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Fractal Fract
Special Issues
Mathematical and Fractional-Order Modeling for Infectious and Non-Infectious Diseases
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Mathematical and Fractional-Order Modeling for Infectious and Non-Infectious Diseases

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "General Mathematics, Analysis".

Deadline for manuscript submissions: closed (30 September 2024) | Viewed by 6997

Special Issue Editors

Dr. Chidozie Williams Chukwu

E-Mail Website
Guest Editor
Department of Mathematical Sciences, DePaul University, Chicago, IL 60614, USA
Interests: mathematical biology; mathematical modeling; optimal control; applied mathematics; data analysis
Dr. Fatmawati Fatmawati

E-Mail Website
Guest Editor
Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya 60115, Indonesia
Interests: optimal control; mathematical modeling; biomathematics; fractional modeling; robust control

Special Issue Information

Dear Colleagues,

Mathematical biology is one of the fastest growing fields because it helps to predict the emergence/resurgence of infectious and non-infectious diseases. Mathematical modeling recently played a crucial role in guiding public health for all governments worldwide, predicting and implementing several laws required for disease prevention and eradication. These predictions and forecasts are achievable using integer and fractional-order modeling, encompassing ordinary or partial differential equations. In particular, fractional derivatives have proven to have a memory effect and hereditary properties, becoming a more reliable tool in predicting the inherent dynamics of real-world systems across many fields of science and engineering applications. The goal of this Special Issue is to contribute to the research on mathematical modeling with rigorous applications to predict results that could help to prevent or control the emergence and resurgence of disease outbreaks in the near future while addressing the current public health issues faced by humans.

Topics of interest include the following:

  • Mathematical modeling;
  • Fractional-order modeling;
  • Agent-based modeling;
  • Optimal control theory;
  • Simulation-based models;
  • Application of network modeling to epidemics;
  • Application of data analysis and artificial intelligence to disease modeling.

Dr. Chidozie Williams Chukwu
Dr. Fatmawati Fatmawati
Guest Editors

Manuscript Submission Information

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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

  • mathematical modeling
  • fractional modeling
  • simulation
  • data analysis
  • disease modeling
  • optimal control

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Published Papers (4 papers)

