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Mathematics
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Advances in Mathematical Biology and Applications
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Advances in Mathematical Biology and Applications

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

Deadline for manuscript submissions: 28 February 2025 | Viewed by 4547

Special Issue Editor

Dr. Necibe Tuncer

E-Mail Website
Guest Editor
Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, USA
Interests: mathematical epidemiology; age structured PDE models; immuno-epidemiological models; structural and practical identifiability of nested epidemiological models

Special Issue Information

Dear Colleagues,

In recent years, there has been growing interest many exciting developments in the application of mathematics to understand biological systems. Mathematical modeling has been used to study various aspects of biological systems, including gene regulation, cell signaling, epidemiology, population dynamics, and ecosystem interactions. These models have provided insights into the behavior of biological systems, helping to explain the observed phenomena and predict the outcomes of experiments.

To further advance the field of mathematics in biological systems, we invite papers that explore new mathematical models, develop innovative techniques for analyzing biological data, or apply existing mathematical tools to address important questions in biology.

We welcome papers from a range of disciplines, including mathematics, biology, physics, and computer science, among others. Our goal is to provide a platform for researchers to share their latest findings and insights and to foster collaborations that will lead to new discoveries in this exciting and rapidly evolving field.

Dr. Necibe Tuncer
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 modeling
  • differential equations
  • network analysis
  • systems biology
  • computational biology
  • biomathematics
  • population dynamics
  • epidemiology
  • bioinformatics
  • stochastic processes
  • nonlinear dynamics
  • optimization
  • data analysis

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

Published Papers (6 papers)

