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Axioms
Special Issues
Applied Mathematics in Biology and Medicine
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Applied Mathematics in Biology and Medicine

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (30 May 2023) | Viewed by 4837

Special Issue Editor

Prof. Dr. Hsing Luh

E-Mail Website
Guest Editor
Department of Mathematical Sciences, National Chengchi University, Taipei City 116, Taiwan
Interests: operations research; mathematical modeling

Special Issue Information

Dear Colleagues,

Mathematical models have been developed with significant mathematical contents addressing topics in medicine and biology. Since the beginning of the COVID-19 pandemic, many mathematical prediction models have also been developed in public health and government administration. Modeling the number of infected individuals is a principal tool in the event of an epidemic.  Meanwhile, studying the natural disease transition of viruses between possible variated states often includes statistics in biology and medicine research. Several medical and biological problems can be formulated into mathematical models, and can be analyzed using sophisticated optimization and computational techniques. Papers that exploit modern developments in applied mathematics are particularly welcome.

Prof. Dr. Hsing Luh
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. Axioms is an international peer-reviewed open access monthly 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 2400 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

  • survival analysis
  • optimization
  • machine learning
  • neural networks
  • simulation
  • Markov chains
  • SIR models

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Published Papers (3 papers)

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Research

18 pages, 670 KiB  
Article
Limiting Behaviors of Stochastic Spread Models Using Branching Processes
by Jyy-I Hong
Axioms 2023, 12(7), 652; https://doi.org/10.3390/axioms12070652 - 30 Jun 2023
Viewed by 768
Abstract
In this paper, we introduce a spread model using multi-type branching processes to investigate the evolution of the population during a pandemic in which individuals are classified into different types. We study some limiting behaviors of the population including the growth rate of [...] Read more.
In this paper, we introduce a spread model using multi-type branching processes to investigate the evolution of the population during a pandemic in which individuals are classified into different types. We study some limiting behaviors of the population including the growth rate of the population and the spread rate of each type. In particular, the work in this paper focuses on the cases where the offspring mean matrices are non-primitive but can be decomposed into two primitive components, A and B, with maximal eigenvalues ρA and ρB, respectively. It is shown that the growth rate and the spread rate heavily depend on the conditions of these two maximal eigenvalues and are related to the corresponding eigenvectors. In particular, we find the spread rates for the case with ρB>ρA>1 and the case with ρA>ρB>1. In addition, some numerical examples and simulations are also provided to support the theoretical results. Full article
(This article belongs to the Special Issue Applied Mathematics in Biology and Medicine)
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13 pages, 321 KiB  
Article
Proportional Hazard Model and Proportional Odds Model under Dependent Truncated Data
by Jin-Jian Hsieh and Yun-Jhu Chen
Axioms 2022, 11(10), 521; https://doi.org/10.3390/axioms11100521 - 1 Oct 2022
Viewed by 1503
Abstract
Truncation data arise when the interested event time can be observed only if it satisfies a certain condition. Most of the existing approaches analyze this kind of data by assuming the truncated variable is quasi-independent of the interested event time. However, in many [...] Read more.
Truncation data arise when the interested event time can be observed only if it satisfies a certain condition. Most of the existing approaches analyze this kind of data by assuming the truncated variable is quasi-independent of the interested event time. However, in many situations, the quasi-independence assumption may be not suitable. In this article, the authors consider the copulas to relax the quasi-independence assumption. Additionally, the survival function of the interested event time is estimated by a copula-graphic approach. Then, the authors propose two estimation procedures for the proportional hazard (PH) model and the proportional odds (PO) model, which can be applied to the right-truncated data, and the left-truncated and right-censoring data. Subsequently, the performance of the proposed estimation approaches is assessed via simulation studies. Finally, the proposed methodologies are applied to analyze two real datasets (the retirement center dataset and the transfusion-related AIDS dataset). Full article
(This article belongs to the Special Issue Applied Mathematics in Biology and Medicine)
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29 pages, 642 KiB  
Article
A New Family of Lifetime Models: Theoretical Developments with Applications in Biomedical and Environmental Data
by Ibrahim Elbatal, Sadaf Khan, Tassaddaq Hussain, Mohammed Elgarhy, Naif Alotaibi, Hatem E. Semary and Mahmoud M. Abdelwahab
Axioms 2022, 11(8), 361; https://doi.org/10.3390/axioms11080361 - 25 Jul 2022
Cited by 3 | Viewed by 1733
Abstract
With the aim of identifying a probability model that not only correctly describes the stochastic behavior of extreme environmental factors such as excess rain, acid rain pH level, and concentrations of ozone, but also measures concentrations of NO2 and leads deliberations, etc., [...] Read more.
With the aim of identifying a probability model that not only correctly describes the stochastic behavior of extreme environmental factors such as excess rain, acid rain pH level, and concentrations of ozone, but also measures concentrations of NO2 and leads deliberations, etc., for a specific site or multiple site forms as well as for life testing experiments, we introduced a novel class of distributions known as the Sine Burr X−G family. Some exceptional prototypes of this class are proposed. Statistical assets of the presented class, such as density function, complete and incomplete moments, average deviation, and Lorenz and Bonferroni graphs, are proposed. Parameter estimation is made via the likelihood method. Moreover, the application is explained by using four real data sets. We have also illustrated the significance and elasticity of the proposed class in the above-mentioned stochastic phenomenon. Full article
(This article belongs to the Special Issue Applied Mathematics in Biology and Medicine)
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