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Research

24 pages, 873 KiB  
Article
Dynamics and Simulations of Impulsive Population Models Involving Integrated Mosquito Control Strategies and Fractional Derivatives for Dengue Control
by Xianghong Zhang, Hua He, Kaifa Wang and Huaiping Zhu
Fractal Fract. 2024, 8(11), 624; https://doi.org/10.3390/fractalfract8110624 - 24 Oct 2024
Cited by 2 | Viewed by 1057
Abstract
Dengue fever, a mosquito-borne disease caused by the dengue virus, imposes a substantial disease burden on the world. Wolbachia not only manipulates the reproductive processes of mosquitoes through maternal inheritance and cytoplasmic incompatibility (CI) but also restrain the replication of dengue viruses within [...] Read more.
Dengue fever, a mosquito-borne disease caused by the dengue virus, imposes a substantial disease burden on the world. Wolbachia not only manipulates the reproductive processes of mosquitoes through maternal inheritance and cytoplasmic incompatibility (CI) but also restrain the replication of dengue viruses within mosquitoes, becoming a novel approach for biologically combating dengue fever. A combined use of Wolbachia and insecticides may help to prevent pesky mosquito bites and dengue transmission. A model with impulsive spraying insecticide is introduced to examine the spread of Wolbachia in wild mosquitoes. We prove the stability and permanence results of periodic solutions in the system. Partial rank correlation coefficients (PRCCs) can determine the importance of the contribution of input parameters on the value of the outcome variable. PRCCs are used to analyze the influence of input parameters on the threshold condition of the population replacement strategy. We then explore the impacts of mosquito-killing rates and pulse periods on both population eradication and replacement strategies. To further investigate the effects of memory intensity on the two control strategies, we developed a Caputo fractional-order impulsive mosquito population model with integrated control measures. Simulation results show that for the low fecundity scenario of individuals, as memory intensity increases, the mosquito eradication strategy will occur at a slower speed, potentially even leading to the mosquito replacement strategy with low female numbers. For the high fecundity scenario of individuals, with increasing memory intensity, the mosquito replacement strategy will be achieved more quickly, with lower mosquito population amplitudes and overall numbers. It indicates that although memory factors are not conducive to implementing a mosquito eradication strategy, achieving the replacement strategy with a lower mosquito amount is helpful. This work will be advantageous for developing efficient integrated control strategies to curb dengue transmission. Full article
(This article belongs to the Special Issue Mathematical and Fractional-Order Modeling for Infectious and Non-Infectious Diseases)
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29 pages, 3707 KiB  
Article
Investigating a Fractal–Fractional Mathematical Model of the Third Wave of COVID-19 with Vaccination in Saudi Arabia
by Fawaz K. Alalhareth, Mohammed H. Alharbi, Noura Laksaci, Ahmed Boudaoui and Meroua Medjoudja
Fractal Fract. 2024, 8(2), 95; https://doi.org/10.3390/fractalfract8020095 - 2 Feb 2024
Cited by 1 | Viewed by 1846
Abstract
The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is responsible for coronavirus disease-19 (COVID-19). This virus has caused a global pandemic, marked by several mutations leading to multiple waves of infection. This paper proposes a comprehensive and integrative mathematical approach to the third [...] Read more.
The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is responsible for coronavirus disease-19 (COVID-19). This virus has caused a global pandemic, marked by several mutations leading to multiple waves of infection. This paper proposes a comprehensive and integrative mathematical approach to the third wave of COVID-19 (Omicron) in the Kingdom of Saudi Arabia (KSA) for the period between 16 December 2022 and 8 February 2023. It may help to implement a better response in the next waves. For this purpose, in this article, we generate a new mathematical transmission model for coronavirus, particularly during the third wave in the KSA caused by the Omicron variant, factoring in the impact of vaccination. We developed this model using a fractal-fractional derivative approach. It categorizes the total population into six segments: susceptible, vaccinated, exposed, asymptomatic infected, symptomatic infected, and recovered individuals. The conventional least-squares method is used for estimating the model parameters. The Perov fixed point theorem is utilized to demonstrate the solution’s uniqueness and existence. Moreover, we investigate the Ulam–Hyers stability of this fractal–fractional model. Our numerical approach involves a two-step Newton polynomial approximation. We present simulation results that vary according to the fractional orders (γ) and fractal dimensions (θ), providing detailed analysis and discussion. Our graphical analysis shows that the fractal-fractional derivative model offers more biologically realistic results than traditional integer-order and other fractional models. Full article
(This article belongs to the Special Issue Mathematical and Fractional-Order Modeling for Infectious and Non-Infectious Diseases)
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29 pages, 1191 KiB  
Article
Theoretical and Numerical Simulations on the Hepatitis B Virus Model through a Piecewise Fractional Order
by K. A. Aldwoah, Mohammed A. Almalahi and Kamal Shah
Fractal Fract. 2023, 7(12), 844; https://doi.org/10.3390/fractalfract7120844 - 28 Nov 2023
Cited by 21 | Viewed by 1639
Abstract
In this study, we introduce the dynamics of a Hepatitis B virus (HBV) model with the class of asymptomatic carriers and conduct a comprehensive analysis to explore its theoretical aspects and examine the crossover effect within the HBV model. To investigate the crossover [...] Read more.
In this study, we introduce the dynamics of a Hepatitis B virus (HBV) model with the class of asymptomatic carriers and conduct a comprehensive analysis to explore its theoretical aspects and examine the crossover effect within the HBV model. To investigate the crossover behavior of the operators, we divide the study interval into two subintervals. In the first interval, the classical derivative is employed to study the qualitative properties of the proposed system, while in the second interval, we utilize the ABC fractional differential operator. Consequently, the study is initiated using the piecewise Atangana–Baleanu derivative framework for the systems. The HBV model is then analyzed to determine the existence, Hyers–Ulam (HU) stability, and disease-free equilibrium point of the model. Moreover, we showcase the application of an Adams-type predictor-corrector (PC) technique for Atangana–Baleanu derivatives and an extended Adams–Bashforth–Moulton (ABM) method for Caputo derivatives through numerical results. Subsequently, we employ computational methods to numerically solve the models and visually present the obtained outcomes using different fractional-order values. This network is designed to provide more precise information for disease modeling, considering that communities often interact with one another, and the rate of disease spread is influenced by this factor. Full article
(This article belongs to the Special Issue Mathematical and Fractional-Order Modeling for Infectious and Non-Infectious Diseases)
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16 pages, 1382 KiB  
Article
Modeling the Transmission Dynamics of Coronavirus Using Nonstandard Finite Difference Scheme
by Ihsan Ullah Khan, Amjid Hussain, Shuo Li and Ali Shokri
Fractal Fract. 2023, 7(6), 451; https://doi.org/10.3390/fractalfract7060451 - 31 May 2023
Cited by 2 | Viewed by 1480
Abstract
A nonlinear mathematical model of COVID-19 containing asymptomatic as well as symptomatic classes of infected individuals is considered and examined in the current paper. The largest eigenvalue of the next-generation matrix known as the reproductive number is obtained for the model, and serves [...] Read more.
A nonlinear mathematical model of COVID-19 containing asymptomatic as well as symptomatic classes of infected individuals is considered and examined in the current paper. The largest eigenvalue of the next-generation matrix known as the reproductive number is obtained for the model, and serves as an epidemic indicator. To better understand the dynamic behavior of the continuous model, the unconditionally stable nonstandard finite difference (NSFD) scheme is constructed. The aim of developing the NSFD scheme for differential equations is its dynamic reliability, which means discretizing the continuous model that retains important dynamic properties such as positivity of solutions and its convergence to equilibria of the continuous model for all finite step sizes. The Schur–Cohn criterion is used to address the local stability of disease-free and endemic equilibria for the NSFD scheme; however, global stability is determined by using Lyapunov function theory. We perform numerical simulations using various values of some key parameters to see more characteristics of the state variables and to support our theoretical findings. The numerical simulations confirm that the discrete NSFD scheme maintains all the dynamic features of the continuous model. Full article
(This article belongs to the Special Issue Mathematical and Fractional-Order Modeling for Infectious and Non-Infectious Diseases)
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