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Advances in Mathematical Modeling: Numerical Approaches and Simulation for Computational Biology

Submission Deadline: 31 March 2026 (closed) View: 5395 Submit to Special Issue

Guest Editor(s)

Dr. Faranak Rabiei, Texas A & M University Kingsville, USA
Dr. Dongwook Kim, Texas A & M University Kingsville, USA
Dr. Zeeshan Ali, Monash University- Malaysia Campus, Malaysia

Summary

This special issue explores the dynamic collaboration between mathematics and biology by highlighting the advanced methodologies and theoretical developments. In recent years, there has been a growing interest in the application of mathematics to understand biological systems and the behavior of various diseases. Mathematical modeling has been used to study different aspects of biological systems, epidemiology, population dynamics, cell signaling, gene regulation, ecosystem interactions, and others. These models have offered insights into the behavior of biological systems, helping in the explanation of observed phenomena and the prediction of experimental outcomes. The special issue titled "Advances in Mathematical Modeling: Numerical Approaches and Simulation for Computational Biology" focuses on the latest developments and applications of mathematical modeling techniques in the field of computational biology. It aims to explore how numerical approaches and simulations are being utilized to advance our understanding of biological systems, with a particular focus on their applications in computational biology and modeling.


This special issue covers following area and topics:

· Numerical analysis and computational approaches in biology

· Epidemiology

· Computational neuroscience

· Dynamical system of mathematical biology models

· Infectious Disease Dynamics

· Cancer mathematical modeling

· Oncolytic or immunotherapy

· Stability Analysis

· Time Delay ODE/PDE biological Models


Published Papers

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  • Open Access

    ARTICLE

    Physics-Informed Neural Networks for Osteosarcoma Tumor-Immune Dynamics

    Pasquale De Luca, Livia Marcellino
    CMES-Computer Modeling in Engineering & Sciences, DOI:10.32604/cmes.2026.082664
    （This article belongs to the Special Issue: Advances in Mathematical Modeling: Numerical Approaches and Simulation for Computational Biology)
    Abstract Osteosarcoma is the most common primary malignant bone tumor in pediatric populations. This work presents an extended Physics-Informed Neural Network framework that incorporates interferon-gamma (IFN-γ) as a fifth biological variable, complementing previous four-variable formulations with an explicit cytokine-mediated macrophage activation pathway. The model couples five biological fields with mechanical tissue response through Biot’s poroelastic theory over a two-dimensional domain. Four distinct initial macrophage distributions were investigated. Numerical stability was achieved across all scenarios, with total loss values between 0.056 and 0.158 and mechanical residuals below 3.2×10−5. The boundary-concentrated configuration yielded the lowest biological loss. More >

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    198

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    51

  • Open Access

    ARTICLE

    Assessment of Regional Structural Optimality in a 2D Synthetic Proximal Femur Model under Varying Loading Angles

    Jisun Kim, Jung Jin Kim
    CMES-Computer Modeling in Engineering & Sciences, Vol.147, No.2, 2026, DOI:10.32604/cmes.2026.079665
    （This article belongs to the Special Issue: Advances in Mathematical Modeling: Numerical Approaches and Simulation for Computational Biology)
    Abstract Synthetic proximal femur models avoid the ethical and technical limitations of human specimens and thus serve as an effective alternative for studying the proximal femur. This structure is directly connected to the hip joint, endures complex multi-directional loads, and exhibits region-specific structural adaptations due to its unique triangular geometry. However, most previous studies have examined only global load distributions or restricted regions, limiting the understanding of regional structural optimality. Therefore, this study aims to quantitatively evaluate the load adaptability and structural optimality of the proximal femur across individual regions of interest (ROIs). Three types of… More >

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    392

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    156

  • Open Access

    ARTICLE

    Optimal Resource Allocation in a Bacterial Growth Model Under Cold Stress and Temperature

    Saira Batool, Muhammad Imran, Brett McKinney
    CMES-Computer Modeling in Engineering & Sciences, Vol.146, No.3, 2026, DOI:10.32604/cmes.2026.079067
    （This article belongs to the Special Issue: Advances in Mathematical Modeling: Numerical Approaches and Simulation for Computational Biology)
    Abstract Bacterial growth requires strategic allocation of limited intracellular resources, especially under cold stress, where stabilized messenger ribonucleic acid (mRNA) secondary structures slow translation by impairing ribosome binding. Escherichia coli (E. coli) counters this bottleneck by inducing the cold-shock protein A (CspA), an RNA chaperone that remodels inhibitory structures. However, synthesizing CspA diverts biosynthetic capacity from ribosome production and metabolism, creating a fundamental resource-allocation trade-off. In this work, we develop a dynamical model capturing the interplay between metabolic precursors, ribosomes, and CspA, and use it to examine how growth and allocation patterns shift with temperature. Steady-state analysis shows… More >

