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A Special Issue of Mathematics (ISSN 2227-7390) belonging to the section "E3: Mathematical Biology".

Deadline for manuscript submissions: 20 September 2026 | Viewed by 4365

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Prof. Dr. Junyuan Yang

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Guest Editor

Complex Systems Research Center, Shanxi University, Taiyuan 030006, China
Interests: game theory; epidemiology; complex networks

Special Issue Information

Dear Colleagues,

Biological systems, from cellular pathways to ecosystems, exhibit intricate dynamics shaped by nonlinear interactions. Advances in biological systems, computational tools and synthetic biology have created opportunities to model, control and optimize these systems for transformative applications in healthcare, biomanufacturing and environmental sustainability. However, challenges persist in balancing model accuracy, scalability and real-world applicability. This proposal aims to achieve specific goals such as maintaining homeostasis, improving bioprocesses or developing novel therapeutic approaches. By integrating modeling, control and optimization techniques, researchers can gain a deeper understanding of biological systems and potentially develop more effective strategies for their manipulation and application.

Prof. Dr. Junyuan Yang
Guest Editor

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Keywords

ecological modeling
mutiscale immuno-epidemiologial models
parameter identifiaction
disease-informed neural networks
optimal control theory

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Published Papers (5 papers)

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Research

27 pages, 1757 KB

Open AccessFeature PaperArticle

A Bounded Adaptive Random Local Mutation Algorithm for Sparse-Data Parameter Identification in Nonlinear Bioprocess Models

by Velislava Lyubenova, Olympia Roeva, Elena Chorukova, Maya Ignatova, Anastasiya Zlatkova, Denitsa Kristeva and Gergana Roeva

Mathematics 2026, 14(18), 3315; https://doi.org/10.3390/math14183315 - 12 Sep 2026

Viewed by 201

Abstract

Sparse and unevenly informative observations can substantially limit parameter estimation in nonlinear bioprocess models. This proof-of-concept study investigates Bounded Adaptive Random Local Mutation (B-ARLM), a derivative-free algorithm for bounded parameter calibration, using a product-inhibited Andrews-type model of biological hydrogen production calibrated to six interval-average observations over 0–8 days. Andrews–P achieved the lowest in-sample calibration error among the three examined kinetic formulations, with a best-run NMSE of 1.29 × 10⁻³. Under a common budget of 2250 objective-function evaluations and 30 repeated runs, B-ARLM significantly outperformed the Fixed-EA ablation and the study-specific sCA-ES reference, while its terminal performance was not statistically distinguishable from canonical CMA-ES or jDE after Holm correction. Hyperparameter, broad-start, profile-NMSE, and observation-error sensitivity analyses were additionally performed. Broad-start optimization and two-dimensional profiling revealed widely separated near-optimal parameter vectors and pronounced parameter compensation, showing that accurate trajectory reconstruction does not imply unique kinetic-parameter recovery. The results support B-ARLM as a competitive bounded calibration strategy for the examined sparse-data problem while emphasizing the distinction between optimization performance, practical identifiability, and biological interpretation. Full article

(This article belongs to the Special Issue Modeling, Control and Optimization of Biological Systems)

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38 pages, 3910 KB

Open AccessArticle

Modeling, Control, and Management of a Nonlinear Tumor–Immune Biological System via Adaptive Smooth Sliding Mode Radiochemotherapy

by Muhammad Arsalan, Xiaojun Yu, Sadiq Muhammad and Jaeyoung Choi

Mathematics 2026, 14(16), 2973; https://doi.org/10.3390/math14162973 - 17 Aug 2026

Viewed by 246

Abstract

Nonlinear biological systems exhibit complex interactions, uncertain parameters, and strong treatment-dependent dynamics, making mathematical modeling and control essential for designing reliable therapeutic intervention strategies. This study proposes a multi-input adaptive smooth sliding mode control (AMIS-SMC) framework for regulating combined radiotherapy and chemotherapy in a nonlinear tumor–immune dynamical system described by ordinary differential equations. The proposed controller integrates a hyperbolic tangent smoothing mechanism with adaptive parameter-estimation laws to compensate for uncertainty in tumor and healthy-cell growth dynamics. In this way, the method explicitly links biological-system modeling, feedback control, treatment-dose management, and parameter adaptation within a single mathematically analyzable framework. Fundamental closed-loop properties are established analytically, including positivity and boundedness of all biological state variables, asymptotic convergence of the sliding surfaces, and explicit upper bounds on the administered radiation and chemotherapeutic drug dosages. Lyapunov-based stability analysis is used to guarantee boundedness of the closed-loop signals and convergence of the sliding manifold. Numerical simulations based on a brain-tumor case study demonstrate that the proposed AMIS-SMC algorithm achieves rapid tumor suppression while administering substantially lower treatment intensities than conventional and integral SMC approaches. Under nominal conditions, the proposed controller reduces cumulative radiation and chemotherapy dosages while maintaining effective tumor mitigation. Under mismatched parameter conditions, AMIS-SMC consistently drives the tumor-cell population toward the desired equilibrium across all tested scenarios, whereas conventional and integral SMC show limited adaptability. Statistical analysis using Mann–Whitney U and Fisher’s tests further indicates that AMIS-SMC provides an effective mathematical-control and treatment-management strategy for tumor suppression in a simplified nonlinear tumor–immune biological system under parameter uncertainty. Full article

