Special Issue "Modelling and Analysis in Biomathematics"

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

Deadline for manuscript submissions: 31 December 2020.

Special Issue Editors

Prof. Dr. M. Victoria Otero-Espinar
Website
Guest Editor
Departamento de Estatística, Análise Matemática e Optimización, Instituto de Matemáticas, Universidade de Santiago de Compostela, Galicia, Spain
Interests: differential and difference equations; dynamical systems; time scales; nonlinear analysis; biomatemathical models
Prof. Dr. Àngel Calsina
Website
Guest Editor
Departament de Matemàtiques, Universitat Autònoma de Barcelona, Spain
Interests: partial differential equations; mathematical biology

Special Issue Information

Dear Colleagues,

There are many current scientific challenges in the field of biosciences. Mathematical models are a powerful tool to advance scientific research in these fields.

The purpose of this Special Issue is to gather the latest contributions with the recent advances in the theory and applications of mathematical models arising in the broad fields of cell and developmental biology, systems biology, ecology, epidemiology, population dynamics, medicine, pharmacy, therapy and vaccination strategies, biotechnology, bioengineering, environmental science, etc.

We invite the authors to submit original research articles and high-quality review articles in biomathematics obtained from development, analysis, and simulation of mathematical models based on ordinary differential equations, difference equations, dynamical systems, partial differential equations, integrodifferential equations, impulsive differential equations, fractional order differential equations, variational methods, optimal control, Markov models, and others.

Prof. Dr. M. Victoria Otero-Espinar
Prof. Dr. Àngel Calsina
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 papers will be 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 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 1200 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

  • Biomathematics
  • Mathematical models in biosciences
  • Mathematical ecology and epidemiology
  • Differential and difference equations
  • Partial differential equations
  • Integro-differential equations
  • Fractional differential equations
  • Variational methods
  • Dynamical systems
  • Computational and numerical methods

Published Papers (2 papers)

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Research

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Open AccessArticle
On the Zero-Hopf Bifurcation of the Lotka–Volterra Systems in R3
Mathematics 2020, 8(7), 1137; https://doi.org/10.3390/math8071137 (registering DOI) - 12 Jul 2020
Abstract
Here we study 3-dimensional Lotka–Volterra systems. It is known that some of these differential systems can have at least four periodic orbits bifurcating from one of their equilibrium points. Here we prove that there are some of these differential systems exhibiting at least [...] Read more.
Here we study 3-dimensional Lotka–Volterra systems. It is known that some of these differential systems can have at least four periodic orbits bifurcating from one of their equilibrium points. Here we prove that there are some of these differential systems exhibiting at least six periodic orbits bifurcating from one of their equilibrium points. We remark that these systems with such six periodic orbits are non-competitive Lotka–Volterra systems. The proof is done using the algorithm that we provide for computing the periodic solutions that bifurcate from a zero-Hopf equilibrium based in the averaging theory of third order. This algorithm can be applied to any differential system having a zero-Hopf equilibrium. Full article
(This article belongs to the Special Issue Modelling and Analysis in Biomathematics)

Review

Jump to: Research

Open AccessReview
A Review on a Class of Second Order Nonlinear Singular BVPs
Mathematics 2020, 8(7), 1045; https://doi.org/10.3390/math8071045 (registering DOI) - 28 Jun 2020
Abstract
Several real-life problems are modeled by nonlinear singular differential equations. In this article, we study a class of nonlinear singular differential equations, explore its various aspects, and provide a detailed literature survey. Nonlinear singular differential equations are not easy to solve and their [...] Read more.
Several real-life problems are modeled by nonlinear singular differential equations. In this article, we study a class of nonlinear singular differential equations, explore its various aspects, and provide a detailed literature survey. Nonlinear singular differential equations are not easy to solve and their exact solution does not exist in most cases. Since the exact solution does not exist, it is natural to look for the existence of the analytical solution and numerical solution. In this survey, we focus on both aspects of nonlinear singular boundary value problems (SBVPs) and cover different analytical and numerical techniques which are developed to deal with a class of nonlinear singular differential equations ( p ( x ) y ( x ) ) = q ( x ) f ( x , y , p y ) for x ( 0 , b ) , subject to suitable initial and boundary conditions. The monotone iterative technique has also been briefed as it gained a lot of attention during the last two decades and it has been merged with most of the other existing techniques. A list of SBVPs is also provided which will be of great help to researchers working in this area. Full article
(This article belongs to the Special Issue Modelling and Analysis in Biomathematics)

Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: On the zero--Hopf bifurcation of the Lotka--Volterra systems in R^3
Authors: Maoan Han1, Jaume Llibre 2,* and Yun Tian 3
Affiliation: 1. Department of Mathematics, Shanghai Normal University, 100 Guilin Road, Xuhui District, 200234, Shanghai, China; [email protected] 2. Departament de Matemàtiques, Universitat Autònoma de Barceona, 08193 Bellaterra, Barcelona, Catalonia, Spain; [email protected] 3. Department of Mathematics, Shanghai Normal University, 100 Guilin Road, Xuhui District, 200234, Shanghai, China; [email protected]
Abstract: Here we study 3-dimensional Lotka-Volterra systems. It is known that some of these differential systems can have at least four periodic orbits bifurcating from one of their equilibrium points. Here we prove that there are some of these differential systems exhibiting at least six periodic orbits bifurcating from one of their equilibrium points. We remark that these systems with such six periodic orbits are non-competitive Lotka-Volterra systems. The proof is done using the algorithm that we provide for computing the periodic solutions that bifurcate from a zero-Hopf equilibrium based in the averaging theory of third order. This algorithm can be applied to any differential system having a zero-Hopf equilibrium.

Title: A Review on a Class of Second Order Nonlinear Singular BVPs
Authors: Amit Verma 1, Biswajit Pandit 1, Lajja Verma 2 and Ravi Agarwal 3,*
Affiliation: 1. Indian Institute of Technology Patna; [email protected] (A.V.); [email protected] (B.P.) 2. Netaji Subhas Institute of Technology Patna; [email protected] 3. Texas A&M University Kingsville; [email protected]
Abstract: In this article we provide a bucket of research works and present the importance of nonlinear singular two point BVPs. Singular BVPs are not easy to handle and exact solution does not exist in most cases. Since exact solutions do not exist researchers started working on the numerical solutions as well as also explored conditions under which there exist a solution, and if it exits, is it unique? Here, we focus on both aspects of SBVPs and cover different analytical and numerical techniques which are used to deal with a class of singular BVPs $-(p(x)y'(x))'=q(x)f(x,y,py')$ for $x\in (0,b)$, subject to suitable initial and boundary conditions. Monotone iterative technique has also been briefed as it gained lot of attention during last two decades and it has been merged with most of the other existing techniques. A list of SBVPs are also provided which will be of great help to people working in this area.

Title: Parameter Quantification to Predict Tissue Dynamics using Vertex Model
Authors: Pilar Guerrero 1,* and Ruben Perez-Carrasco 2
Affiliation: 1 Grupo Interdisciplinar de Sistemas Complejos, Departamento de Matemáticas, Universidad Carlos III; [email protected] 2 Department of Life Sciences - Imperial College London 2; [email protected]
Abstract: To understand the dynamics and coordination of biological tissues, the use of numerical implementation is increasing. Computational modelling is a challenge. We will study in particular the vertex models which are cell-based models used to study epithelial tissue. We will analyse the dynamics of the model according to numerical parameters, observing the behaviour of the tissue and the regrouping properties. We will discuss the relaxation times required for the correct use of these models.

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