Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.0
2.3
Journals
Mathematics
Special Issues
Dynamics and Differential Equations in Mathematical Biology
share announcement

Dynamics and Differential Equations in Mathematical Biology

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

Deadline for manuscript submissions: closed (31 January 2025) | Viewed by 4719

Special Issue Editor

Dr. Gonzalo Robledo

E-Mail Website
Guest Editor
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Las Palmeras 3425, Nuñoa, Santiago, Chile
Interests: nonautonomous ODE; dichotomies; chemostat equations

Special Issue Information

Dear Colleagues,

The first half of the 20th century can be seen as a golden age for the use of differential equations in the modeling of phenomena arising from the life sciences. This period gathers significant milestones: the rediscovering of the Verhulst logistic equation by Pearl, the predator–prey equations introduced by Lotka and Volterra, the Mosquito’s theorem of Ross, the SIR-SIS epidemiological models introduced by Kermack and McKendrick, the chemostat equations proposed by Slizard and Novick,  the Nicholson’s Blowflies equation, the action potential in neurons described by the FitzHugh–Nagumo and Hodgkin–Huxley models, etc. These models describe a long and well-known history of achievements.

At the same time, the research on the qualitative properties of the solutions of differential equations biologically oriented has stimulated the development of new mathematical concepts and theories, e.g, the notion of uniform persistence and the theory of monotone dynamical systems (population dynamics) or the theory of indirect effects in trophic chains (ecology). Some ideas in chaos theory were suggested using models inspired in biology. In addition, several conjectures (solved and unsolved) of mathematical interest arise from equations describing a biological phenomenon, such as the Wright conjecture, for example.

This Special Issue focuses on the virtuous and endless encounters among modeling of natural phenomena, the theoretical questions arising from these models and the development of new concepts and theories.

Contributions are invited from those working in the mathematical modeling of biological phenomena using differential equations (partial, ordinary, delay or impulsive) and those who are interested in the development of the qualitative theory inspired by biologically oriented models.

We look forward to receiving your submissions.

Dr. Gonzalo Robledo
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

  • population dynamics
  • mathematical epidemiology
  • uniform persistence
  • bioprocesses
  • optimal control applied to life sciences

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

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

Published Papers (3 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

26 pages, 20364 KiB  
Article
Seasonal Mathematical Model of Salmonellosis Transmission and the Role of Contaminated Environments and Food Products
by Mohammed H. Alharbi, Fawaz K. Alalhareth and Mahmoud A. Ibrahim
Mathematics 2025, 13(2), 322; https://doi.org/10.3390/math13020322 - 20 Jan 2025
Viewed by 562
Abstract
Salmonellosis continues to be a global public health priority in which humans, livestock, and the contaminated environment interact with food to create complex interactions. Here, a new non-autonomous model is proposed to capture seasonal dynamics of Salmonella typhimurium transmission with key compartments that [...] Read more.
Salmonellosis continues to be a global public health priority in which humans, livestock, and the contaminated environment interact with food to create complex interactions. Here, a new non-autonomous model is proposed to capture seasonal dynamics of Salmonella typhimurium transmission with key compartments that include humans, cattle, and bacteria in environmental and food sources. The model explores how bacterial growth, shedding, and ingestion rates, along with contamination pathways, determine disease dynamics. Some analytical derivations of the basic reproduction number (R0) and threshold conditions for disease persistence or extinction are derived by using the spectral radius of a linear operator associated with the monodromy matrix. Parameter estimation for the model was accomplished with the aid of Latin hypercube sampling and least squares methods on Salmonella outbreak data from Saudi Arabia ranging from 2018 to 2021. The model was able to conduct an analysis based on the estimated 0.606 value of R0, and this meant that the model was able to fit reasonably well for both the cumulative and the new individual case data, which in turn, suggests the disease is curable. Predictions indicate a gradual decline in the number of new cases, with stabilization anticipated at approximately 40,000 cumulative cases. Further simulations examined the dynamics of disease extinction and persistence based on R0. When R0 is less than 1, the disease-free equilibrium is stable, resulting in the extinction of the disease. Conversely, when R0 exceeds 1, the disease persists, exhibiting endemic characteristics with recurrent outbreaks. Sensitivity analysis identified several parameters as having a significant impact on the model’s outcomes, specifically mortality and infection rates, along with decay rates. These findings highlight the critical importance of precise parameter estimation in understanding and controlling the transmission dynamics of Salmonella. Sensitivity indices and contour plots were employed to assess the impact of various parameters on the basic reproduction number and provide insights into the factors most influencing disease transmission. Full article
(This article belongs to the Special Issue Dynamics and Differential Equations in Mathematical Biology)
►▼ Show Figures

