Advances in Mathematical Modelling and Control Strategies of Infectious Diseases

Deadline for manuscript submissions: 15 August 2026

Special Issue Editors

Dr. Muhammad Rafiq Website E-Mail: muhammad.rafiq@namal.edu.pk
Guest Editor
Department of Mathematics, Namal University, Pakistan
Interests: Mathematical Modelling; Disease Modelling

Dr. Waheed Ahmad Website E-Mail: waheed.ahmad@gcu.edu.pk
Guest Editor
Department of Mathematics, Government College University, Pakistan
Interests: Stability; optimal control; Epidemiology

Special Issue Information

Delay differential equations are particularly well-suited for capturing these time-related effects. They offer powerful tools for analysing how diseases progress over time. At the same time, effective control strategies, including feedback mechanisms and state-dependent interventions, are essential for shaping prevention and 4. Summary: Over the years, mathematical modelling has played a key role in helping scientists understand how complex systems work and in predicting their behaviour based on experimental data. In fields like medicine, ecology, and the study of infectious diseases, such models have not only supported hypothesis testing but also enabled the development of predictions that can be verified through real-world experiments. These models often provide fresh insights into how the different parts of biological systems interact and influence the system as a whole. Biological modelling also draws from other well-established sciences, such as physics and chemistry, while continuing to develop its own specialized mathematical and computational tools. In recent years, there has been increasing interest in using delay differential equations (DDEs) to study how infectious diseases spread and how their impacts can be controlled. Modelling such processes accurately is complex, and this challenge has been widely discussed, especially in light of recent global health crises, including COVID-19 and other emerging infectious diseases. These experiences have shown a clear need for advanced mathematical frameworks that can account for delays, such as incubation periods, treatment lags, and human behavioural responses, to improve outbreak predictions and support timely public health interventions.

This Special Issue highlights the latest research in this rapidly evolving field. It focuses on delay-based epidemic models and innovative approaches to controlling disease spread, including optimization techniques. We are especially interested in contributions that explore stability analysis, bifurcation phenomena, parameter estimation, and the use of stochastic or fractional dynamics, as well as numerical and computational methods tailored to complex disease systems.

Submissions that connect theory with real-world applications, such as studies on vector-borne illnesses, emerging pathogens, or data-driven public health strategies are highly encouraged. We welcome a broad range of manuscript types, including conceptual and applied studies, methodological innovations, and data-driven analyses. Researchers from mathematics, epidemiology, computational science, and related disciplines are invited to contribute to this Special Issue.

Keywords:

Delay differential equations;

Fractional delay differential equations;

Infectious disease modeling;

Optimal control;

Feedback control;

Stability analysis;

Bifurcation;

Numerical methods;

Stochastic delay systems;

Fractional dynamics;

Vector-borne diseases;

Epidemic modeling;

Parameter estimation.

Early fault signals of the rolling bearing in the rotor are weak and present the characteristics of non-periodic and non-stationary; it is more difficult to carry out fault diagnosis on it. In this regard, this paper proposes a weak rolling bearing fault diagnosis algorithm based on whale optimization algorithm, simplistic geometry mode decomposition, and maximum correlated kurtosis deconvolution (WOA-SGMD-MCKD). Firstly, the vibration signal of the rotor platform is obtained, and the Symmetric Geometric Mode Decomposition (SGMD) is used to reconstruct the vibration signal. To obtain the best decomposition effect of the SGMD and overcome modal aliasing, the Whale Optimization Algorithm (WOA) is used to optimize the embedding dimension. Secondly, for the reconstructed vibration signal, the Maximum Correlated Kurtosis Deconvolution (MCKD) is used to extract its impulse component, and the WOA is used to optimize the filter length and deconvolution period of the MCKD so that the frequency envelope spectrum of the vibration signal can be obtained, which can provide the basis for the fault diagnosis of rolling bearings. Finally, the effectiveness and feasibility of the algorithm proposed are verified by a non-periodic and non-stationary simulation platform and rotor maneuvering platform in this paper.

Numerical solution of a 3D mathematical model for the progression of tumor angiogenic factor in a tissue

In this work, the movement of tumor angiogenic factor in a three-dimensional tissue is obtained by the Method of Lines. This method transforms a partial differential equation into a system of ordinary differential equations together with the initial and boundary conditions. The more the number of lines is increased, the more the accuracy of the method increases. This method results in very accurate numerical solutions for linear and non-linear problems in contrast with other existing methods. We present Matlab-generated figures, which are the movement of tumor angiogenic factor in porous medium and explain the biological importance of this progression. The computer codes are also provided.

Mathematical modelling and controllability analysis of fractional order coal mill pulverizer model

This paper investigates the controllability of nonlinear dynamical systems and their applications, with a focus on fractional-order systems and coal mill models. A novel theorem is proposed, providing sufficient conditions for controllability, including constraints on the steering operator and nonlinear perturbation bounds. The theorem establishes the existence of a contraction mapping for the nonlinear operator, enabling effective control strategies for fractional systems. The methodology is demonstrated through rigorous proof and supported by an iterative algorithm for controller design. Additionally, the controllability of a coal mill system represented as a nonlinear differential system, is analyzed. The findings present new insights into the interplay of fractional dynamics and nonlinear systems, offering practical solutions for real-world control problems.