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Mathematics
Special Issues
Modeling, Control and Optimization of Biological Systems
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Modeling, Control and Optimization of Biological Systems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E3: Mathematical Biology".

Deadline for manuscript submissions: 20 September 2026 | Viewed by 2519

Special Issue Editor

Prof. Dr. Junyuan Yang

E-Mail Website
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

Manuscript Submission Information

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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-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

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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 (3 papers)

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Research

27 pages, 3472 KB  
Article
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
Viewed by 552
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 [...] Read more.
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  
Article
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 3 | Viewed by 580
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 CD4+ 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 CD4+ 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, R0, as two components, R01 and R02, which quantify the respective contributions of CD4+ T cells and macrophages to viral spread. It is deduced that the infection-free steady state is globally asymptotically stable once R0≤1, ensuring viral eradication. For R0>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∗=1−1R0, 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  
Article
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 853
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 [...] Read more.
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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