Figure 1

19 pages, 964 KiB  
Article
Bifurcation Analysis in a Coffee Berry-Borer-and-Ants Prey–Predator Model
by Carlos Andrés Trujillo-Salazar, Gerard Olivar-Tost and Deissy Milena Sotelo-Castelblanco
Mathematics 2024, 12(11), 1670; https://doi.org/10.3390/math12111670 - 27 May 2024
Viewed by 913
Abstract
One of the most important agricultural activities worldwide, coffee cultivation, is severely affected by the Coffee Berry Borer (CBB), Hypothenemus hampei, considered the primary coffee pest. The CBB is a tiny beetle that diminishes the quantity and quality of coffee beans by [...] Read more.
One of the most important agricultural activities worldwide, coffee cultivation, is severely affected by the Coffee Berry Borer (CBB), Hypothenemus hampei, considered the primary coffee pest. The CBB is a tiny beetle that diminishes the quantity and quality of coffee beans by penetrating them to feed on the endosperm and deposit its eggs, continuing its life cycle. One strategy to combat CBBs is using biological control agents, such as certain species of ants. Here, a mathematical model (consisting of a system of nonlinear ordinary differential equations) is formulated to describe the prey–predator interaction between CBBs and an unspecified species of ants. From this mathematical perspective, the model allows us to determine conditions for the existence and stability of extinction, persistence or co-existence equilibria. Transitions among those equilibrium states are investigated through the maximum per capita consumption rate of the predator as a bifurcation parameter, allowing us to determine the existence of transcritical and saddle-node bifurcations. Phase portraits of the system are presented for different values of bifurcation parameter, to illustrate stability outcomes and the occurrence of bifurcations. It is concluded that an increase in bifurcation parameters significantly reduces the CBB population, suggesting that ant predation is an effective control strategy, at least theoretically. Full article
(This article belongs to the Special Issue Dynamics and Differential Equations in Mathematical Biology)
►▼ Show Figures

Figure 1

26 pages, 2070 KiB  
Article
Modeling Typhoid Fever Dynamics: Stability Analysis and Periodic Solutions in Epidemic Model with Partial Susceptibility
by Fawaz K. Alalhareth, Mohammed H. Alharbi and Mahmoud A. Ibrahim
Mathematics 2023, 11(17), 3713; https://doi.org/10.3390/math11173713 - 29 Aug 2023
Cited by 3 | Viewed by 2349
Abstract
Mathematical models play a crucial role in predicting disease dynamics and estimating key quantities. Non-autonomous models offer the advantage of capturing temporal variations and changes in the system. In this study, we analyzed the transmission of typhoid fever in a population using a [...] Read more.
Mathematical models play a crucial role in predicting disease dynamics and estimating key quantities. Non-autonomous models offer the advantage of capturing temporal variations and changes in the system. In this study, we analyzed the transmission of typhoid fever in a population using a compartmental model that accounted for dynamic changes occurring periodically in the environment. First, we determined the basic reproduction number, R0, for the periodic model and derived the time-average reproduction rate, [R0], for the non-autonomous model as well as the basic reproduction number, R0A, for the autonomous model. We conducted an analysis to examine the global stability of the disease-free solution and endemic periodic solutions. Our findings demonstrated that when R0<1, the disease-free solution was globally asymptotically stable, indicating the extinction of typhoid fever. Conversely, when R0>1, the disease became endemic in the population, confirming the existence of positive periodic solutions. We also presented numerical simulations that supported these theoretical results. Furthermore, we conducted a sensitivity analysis of R0A, [R0] and the infected compartments, aiming to assess the impact of model parameters on these quantities. Our results showed that the human-to-human infection rate has a significant impact on the reproduction number, while the environment-to-human infection rate and the bacteria excretion rate affect long-cycle infections. Moreover, we examined the effects of parameter modifications and how they impact the implementing of efficient control strategies to combat TyF. Although our model is limited by the lack of precise parameter values, the qualitative results remain consistent even with alternative parameter settings. Full article
(This article belongs to the Special Issue Dynamics and Differential Equations in Mathematical Biology)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-3
Back to TopTop