(This article belongs to the Special Issue Modeling, Control and Optimization of Biological Systems)

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27 pages, 3472 KB

Open AccessArticle

A Mathematical Model to Study the Combined Uses of Infected Pests and Nutrients in Crop Pest Control: Stability Changes and Optimal Control

by Aeshah A. Raezah, Fahad Al Basir, Pankaj Kumar Tiwari, Animesh Sinha and Jahangir Chowdhury

Mathematics 2026, 14(1), 16; https://doi.org/10.3390/math14010016 - 21 Dec 2025

Cited by 1 | Viewed by 1198

Abstract

This study presents a comprehensive analysis of farming-awareness campaigns aimed at enhancing crop pest management through the strategic deployment of infected pests as a biological control mechanism. Additionally, the role of nutrient supplementation is examined within these campaigns to facilitate crop recovery and improve overall agricultural yield. A mathematical model is developed and rigorously analyzed to assess the efficacy of these integrated pest control strategies. The model is investigated with a focus on equilibrium states, stability analysis, and the conditions leading to Hopf bifurcation. Furthermore, optimal control theory is employed to optimize the release of infected pests, ensuring maximum crop yield while maintaining ecological balance. Our study not only underscores the critical influence of nutrient supplementation in augmenting crop productivity but also highlights the risk of excessive nutrient application, which may destabilize the system. These results emphasize the necessity of maintaining an optimal nutrient threshold. By integrating farming-awareness campaigns with precise biological control measures and nutrient management, our study establishes a robust framework for sustainable pest mitigation and agricultural productivity enhancement. The findings suggest that the synergistic application of infected pests and nutrient enrichment not only suppresses pest populations but also enhances crop resilience and productivity. Full article

(This article belongs to the Special Issue Modeling, Control and Optimization of Biological Systems)

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26 pages, 2983 KB

Open AccessArticle

Global Dynamics and Optimal Control of a Dual-Target HIV Model with Latent Reservoirs

by Fawaz K. Alalhareth, Fahad K. Alghamdi, Mohammed H. Alharbi and Miled El Hajji

Mathematics 2025, 13(23), 3868; https://doi.org/10.3390/math13233868 - 2 Dec 2025

Cited by 4 | Viewed by 903

Abstract

In this paper, we develop a mathematical model to investigate HIV infection dynamics, where we focus on the virus’s dual-target mechanism involving both CD

4^{+}

T cells and macrophages. Our model is structured as a system of seven nonlinear ordinary differential equations [...] Read more.

In this paper, we develop a mathematical model to investigate HIV infection dynamics, where we focus on the virus’s dual-target mechanism involving both CD

4^{+}

T cells and macrophages. Our model is structured as a system of seven nonlinear ordinary differential equations describing the interactions between susceptible, latent, and infected cells, alongside free virus particles. We derive the basic reproduction number,

R_{0}

, as two components,

R_{01}

and

R_{02}

, which quantify the respective contributions of CD

4^{+}

T cells and macrophages to viral spread. It is deduced that the infection-free steady state is globally asymptotically stable once

R_{0} \leq 1

, ensuring viral eradication. For

R_{0} > 1

, a stable endemic steady state emerges, indicating the persistence of the infection. Later, we develop an optimal control strategy to study the impact of reverse transcriptase and protease inhibitors. This analysis identifies a critical drug efficacy threshold,

ϵ^{*} = 1 - \frac{1}{R_{0}}

, necessary for viral eradication. The numerical simulations and the sensitivity analysis provide key parameters that drive viral dynamics, offering practical insights for designing targeted therapies, particularly during the early stages of infection. Full article

(This article belongs to the Special Issue Modeling, Control and Optimization of Biological Systems)

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26 pages, 387 KB

Open AccessArticle

Identification and Empirical Likelihood Inference in Nonlinear Regression Model with Nonignorable Nonresponse

by Xianwen Ding and Xiaoxia Li

Mathematics 2025, 13(9), 1388; https://doi.org/10.3390/math13091388 - 24 Apr 2025

Viewed by 1048

Abstract

The identification of model parameters is a central challenge in the analysis of nonignorable nonresponse data. In this paper, we propose a novel penalized semiparametric likelihood method to obtain sparse estimators for a parametric nonresponse mechanism model. Based on these sparse estimators, an instrumental variable is introduced, enabling the identification of the observed likelihood. Two classes of estimating equations for the nonlinear regression model are constructed, and the empirical likelihood approach is employed to make inferences about the model parameters. The oracle properties of the sparse estimators in the nonresponse mechanism model are systematically established. Furthermore, the asymptotic normality of the maximum empirical likelihood estimators is derived. It is also shown that the empirical log-likelihood ratio functions are asymptotically weighted chi-squared distributed. Simulation studies are conducted to validate the effectiveness of the proposed estimation procedure. Finally, the practical utility of our approach is demonstrated through the analysis of ACTG 175 data. Full article

(This article belongs to the Special Issue Modeling, Control and Optimization of Biological Systems)

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