Mathematical Modeling and Numerical Optimization with Its Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 31 January 2027 | Viewed by 1477

Special Issue Editor


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Guest Editor
Department of Mathematics, Universidad del Valle, Cali 760032, Colombia
Interests: biomathematical modeling; optimization algorithms; epidemiology modeling; numerical linear algebra; estimation methods

Special Issue Information

Dear Colleagues,

Mathematical models, as part of the scientific method, are mathematical pictures of reality and represent a description of an object or system by applying particular mathematical concepts and symbols. They are often expressed in terms of ordinary differential equations and partial differential equations. Mathematical models can also be statistical models, fuzzy logic models, and empirical relationships. In fact, any model description using mathematical language can be called a mathematical model. On the other hand, numerical optimization, also called mathematical programming, is an area of applied mathematics that allows for finding “the best” alternative for a given situation through the systematic analysis of the possible alternatives of the situation at hand.

Good mathematical models and the proper use of classical and modern mathematical theory, as well as current numerical optimization techniques, are of vital importance to improve reliability and precision in the management of practical applications in real life.

We are pleased to invite you to submit original research articles and reviews where mathematical modeling or numerical optimization techniques are used to solve any type of real-life problem in the fields of engineering and natural, medical, or social sciences, among others. Please feel free to share this invitation with your colleagues.

If you have any questions regarding this Special Issue, please do not hesitate to contact us. We look forward to receiving your contributions.

Prof. Dr. Héctor Jairo Martínez-Romero
Guest Editor

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Keywords

  • mathematical modeling
  • numerical optimization
  • artificial neural network
  • operations research
  • genetic algorithm
  • linear and nonlinear programming
  • integer programming
  • complementary problem
  • complex networks
  • experimental data
  • mathematical epidemiology
  • optimal control
  • biological control

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Published Papers (2 papers)

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Research

29 pages, 833 KB  
Article
Optimizing Preventive and Treatment Strategies for Obesity Reduction: A Mathematical Modeling and Cost-Effectiveness Analysis
by Amr Radwan, Khalid Almohammdi, Mohamed I. Youssef and Olga Vasilieva
Mathematics 2026, 14(7), 1116; https://doi.org/10.3390/math14071116 - 26 Mar 2026
Viewed by 397
Abstract
Numerous studies have shown that overweight and obesity significantly increase the risk of severe illnesses, including type 2 diabetes, hypertension, and knee osteoarthritis. This study aims to develop a generalized mathematical model to manage the growing prevalence of overweight and obesity. We first [...] Read more.
Numerous studies have shown that overweight and obesity significantly increase the risk of severe illnesses, including type 2 diabetes, hypertension, and knee osteoarthritis. This study aims to develop a generalized mathematical model to manage the growing prevalence of overweight and obesity. We first demonstrate that the model’s solution remains positive and bounded under specific conditions. To determine optimal intervention strategies, we apply Pontryagin’s minimum principle (PMP) to establish necessary optimality conditions. The Forward–Backward Sweeping Method (FBSM) is then used to obtain numerically optimal controls and to demonstrate their effect over a fixed time interval. The results indicate that the proposed approach effectively reduces overweight and obesity while ensuring cost-effectiveness. Full article
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14 pages, 429 KB  
Article
Low-Complexity Numerical Approach for the Diffusion Equation with Variable Diffusion Coefficient
by Marta Zárraga-Rodríguez, Patricio Fuentes and Xabier Insausti
Mathematics 2026, 14(2), 285; https://doi.org/10.3390/math14020285 - 13 Jan 2026
Viewed by 506
Abstract
The diffusion equation models a wide variety of physical and chemical processes and has significant interest in many scientific disciplines. Analytical and numerical methods found in the literature for solving the diffusion equation consider a constant diffusion coefficient. However, in reality, it is [...] Read more.
The diffusion equation models a wide variety of physical and chemical processes and has significant interest in many scientific disciplines. Analytical and numerical methods found in the literature for solving the diffusion equation consider a constant diffusion coefficient. However, in reality, it is not constant. In this paper, we present a numerical approach to solve the diffusion equation when the diffusion coefficient is not constant. Unlike existing methods that require solving non-linear systems with iterative schemes, our approach transforms the problem into a linear system, drastically reducing computational cost while preserving temporal accuracy. Full article
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