Analysis and Numerical Simulation for the Dynamics of Infectious Diseases with Applications in Medicine

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

Deadline for manuscript submissions: 31 October 2025 | Viewed by 2495

Special Issue Editors

Special Issue Information

Dear Colleagues,

Infectious diseases are caused by pathogenic microorganisms, such as bacteria, viruses, parasites or fungi, and can be spread, directly or indirectly, from one person to another. These diseases can be grouped into three categories: diseases which cause high levels of mortality; diseases which place heavy burdens of disability on populations; and diseases which, owing to the rapid and unexpected nature of their spread, can have serious global repercussions. Many of the key determinants of health and the causes of infectious diseases lie outside the direct control of the health sector. Other sectors involved are those dealing with sanitation and water supply, the environment and climate change, education, agriculture, trade, tourism, transport, industrial development and housing.

The World Health Organization (WHO) is dedicated to creating a world free from disease and addressing the social conditions that influence human health and well-being. However, unfortunately, the WHO is recording continuously increasing cases of death and infection, particularly resulting from infectious diseases such as HIV/AIDS, COVID-19, etc.

The current treatments still present substantial limitations: they do not fully restore health and the offered medications are not strictly curative. In fact, there is no cure or vaccine for the above deadly diseases, but medications can dramatically slow the progression of a disease, ultimately leading to either recovery or death.

In light of the above, we were motivated to investigate and contribute to this controversial subject using the best aspects of mathematical modelling.

Fractional dynamic systems are powerful tools with more accurate and successful results in modelling several complex phenomena in many diverse and widespread fields of science and engineering. As this challenging subject develops, it is paramount to focus on the theoretical and numerical techniques of applied mathematics in biology and medicine.

We invite original and compelling results obtained from modern computational techniques utilising theoretical, experimental and applied aspects of (fractional) dynamic systems in biosciences; detours from this are welcomed. It is necessary for these papers to be strongly grounded in high-level mathematics. Note that submitted papers should explicitly meet the aims and scope of this journal.

The papers should be written in English and carefully checked for correct grammar and spelling. Each paper should clearly indicate the nature of its scientific contribution. Manuscripts should be prepared using LaTeX and follow the journal’s instruction. Submission of a manuscript will be understood to mean that the paper is not being considered for publication elsewhere. Papers that are not prepared according to the above instructions or are badly written will be immediately rejected. All papers will be subject to a peer review process.

Prof. Dr. Amar Debbouche
Dr. Ivanka Stamova
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

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.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fractional integrals and derivatives
  • discrete and continuous dynamic systems
  • ill-posed, regularized, and inverse problems
  • difference equations and finite element methods
  • stochastic processes and random variables
  • operator theory
  • integral transformations and special functions
  • optimization
  • optimal control and stability analysis
  • mathematical modelling
  • epidemiological models
  • sensitivity analysis
  • communicable/infectious diseases models
  • epidemiological models
  • virus transmission
  • numerical methods for PDEs
  • computational techniques
  • numerical simulation
  • applications of fractional models in biology and medicine

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (1 paper)

Order results
Result details
Select all
Export citation of selected articles as:

Research

29 pages, 2623 KiB  
Article
Stability and Optimality Criteria for an SVIR Epidemic Model with Numerical Simulation
by Halet Ismail, Amar Debbouche, Soundararajan Hariharan, Lingeshwaran Shangerganesh and Stanislava V. Kashtanova
Mathematics 2024, 12(20), 3231; https://doi.org/10.3390/math12203231 - 15 Oct 2024
Cited by 4 | Viewed by 1415
Abstract
The mathematical modeling of infectious diseases plays a vital role in understanding and predicting disease transmission, as underscored by recent global outbreaks; to delve deep into the dynamic of infectious disease considering latent period presciently is inevitable as it bridges the gap between [...] Read more.
The mathematical modeling of infectious diseases plays a vital role in understanding and predicting disease transmission, as underscored by recent global outbreaks; to delve deep into the dynamic of infectious disease considering latent period presciently is inevitable as it bridges the gap between realistic nature and mathematical modeling. This study extended the classical Susceptible–Infected–Recovered (SIR) model by incorporating vaccination strategies during incubation. We introduced multiple time delays to an account incubation period to capture realistic disease dynamics better. The model is formulated as a system of delay differential equations that describe the transmission dynamics of diseases such as polio or COVID-19, or diseases for which vaccination exists. Critical aspects of the study include proving the positivity of the model’s solutions, calculating the basic reproduction number (R0) using next-generation matrix theory, and identifying disease-free and endemic equilibrium points. The local stability of these equilibria is then analyzed using the Routh–Hurwitz criterion. Due to the complexity introduced by the delay components, we examine the stability by studying the roots of a fourth-degree exponential polynomial. The effects of educational campaigns and vaccination efficacy are also investigated as control measures. Furthermore, an optimization problem is formulated, based on Pontryagin’s maximum principle, to minimize the number of infections and associated intervention costs. Numerical simulations of the delay differential equations are conducted, and a modified Runge–Kutta method with delays is used to solve the optimal control problem. Finally, we present a few simulation results to illustrate the analytical findings. Full article
Show Figures

Figure 1

Back to TopTop