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Research

16 pages, 534 KiB  
Article
Analysis Time-Delayed SEIR Model with Survival Rate for COVID-19 Stability and Disease Control
by M. H. Hassan, Tamer El-Azab, Ghada AlNemer, M. A. Sohaly and H. El-Metwally
Mathematics 2024, 12(23), 3697; https://doi.org/10.3390/math12233697 - 26 Nov 2024
Viewed by 126
Abstract
This paper presents a mathematical model to examine the transmission and stability dynamics of the SEIR model for COVID-19. To assess disease progression, the model incorporates a time delay for the time delay and survival rates. Then, we use the Routh–Hurwitz criterion, the [...] Read more.
This paper presents a mathematical model to examine the transmission and stability dynamics of the SEIR model for COVID-19. To assess disease progression, the model incorporates a time delay for the time delay and survival rates. Then, we use the Routh–Hurwitz criterion, the LaSalle stability principle, and Hopf bifurcation analysis to look at disease-free and endemic equilibrium points. We investigate global stability using the Lyapunov function and simulate the model behavior with real COVID-19 data from Indonesia. The results confirm the impact of time delay on disease transmission, mitigation strategies, and population recovery rates, demonstrating that rapid interventions can significantly impact the course of the epidemic. The results indicate that a balance between transmission reduction and vaccination efforts is crucial for achieving long-term stability and controlling disease outbreaks. Finally, we estimate the degree of disease control and look at the rate of disease spread by simulating the genuine data. Full article
(This article belongs to the Special Issue Advances in Mathematical Biology and Applications)
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17 pages, 435 KiB  
Article
Short-Term Predictions of the Trajectory of Mpox in East Asian Countries, 2022–2023: A Comparative Study of Forecasting Approaches
by Aleksandr Shishkin, Amanda Bleichrodt, Ruiyan Luo, Pavel Skums, Gerardo Chowell and Alexander Kirpich
Mathematics 2024, 12(23), 3669; https://doi.org/10.3390/math12233669 - 23 Nov 2024
Viewed by 334
Abstract
The 2022–2023 mpox outbreak exhibited an uneven global distribution. While countries such as the UK, Brazil, and the USA were most heavily affected in 2022, many Asian countries, specifically China, Japan, South Korea, and Thailand, experienced the outbreak later, in 2023, with significantly [...] Read more.
The 2022–2023 mpox outbreak exhibited an uneven global distribution. While countries such as the UK, Brazil, and the USA were most heavily affected in 2022, many Asian countries, specifically China, Japan, South Korea, and Thailand, experienced the outbreak later, in 2023, with significantly fewer reported cases relative to their populations. This variation in timing and scale distinguishes the outbreaks in these Asian countries from those in the first wave. This study evaluates the predictability of mpox outbreaks with smaller case counts in Asian countries using popular epidemic forecasting methods, including the ARIMA, Prophet, GLM, GAM, n-Sub-epidemic, and Sub-epidemic Wave frameworks. Despite the fact that the ARIMA and GAM models performed well for certain countries and prediction windows, their results were generally inconsistent and highly dependent on the country, i.e., the dataset, as well as the prediction interval length. In contrast, n-Sub-epidemic Ensembles demonstrated more reliable and robust performance across different datasets and predictions, indicating the effectiveness of this model on small datasets and its utility in the early stages of future pandemics. Full article
(This article belongs to the Special Issue Advances in Mathematical Biology and Applications)
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20 pages, 2175 KiB  
Article
Validation of a Multi-Strain HIV Within-Host Model with AIDS Clinical Studies
by Necibe Tuncer, Kia Ghods, Vivek Sreejithkumar, Adin Garbowit, Mark Zagha and Maia Martcheva
Mathematics 2024, 12(16), 2583; https://doi.org/10.3390/math12162583 - 21 Aug 2024
Viewed by 757
Abstract
We used a previously introduced HIV within-host model with sensitive and resistant strains and validated it with two data sets. The first data set is from a clinical study that investigated multi-drug treatments and measured the total CD4+ cell count and viral [...] Read more.
We used a previously introduced HIV within-host model with sensitive and resistant strains and validated it with two data sets. The first data set is from a clinical study that investigated multi-drug treatments and measured the total CD4+ cell count and viral load. All nine patients in this data set experienced virologic failure. The second data set includes a unique patient who was treated with a unique drug and for whom both the sensitive and resistant strains were measured as well as the CD4+ cells. We studied the structural identifiability of the model with respect to each data set. With respect to the first data set, the model was structurally identifiable when the viral production rate of the sensitive strain was fixed and distinct from the viral production rate of the resistant strain. With respect to the second data set, the model was always structurally identifiable. We fit the model to the first data set using nonlinear mixed effect modeling in Monolix and estimated the population-level parameters. We inferred that the average time to emergence of a resistant strain is 844 days after treatment starts. We fit the model to the second data set and found out that the all the parameters except the mutation rate were practically identifiable. Full article
(This article belongs to the Special Issue Advances in Mathematical Biology and Applications)
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10 pages, 471 KiB  
Article
Influence of the Effective Reproduction Number on the SIR Model with a Dynamic Transmission Rate
by Fernando Córdova-Lepe, Juan Pablo Gutiérrez-Jara and Gerardo Chowell
Mathematics 2024, 12(12), 1793; https://doi.org/10.3390/math12121793 - 8 Jun 2024
Cited by 1 | Viewed by 684
Abstract
In this paper, we examine the epidemiological model B-SIR, focusing on the dynamic law that governs the transmission rate B. We define this dynamic law by the differential equation B′/B=F⊕−F⊖, where [...] Read more.
In this paper, we examine the epidemiological model B-SIR, focusing on the dynamic law that governs the transmission rate B. We define this dynamic law by the differential equation B′/B=F⊕−F⊖, where F⊖ represents a reaction factor reflecting the stress proportional to the active group’s percentage variation. Conversely, F⊕ is a factor proportional to the deviation of B from its intrinsic value. We introduce the notion of contagion impulse f and explore its role within the model. Specifically, for the case where F⊕=0, we derive an autonomous differential system linking the effective reproductive number with f and subsequently analyze its dynamics. This analysis provides new insights into the model’s behavior and its implications for understanding disease transmission. Full article
(This article belongs to the Special Issue Advances in Mathematical Biology and Applications)
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25 pages, 929 KiB  
Article
Impulsive Effects and Complexity Dynamics in the Anti-Predator Model with IPM Strategies
by Wenjie Qin, Zhengjun Dong and Lidong Huang
Mathematics 2024, 12(7), 1043; https://doi.org/10.3390/math12071043 - 30 Mar 2024
Cited by 1 | Viewed by 816
Abstract
When confronted with the imminent threat of predation, the prey instinctively employ strategies to avoid being consumed. These anti-predator tactics involve individuals acting collectively to intimidate predators and reduce potential harm during an attack. In the present work, we propose a state-dependent feedback [...] Read more.
When confronted with the imminent threat of predation, the prey instinctively employ strategies to avoid being consumed. These anti-predator tactics involve individuals acting collectively to intimidate predators and reduce potential harm during an attack. In the present work, we propose a state-dependent feedback control predator-prey model that incorporates a nonmonotonic functional response, taking into account the anti-predator behavior observed in pest-natural enemy ecosystems within the agricultural context. The qualitative analysis of this model is presented utilizing the principles of impulsive semi-dynamical systems. Firstly, the stability conditions of the equilibria are derived by employing pertinent properties of planar systems. The precise domain of the impulsive set and phase set is determined by considering the phase portrait of the system. Secondly, a Poincaré map is constructed by utilizing the sequence of impulsive points within the phase set. The stability of the order-1 periodic solution at the boundary is subsequently analyzed by an analog of the Poincaré criterion. Additionally, this article presents various threshold conditions that determine both the existence and stability of an order-1 periodic solution. Furthermore, it investigates the existence of order-k (k≥2) periodic solutions. Finally, the article explores the complex dynamics of the model, encompassing multiple bifurcation phenomena and chaos, through computational simulations. Full article
(This article belongs to the Special Issue Advances in Mathematical Biology and Applications)
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19 pages, 784 KiB  
Article
Ultimate Dynamics of the Two-Phenotype Cancer Model: Attracting Sets and Global Cancer Eradication Conditions
by Anatolij N. Kanatnikov and Konstantin E. Starkov
Mathematics 2023, 11(20), 4275; https://doi.org/10.3390/math11204275 - 13 Oct 2023
Viewed by 1068
Abstract
In this paper we consider the ultimate dynamics of one 4D cancer model which was created for studying the immune response to the two-phenotype tumors. Our approach is based on the localization method of compact invariant sets. The existence of a positively invariant [...] Read more.
In this paper we consider the ultimate dynamics of one 4D cancer model which was created for studying the immune response to the two-phenotype tumors. Our approach is based on the localization method of compact invariant sets. The existence of a positively invariant polytope is shown and its size is calculated depending on the parameters of this cancer model. Various convergence conditions to the tumor free equilibrium point were proposed. This property has the biological meaning of global asymptotic tumor eradication (GATE). Further, the case in which local asymptotic tumor eradication (LATE) conditions entail GATE conditions was found. Our theoretical studies of ultimate dynamics are complemented by numerical simulation results. Full article
(This article belongs to the Special Issue Advances in Mathematical Biology and Applications)
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