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Mathematics
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Mathematical Epidemiological Models: Classical and Interdisciplinary Applications
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Mathematical Epidemiological Models: Classical and Interdisciplinary Applications

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

Deadline for manuscript submissions: 20 June 2025 | Viewed by 1402

Special Issue Editor

Dr. Till D. Frank

E-Mail Website
Guest Editor
1. Psychological Sciences, University of Connecticut, 406 Babbidge Road, Storrs, CT 06269, USA
2. Physics Department, University of Connecticut, 179 Auditorium Road, Storrs, CT 06269, USA
Interests: dynamical diseases; complex systems; self-organization; modeling time-series analysis; stochastic

Special Issue Information

Dear Colleagues,

Mathematical epidemiological models are frequently given in terms of coupled nonlinear differential equations that describe the evolution of interacting populations. They describe how a key property of interest, such as a virus, is passed over from individuals to individuals. In doing so, they describe the spread of that property (e.g., the virus). While classical applications of epidemiological models are concerned with the spread of infectious diseases in populations, there are various fascinating and inspiring applications in related and interdisciplinary fields. For example, the spread of a virus in a human body can be described by virus dynamics models that have much in common with epidemiological models. Likewise, the spread of rumors, the dynamics of drug addiction in populations (e.g., opioid epidemic in the USA), the dynamics of voters, and even sales dynamics can be described with the help of epidemiological models. Accordingly, the topics of interest for this Special Issue include, but are not limited to, the mathematical description and analysis of epidemiological models for:

  • Infectious diseases (SIR model, etc.);
  • Virus dynamics (TIV model, etc.);
  • Computer viruses;
  • Rumor dynamics (Daley-Kendall model, etc.);
  • Racism dynamics and belief dynamics;
  • Drug epidemics (SUU White-Comiskey model, etc.);
  • Voter dynamics;
  • Sales dynamics and innovation diffusion (Bass model, etc.);
  • Viral marketing dynamics (UBI model, etc.).

As such, this Special Issue aims to bridge the gap from classical to interdisciplinary applications of mathematical epidemiological models. It offers a platform for researchers from diverse fields to share their work under a common theme—a platform that is likely to produce cross-disciplinary insights.

Dr. Till D. Frank
Guest Editor

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

  • mathematical epidemiology
  • infectious diseases
  • interdisciplinary applications
  • computer viruses
  • rumor dynamics
  • racism dynamics
  • drug epidemics
  • voter dynamics
  • sales dynamics
  • viral marketing dynamics

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Published Papers (2 papers)

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15 pages, 1447 KiB  
Article
The Waxing and Waning of Fear Influence the Control of Vector-Borne Diseases
by Jing Jiao
Mathematics 2025, 13(5), 879; https://doi.org/10.3390/math13050879 - 6 Mar 2025
Viewed by 464
Abstract
One major challenge in preventing infectious diseases comes from human control behaviors. In the context of vector-borne diseases (VBDs), I explored how the waxing and waning of a human psychological emotion—fear—can generate diverse control actions, which, in turn, influence disease dynamics. Fear may [...] Read more.
One major challenge in preventing infectious diseases comes from human control behaviors. In the context of vector-borne diseases (VBDs), I explored how the waxing and waning of a human psychological emotion—fear—can generate diverse control actions, which, in turn, influence disease dynamics. Fear may diminish over time after being triggered but can also be reinforced when new triggers emerge. By integrating fear dynamics into a generic Ross–MacDonald model tailored for the Zika virus, I found that an increase in initial fear can enhance control efforts, thereby reducing the number of infected individuals and deaths. Once initial fear becomes strong enough to deplete the mosquito population, any further increase in fear no longer impacts disease dynamics. When initial fear is at an intermediate level, the increase in disease caused by greater decay in fear can be counterbalanced by increasing the frequency of fear triggers. Interestingly, when the control period is short and initial fear is at an intermediate level, increasing the frequency of fear reinforcement can lead to a “hydra effect”, which increases disease transmission. These findings help explain variations in human control efforts and provide insights for developing more effective disease control strategies that account for the fear dynamics of local communities. This work also contributes to advancing the theory at the intersection of human behavior, disease ecology, and epidemiology. Full article
(This article belongs to the Special Issue Mathematical Epidemiological Models: Classical and Interdisciplinary Applications)
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23 pages, 400 KiB  
Article
Qualitative Analysis of a COVID-19 Mathematical Model with a Discrete Time Delay
by Abraham J. Arenas, Gilberto González-Parra and Miguel Saenz Saenz
Mathematics 2025, 13(1), 120; https://doi.org/10.3390/math13010120 - 31 Dec 2024
Viewed by 706
Abstract
The aim of this paper is to investigate the qualitative behavior of a mathematical model of the COVID-19 pandemic. The constructed SAIRS-type mathematical model is based on nonlinear delay differential equations. The discrete-time delay is introduced in the model in order to take [...] Read more.
The aim of this paper is to investigate the qualitative behavior of a mathematical model of the COVID-19 pandemic. The constructed SAIRS-type mathematical model is based on nonlinear delay differential equations. The discrete-time delay is introduced in the model in order to take into account the latent stage where the individuals already have the virus but cannot yet infect others. This aspect is a crucial part of this work since other models assume exponential transition for this stage, which can be unrealistic. We study the qualitative dynamics of the model by performing global and local stability analysis. We compute the basic reproduction number R0d, which depends on the time delay and determines the stability of the two steady states. We also compare the qualitative dynamics of the delayed model with the model without time delay. For global stability, we design two suitable Lyapunov functions that show that under some scenarios the disease persists whenever R0d>1. Otherwise, the solution approaches the disease-free equilibrium point. We present a few numerical examples that support the theoretical analysis and the methodology. Finally, a discussion about the main results and future directions of research is presented. Full article
(This article belongs to the Special Issue Mathematical Epidemiological Models: Classical and Interdisciplinary Applications)
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