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    437

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    204

  • Open Access

    ARTICLE

    Non-Newtonian Electroosmotic Flow Effects on a Self-Propelled Undulating Sheet in a Wavy Channel

    Rehman Ali Shah, Zeeshan Asghar, Chenji Li, Arezoo Ardekani, Nasir Ali
    CMES-Computer Modeling in Engineering & Sciences, Vol.145, No.1, pp. 753-778, 2025, DOI:10.32604/cmes.2025.069177
    （This article belongs to the Special Issue: Advances in Mathematical Modeling: Numerical Approaches and Simulation for Computational Biology)
    Abstract The objective of this work is to investigate the dynamics of a self-propelled undulating sheet in a non-Newtonian electrolyte solution inside a wavy channel under the electroosmotic effect. The electrolyte solution, which is non-Newtonian, is modeled as a Carreau-Yasuda fluid. The flow generated by a combination of an undulating sheet and electroosmotic effect is obtained by solving the continuity and momentum equations. The electroosmotic body force term is derived using the Poisson-Boltzmann equation for the electric potential. A fourth-order ordinary differential equation for the stream function is solved under the Stokes flow regime. The dynamics More >

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    833

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    397

  • Open Access

    ARTICLE

    Investigating the Role of Antimalarial Treatment and Mosquito Nets in Malaria Transmission and Control through Mathematical Modeling

    Azhar Iqbal Kashif Butt, Tariq Ismaeel, Sara Khan, Muhammad Imran, Waheed Ahmad, Ismail Abdulrashid, Muhammad Sajid Riaz
    CMES-Computer Modeling in Engineering & Sciences, Vol.144, No.3, pp. 3463-3492, 2025, DOI:10.32604/cmes.2025.069277
    （This article belongs to the Special Issue: Advances in Mathematical Modeling: Numerical Approaches and Simulation for Computational Biology)
    Abstract Malaria is a significant global health challenge. This devastating disease continues to affect millions, especially in tropical regions. It is caused by Plasmodium parasites transmitted by female Anopheles mosquitoes. This study introduces a nonlinear mathematical model for examining the transmission dynamics of malaria, incorporating both human and mosquito populations. We aim to identify the key factors driving the endemic spread of malaria, determine feasible solutions, and provide insights that lead to the development of effective prevention and management strategies. We derive the basic reproductive number employing the next-generation matrix approach and identify the disease-free and… More >

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    2704

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    558

  • Open Access

    ARTICLE

    A Time-Continuous Model for an Untreated HIV-Infection and a Novel Non-Standard Finite-Difference-Method for Its Discretization

    Benjamin Wacker, Jan Christian Schlüter
    CMES-Computer Modeling in Engineering & Sciences, Vol.144, No.2, pp. 2191-2229, 2025, DOI:10.32604/cmes.2025.067397
    （This article belongs to the Special Issue: Advances in Mathematical Modeling: Numerical Approaches and Simulation for Computational Biology)
    Abstract In this work, we re-investigate a classical mathematical model of untreated HIV infection suggested by Kirschner and introduce a novel non-standard finite-difference method for its numerical solution. As our first contribution, we establish non-negativity, boundedness of some solution components, existence globally in time, and uniqueness on a time interval for an arbitrary for the time-continuous problem which extends known results of Kirschner’s model in the literature. As our second analytical result, we establish different equilibrium states and examine their stability properties in the time-continuous setting or discuss some numerical tools to evaluate this question. Our More >

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    2367

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    1676

  • Open Access

    ARTICLE

    Modeling and Simulation of Epidemics Using q-Diffusion-Based SEIR Framework with Stochastic Perturbations

