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Mathematics
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Mathematical Modeling of Disease Dynamics
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Mathematical Modeling of Disease Dynamics

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

Deadline for manuscript submissions: closed (28 February 2025) | Viewed by 3258

Special Issue Editor

Prof. Dr. Glenn Ledder

E-Mail Website
Guest Editor
Department of Mathematics, University of Nebraska–Lincoln, Lincoln, NE 68588, USA
Interests: mathematical modeling; epidemiology; ecology; life history theory; tree physiology

Special Issue Information

Dear Colleagues,

This Special Issue is devoted to mathematical modeling in epidemiology, immunology and immuno-epidemiology, where the host species may be humans, other animals or plants. Papers will focus primarily on modeling questions; that is, it is expected that there will be thoughtful and reflective consideration of appropriate assumptions and conclusions. Papers devoted primarily to data analysis or mathematical methods are outside the scope of this issue.

Prof. Dr. Glenn Ledder
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 biology
  • epidemiology
  • immunology
  • immuno-epidemiology
  • dynamical systems

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Published Papers (3 papers)

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Research

17 pages, 5491 KiB  
Article
Dynamics of the Diphtheria Epidemic in Nigeria: Insights from the Kano State Outbreak Data
by Sani Musa, Salisu Usaini, Idris Ahmed, Chanakarn Kiataramkul and Jessada Tariboon
Mathematics 2025, 13(7), 1189; https://doi.org/10.3390/math13071189 - 4 Apr 2025
Viewed by 352
Abstract
Diphtheria is a severely infectious and deadly bacterial disease with Corynebacterium diphtheriae as the causative agent. Since the COVID-19 pandemic, contagious diseases such as diphtheria have re-emerged due to disruptions in routine childhood immunization programs worldwide. Nigeria is witnessing a significant increase in [...] Read more.
Diphtheria is a severely infectious and deadly bacterial disease with Corynebacterium diphtheriae as the causative agent. Since the COVID-19 pandemic, contagious diseases such as diphtheria have re-emerged due to disruptions in routine childhood immunization programs worldwide. Nigeria is witnessing a significant increase in diphtheria outbreaks likely due to an inadequate health care system and insufficient public enlightenment campaign. This paper presents a mathematical epidemic diphtheria model in Nigeria, which includes a public enlightenment campaign to assess its positive impact on the prevalence of the disease. The mathematical analysis of the model reveals two equilibrium points: the diphtheria infection-free equilibrium and the endemic equilibrium. These equilibrium points are shown to be stable globally asymptotically if Rc<1 and Rc>1, respectively. The model was fit using the confirmed diphtheria cases data of Kano State from January to December 2023. Sensitivity analysis indicates that the transmission rate and recovery rate of asymptomatic peopleare crucial parameters to be considered in developing effective strategies for diphtheria control and prevention. This analysis also reveals that the implementation of a high-level public enlightenment campaign and its high efficacy effectively reduce the prevalence of diphtheria. Finally, numerical simulations show that combining the public enlightenment campaign and isolating infected individuals is the best strategy to contain the spread of diphtheria. Full article
(This article belongs to the Special Issue Mathematical Modeling of Disease Dynamics)
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21 pages, 1870 KiB  
Article
Modeling the Impact of Human Awareness and Insecticide Use on Malaria Control: A Fractional-Order Approach
by Mlyashimbi Helikumi, Thobias Bisaga, Kimulu Ancent Makau and Adquate Mhlanga
Mathematics 2024, 12(22), 3607; https://doi.org/10.3390/math12223607 - 19 Nov 2024
Viewed by 823
Abstract
In this research work, we developed a fractional-order model for the transmission dynamics of malaria, incorporating two control strategies: health education campaigns and the use of insecticides. The theoretical analysis of the model is presented, including the computation of disease-free equilibrium and basic [...] Read more.
In this research work, we developed a fractional-order model for the transmission dynamics of malaria, incorporating two control strategies: health education campaigns and the use of insecticides. The theoretical analysis of the model is presented, including the computation of disease-free equilibrium and basic reproduction number. We analyzed the stability of the proposed model using a well-formulated Lyapunov function. Furthermore, model parameter estimation was carried out using real data from malaria cases reported in Zimbabwe. We found that the fractional-order model provided a better fit to the real data compared to the classical integer-order model. Sensitivity analysis of the basic reproduction number was performed using computed partial rank correlation coefficients to assess the effect of each parameter on malaria transmission. Additionally, we conducted numerical simulations to evaluate the impact of memory effects on the spread of malaria. The simulation results indicated that the order of derivatives significantly influences the dynamics of malaria transmission. Moreover, we simulated the model to assess the effectiveness of the proposed control strategies. Overall, the interventions were found to have the potential to significantly reduce the spread of malaria within the population. Full article
(This article belongs to the Special Issue Mathematical Modeling of Disease Dynamics)
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30 pages, 1038 KiB  
Article
Mathematical Modeling and Transmission Dynamics Analysis of the African Swine Fever Virus in Benin
by Sèna Yannick Ayihou, Têlé Jonas Doumatè, Cedric Hameni Nkwayep, Samuel Bowong Tsakou and Romain Glèlè Kakai
Mathematics 2024, 12(11), 1749; https://doi.org/10.3390/math12111749 - 4 Jun 2024
Viewed by 1575
Abstract
African swine fever (ASF) is endemic in many African countries, and its control is challenging because no vaccine or treatment is available to date. Nowadays, mathematical modeling is a key tool in infectious disease studies, complementing traditional biological investigations. In this study, we [...] Read more.
African swine fever (ASF) is endemic in many African countries, and its control is challenging because no vaccine or treatment is available to date. Nowadays, mathematical modeling is a key tool in infectious disease studies, complementing traditional biological investigations. In this study, we propose and analyze a mathematical model for the transmission dynamics of African swine fever (ASF) in Benin that considers the free-living virus in the environment. We provide the theoretical results of the model. The study of the model is conducted by first proving that the model is well posed by showing the positivity and the boundedness of solutions as well as the existence and uniqueness of the solution. We compute the control reproduction number Rc as well as the basic reproduction number R0, which helps to analyze the extinction or the persistence of the disease in the pig population. We provide the global attractivity of the disease-free equilibrium and the endemic equilibrium and study their stabilities. After, we estimate some unknown parameters from the proposed model, and the sensitivity analysis is carried out to determine the parameters that influence the control reproduction number. Finally, through numerical simulations, in the current situation, we find that R0=2.78, which implies that the disease will not die out without any control measures and Rc=1.55 showing that the eradication of the disease highly depends on the control measures taken to reduce disease transmission. Full article
(This article belongs to the Special Issue Mathematical Modeling of Disease Dynamics)
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