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Mathematics
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Mathematical Biology and Its Applications to Disease Modeling
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Mathematical Biology and Its Applications to Disease Modeling

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

Deadline for manuscript submissions: closed (30 September 2024) | Viewed by 3068

Special Issue Editor

Dr. Chidozie Williams Chukwu

E-Mail Website
Guest Editor
Department of Mathematics, Wake Forest University, Winston-Salem, NC 27109, USA
Interests: mathematical modeling; applied mathematics; data analysis; multiscale modeling; optimal control

Special Issue Information

Dear Colleagues,

In recent years, there has been a surge of interest and significant progress in the application of mathematical methodologies to unravel the complexities inherent in biological systems. Mathematical modeling, particularly within the realms of within-host dynamics, differential equations, biomathematics, population dynamics, mathematical epidemiology, optimal control in biological systems, multiscale modeling, data analysis applied to biological systems, and machine learning applied to health, has played a pivotal role in enhancing our understanding of these intricate systems.

To further catalyze advancements in the field, we invite submissions of high-quality research papers for a Special Issue dedicated to the exploration of mathematical modeling and analysis in biological systems. We encourage contributions that focus on, but are not limited to, the key areas listed below. Our objective is to create a collaborative platform for knowledge exchange, fostering interdisciplinary dialogues that will propel the detection as well as control of the spread of infectious and non-infectious diseases.

We look forward to your valuable contributions and the collective exploration of the exciting frontiers where mathematics intersects with the intricate dynamics of biological systems. Researchers from diverse disciplines, including mathematics, biology, physics, and computer science, are invited to submit papers on their latest findings, innovative techniques, and applications of mathematical tools to address pivotal questions applied to disease modeling.

Dr. Chidozie Williams Chukwu
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
  • within-host modeling
  • population dynamics
  • differential equations
  • multiscale modeling
  • mathematical epidemiology
  • optimal control theory
  • data analysis of biological systems
  • machine learning applied to health

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Published Papers (2 papers)

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Research

31 pages, 480 KiB  
Article
Analysis of a Mathematical Model of Zoonotic Visceral Leishmaniasis (ZVL) Disease
by Goni Umar Modu, Suphawat Asawasamrit, Abdulfatai Atte Momoh, Mathew Remilekun Odekunle, Ahmed Idris and Jessada Tariboon
Mathematics 2024, 12(22), 3574; https://doi.org/10.3390/math12223574 - 15 Nov 2024
Viewed by 1023
Abstract
This research paper attempts to describe the transmission dynamic of zoonotic visceral leishmaniasis with the aid of a mathematical model by considering the asymptomatic stages in humans and animals. The disease is endemic in several countries. Data used in the research are obtained [...] Read more.
This research paper attempts to describe the transmission dynamic of zoonotic visceral leishmaniasis with the aid of a mathematical model by considering the asymptomatic stages in humans and animals. The disease is endemic in several countries. Data used in the research are obtained from the literature while some are assumed based on the disease dynamic. The consideration of both asymptomatic and the symptomatic infected individuals is incorporated in both humans and animals (reservoir), as well as lines of treatment for the human population. It is found that the model has two fixed points; the VL-free fixed point and the VL-endemic fixed point. Stability analysis of the fixed points shows that the VL-free fixed point is globally asymptotically stable whenever the basic reproduction number is less than one and the VL-endemic fixed point is globally asymptotically stable whenever the basic reproduction number is greater than one. Sensitivity analysis is conducted for the parameters in the basic reproduction number, and the profile of each state variable is also depicted using the data obtained from the literature and those assumed. The transmission probability from infected sandflies to animals, transmission probability from infected animals to sandflies, per capita biting rate of sandflies of animals, and rate of transfer from symptomatic infected animals to the recovered class are among the most sensitive parameters that have the greatest influence on the basic reproduction number. Moreover, the value of the basic reproduction number is obtained to be 0.98951, which may require further study, as the margin between potential disease control and outbreak is thin. Full article
(This article belongs to the Special Issue Mathematical Biology and Its Applications to Disease Modeling)
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26 pages, 3739 KiB  
Article
Dynamics of a Dengue Transmission Model with Multiple Stages and Fluctuations
by Zuwen Wang, Shaojian Cai, Guangmin Chen, Kuicheng Zheng, Fengying Wei, Zhen Jin, Xuerong Mao and Jianfeng Xie
Mathematics 2024, 12(16), 2491; https://doi.org/10.3390/math12162491 - 12 Aug 2024
Cited by 3 | Viewed by 1373
Abstract
A vector–host model of dengue with multiple stages and independent fluctuations is investigated in this paper. Firstly, the existence and uniqueness of the positive solution are shown by contradiction. When the death rates of aquatic mosquitoes, adult mosquitoes, and human beings respectively control [...] Read more.
A vector–host model of dengue with multiple stages and independent fluctuations is investigated in this paper. Firstly, the existence and uniqueness of the positive solution are shown by contradiction. When the death rates of aquatic mosquitoes, adult mosquitoes, and human beings respectively control the intensities of white noises, and if R0s>1, then the persistence in the mean for both infective mosquitoes and infective human beings is derived. When R0s>1 is valid, the existence of stationary distribution is derived through constructing several appropriate Lyapunov functions. If the intensities of white noises are controlled and φ<0 is valid, then the extinction for both infective mosquitoes and infective human beings is obtained by applying the comparison theorem and ergodic theorem. Further, the main findings are verified through numerical simulations by using the positive preserving truncated Euler–Maruyama method (PPTEM). Moreover, several numerical simulations on the infection scale of dengue in Fuzhou City were conducted using surveillance data. The main results indicate that the decrease in the transfer proportion from aquatic mosquitoes to adult mosquitoes reduces the infection scale of infective human beings with dengue virus, and the death rates of aquatic mosquitoes and adult mosquitoes affect the value of the critical threshold R0s. Further, the controls of the death rates of mosquitoes are the effective routes by the decision-makers of the Chinese mainland against the spread of dengue. Full article
(This article belongs to the Special Issue Mathematical Biology and Its Applications to Disease Modeling)
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