Theories and Applications of Fractional Order Bio-Mathematics in Medicine and Biology

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Life Science, Biophysics".

Deadline for manuscript submissions: closed (30 September 2022) | Viewed by 5785

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1. Baikal School of BRICS, Irkutsk National Research Technical University, 664074 Irkutsk, Russia
2. Department of Applied Mathematics and Programming, South Ural State University, Lenin Prospect 76, 454080 Chelyabinsk, Russia
Interests: numerical analysis; solving integral equations; solving ODEs and PDEs; solving ill-posed problems; fuzzy mathematics; stochastic arithmetic; CADNA library; CESTAC method; solving biomathematical models; iterative methods; numerical methods
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Russian Academy of Sciences, Melentiev Energy Systems Institute, 664033 Irkutsk, Russia
Interests: nverse problems; integral equations; machine learning; nonlinear systems; bifurcation; numerical methods; energy systems engineering; optimal design and operation; forecasting; energy storage systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We invite you to submit your research papers in the field of bio-mathematics and its applications to this Special Issue, entitled “Theories and Applications of Bio-mathematics in Medicine and Biology”, of the journal Fractal and Fractional. The main goal of this Special Issue is to celebrate the huge increase in and relevance of applications of mathematics to medicine, biology and life sciences. We will focus on both fractional and integer orders of mathematical models. We will focus on both fractional and integer orders of mathematical models.

In this Special Issue, original research articles and reviews are welcome. Topics that are invited for submission include (but are not limited to):

  • Integer and fractional order models
  • All bio-mathematical models such as Covid-19, HIV, Malaria, Diabetes, tuberculosis and other models
  • Theories, convergence analysis, error bound, stability, existence and uniqueness of solution.
  • Fuzzy and crisp multi-dimensional models

We look forward to receiving your contributions.

Prof. Dr. Samad Noeiaghdam
Prof. Dr. Denis Sidorov
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 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. Fractal and Fractional 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 2700 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

  • fractional-order models
  • integer order models
  • bio-mathematical models
  • models of HIV infection
  • models of malaria infection
  • models of COVID-19 infection
  • models of diabetes
  • models of smoking habits
  • models of tuberculosis
  • models of alcohol consumption
  • fuzzy models
  • stability analysis
  • convergence and error analysis
  • data analysis
  • machine learning

Published Papers (3 papers)

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Research

17 pages, 2102 KiB  
Article
Fractional COVID-19 Modeling and Analysis on Successive Optimal Control Policies
by Mohammed Subhi Hadi and Bülent Bilgehan
Fractal Fract. 2022, 6(10), 533; https://doi.org/10.3390/fractalfract6100533 - 20 Sep 2022
Cited by 5 | Viewed by 1266
Abstract
A fractional-order coronavirus disease of 2019 (COVID-19) model is constructed of five compartments in the Caputo-Fabrizio sense. The main aim of the paper is to study the effects of successive optimal control policies in different susceptible classes; a susceptible unaware class where awareness [...] Read more.
A fractional-order coronavirus disease of 2019 (COVID-19) model is constructed of five compartments in the Caputo-Fabrizio sense. The main aim of the paper is to study the effects of successive optimal control policies in different susceptible classes; a susceptible unaware class where awareness control is observed, a susceptible aware class where vaccine control is observed, and a susceptible vaccinated class where optimal vaccination control is observed. These control policies are considered awareness and actions toward vaccination and non-pharmaceuticals to control infection. Equilibrium points are calculated, which subsequently leads to the computation of the basic reproduction ratio. The existence and uniqueness properties of the model are established. The optimal control problem is constructed and subsequently analyzed. Numerical simulations are carried out and the significance of the fractional-order from the biological point of view is established. The results showed that applying various control functions will lead to a decrease in the infected population, and it is evident that introducing the three control measures together causes a drastic decrease in the infected population. Full article
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15 pages, 405 KiB  
Article
A New Incommensurate Fractional-Order Discrete COVID-19 Model with Vaccinated Individuals Compartment
by Amer Dababneh, Noureddine Djenina, Adel Ouannas, Giuseppe Grassi, Iqbal M. Batiha and Iqbal H. Jebril
Fractal Fract. 2022, 6(8), 456; https://doi.org/10.3390/fractalfract6080456 - 21 Aug 2022
Cited by 16 | Viewed by 1425
Abstract
Fractional-order systems have proved to be accurate in describing the spread of the COVID-19 pandemic by virtue of their capability to include the memory effects into the system dynamics. This manuscript presents a novel fractional discrete-time COVID-19 model that includes the number of [...] Read more.
Fractional-order systems have proved to be accurate in describing the spread of the COVID-19 pandemic by virtue of their capability to include the memory effects into the system dynamics. This manuscript presents a novel fractional discrete-time COVID-19 model that includes the number of vaccinated individuals as an additional state variable in the system equations. The paper shows that the proposed compartment model, described by difference equations, has two fixed points, i.e., a disease-free fixed point and an epidemic fixed point. A new theorem is proven which highlights that the pandemic disappears when an inequality involving the percentage of the population in quarantine is satisfied. Finally, numerical simulations are carried out to show that the proposed incommensurate fractional-order model is effective in describing the spread of the COVID-19 pandemic. Full article
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21 pages, 770 KiB  
Article
On the Modeling of COVID-19 Transmission Dynamics with Two Strains: Insight through Caputo Fractional Derivative
by Fatmawati, Endang Yuliani, Cicik Alfiniyah, Maureen L. Juga and Chidozie W. Chukwu
Fractal Fract. 2022, 6(7), 346; https://doi.org/10.3390/fractalfract6070346 - 21 Jun 2022
Cited by 15 | Viewed by 1949
Abstract
The infection dynamics of COVID-19 is difficult to contain due to the mutation nature of the SARS-CoV-2 virus. This has been a public health concern globally with the impact of the pandemic on the world’s economy and mode of living. In the present [...] Read more.
The infection dynamics of COVID-19 is difficult to contain due to the mutation nature of the SARS-CoV-2 virus. This has been a public health concern globally with the impact of the pandemic on the world’s economy and mode of living. In the present work, we formulate and examine a fractional model of COVID-19 considering the two variants of concern on the disease transmission pathways, namely SARS-CoV-2 and D614G on our model formulation. The existence and uniqueness of our model solutions were analyzed using the fixed point theory. Mathematical analyses were presented, and the model’s basic reproduction numbers R01 and R02 were determined. The model has three equilibria: the disease-free equilibrium, that endemic for strain 1, and that endemic for strain 2. The locally asymptotic stability of the equilibria was established based on the R01 and R02 values. Caputo fractional operator was used to simulate the model to study the dynamics of the model solution. Results from numerical simulations envisaged that an increase in the transmission parameters of strain 1 leads to an increase in the number of infected individuals. On the other hand, an increase in the strain 2 transmission rate gives rise to more infection. Furthermore, it was established that there is an increased number of infections with a negative impact of strain 1 on strain 2 dynamics and vice versa. Full article
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