    Amani Baazeem, Muhammad Shoaib Arif, Yasir Nawaz, Kamaleldin Abodayeh
    CMES-Computer Modeling in Engineering & Sciences, Vol.143, No.3, pp. 3463-3489, 2025, DOI:10.32604/cmes.2025.066299
    （This article belongs to the Special Issue: Advances in Mathematical Modeling: Numerical Approaches and Simulation for Computational Biology)
    Abstract The numerical approximation of stochastic partial differential equations (SPDEs), particularly those including q-diffusion, poses considerable challenges due to the requirements for high-order precision, stability amongst random perturbations, and processing efficiency. Because of their simplicity, conventional numerical techniques like the Euler-Maruyama method are frequently employed to solve stochastic differential equations; nonetheless, they may have low-order accuracy and lower stability in stiff or high-resolution situations. This study proposes a novel computational scheme for solving SPDEs arising from a stochastic SEIR model with q-diffusion and a general incidence rate function. A proposed computational scheme can be used to… More >

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    1429

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    575

  • Open Access

    ARTICLE

    Computational Modeling of Streptococcus Suis Dynamics via Stochastic Delay Differential Equations

    Umar Shafique, Ali Raza, Dumitru Baleanu, Khadija Nasir, Muhammad Naveed, Abu Bakar Siddique, Emad Fadhal
    CMES-Computer Modeling in Engineering & Sciences, Vol.143, No.1, pp. 449-476, 2025, DOI:10.32604/cmes.2025.061635
    （This article belongs to the Special Issue: Advances in Mathematical Modeling: Numerical Approaches and Simulation for Computational Biology)
    Abstract Streptococcus suis (S. suis) is a major disease impacting pig farming globally. It can also be transferred to humans by eating raw pork. A comprehensive study was recently carried out to determine the indices through multiple geographic regions in China. Methods: The well-posed theorems were employed to conduct a thorough analysis of the model’s feasible features, including positivity, boundedness equilibria, reproduction number, and parameter sensitivity. Stochastic Euler, Runge Kutta, and Euler Maruyama are some of the numerical techniques used to replicate the behavior of the streptococcus suis infection in the pig population. However, the dynamic… More >

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    1624

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    829

  • Open Access

    ARTICLE

    Biomechanical Study of Different Scaffold Designs for Reconstructing a Traumatic Distal Femur Defect Using Patient-Specific Computational Modeling

    Hsien-Tsung Lu, Ching-Chi Hsu, Qi-Quan Jian, Wei-Ting Chen
    CMES-Computer Modeling in Engineering & Sciences, Vol.142, No.2, pp. 1883-1898, 2025, DOI:10.32604/cmes.2025.057675
    （This article belongs to the Special Issue: Advances in Mathematical Modeling: Numerical Approaches and Simulation for Computational Biology)
    Abstract Reconstruction of a traumatic distal femur defect remains a therapeutic challenge. Bone defect implants have been proposed to substitute the bone defect, and their biomechanical performances can be analyzed via a numerical approach. However, the material assumptions for past computational human femur simulations were mainly homogeneous. Thus, this study aimed to design and analyze scaffolds for reconstructing the distal femur defect using a patient-specific finite element modeling technique. A three-dimensional finite element model of the human femur with accurate geometry and material distribution was developed using the finite element method and material mapping technique. An… More >

    Graphic Abstract

    Biomechanical Study of Different Scaffold Designs for Reconstructing a Traumatic Distal Femur Defect Using Patient-Specific Computational Modeling

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    1658

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    1460

  • Open Access

    ARTICLE

    SEIR Mathematical Model for Influenza-Corona Co-Infection with Treatment and Hospitalization Compartments and Optimal Control Strategies

    Muhammad Imran, Brett McKinney, Azhar Iqbal Kashif Butt
    CMES-Computer Modeling in Engineering & Sciences, Vol.142, No.2, pp. 1899-1931, 2025, DOI:10.32604/cmes.2024.059552
    （This article belongs to the Special Issue: Advances in Mathematical Modeling: Numerical Approaches and Simulation for Computational Biology)
    Abstract The co-infection of corona and influenza viruses has emerged as a significant threat to global public health due to their shared modes of transmission and overlapping clinical symptoms. This article presents a novel mathematical model that addresses the dynamics of this co-infection by extending the SEIR (Susceptible-Exposed-Infectious-Recovered) framework to incorporate treatment and hospitalization compartments. The population is divided into eight compartments, with infectious individuals further categorized into influenza infectious, corona infectious, and co-infection cases. The proposed mathematical model is constrained to adhere to fundamental epidemiological properties, such as non-negativity and boundedness within a feasible region.… More >

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    1840

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    840

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