunji
AppliedMath 2025, 5(4), 174; https://doi.org/10.3390/appliedmath5040174 - 5 Dec 2025
Viewed by 790
Abstract
This paper considers a continuous review inventory system for two interconnected product types, 1 and 2. Product type 1 is purchased from an external agency, whereas type 2 is manufactured in-house through a sequential batching process. The maximum stock position attainable by type [...] Read more.
This paper considers a continuous review inventory system for two interconnected product types, 1 and 2. Product type 1 is purchased from an external agency, whereas type 2 is manufactured in-house through a sequential batching process. The maximum stock position attainable by type 1 is S1 and that of type 2 is S2. Unit demands arise independently for the two products, where type 1 demand arrives following a Poisson process with rate λ1 and that for product B also follows a Poisson process with rate λ2. At the instance of the stock level of type 1 dropping to zero, it is replenished instantaneously to the maximum level S1, such that the stock level is never zero, and hence all demands for type 1 product are satisfied. The production machine attached to type 2 stops manufacturing immediately when its stock level reaches S2, and resumes immediately when the stock level drops to S2−1. In the event of the type 2 product not being available when demand arrives, it is substituted with the type 1 product with probability p. The production time for a single unit of type 2 is exponentially distributed with mean 1γ. We identify the underlying Markov process and analyse the performance of the interconnected inventory system. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling, Dynamics and Applications)
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