Article
Materials Science, Multidisciplinary
Samuel Benkimoun, Celestine Atyame, Marion Haramboure, Pascal Degenne, Helene Thebault, Jean-Sebastien Dehecq, Annelise Tran
Summary: This study developed a method to estimate the spatial distribution of the basic reproduction number (R-0) for dengue transmission risk on Reunion Island using a mosquito population dynamics model and differential equations. The results showed strong agreements between predicted R-0 distribution and temporal dynamics with observed epidemiological patterns, highlighting the relevance of this spatialised R-0 for dengue surveillance and control.
RESULTS IN PHYSICS
(2021)
Article
Engineering, Mechanical
Shidong Zhai, Hui Gao, Guoqiang Luo, Junli Tao
Summary: This paper introduces a multigroup COVID-19 model with immunity and discusses how to design control strategies in cases where the basic reproduction number is greater than one. By reducing the number of exposed individuals and increasing those receiving treatment, the disease can be eradicated in some groups.
NONLINEAR DYNAMICS
(2021)
Article
Engineering, Multidisciplinary
Nur 'Izzati Hamdan, Adem Kilicman
Summary: A deterministic mathematical model of dengue transmission considering temperature effects was developed in this study. The model showed oscillatory behavior and a possibility of backward bifurcation. Evaluation of R-0 at different temperatures revealed that the fractional-order model offers stable solutions compared to the integer order model.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Multidisciplinary Sciences
Dongmin Kim, Sang-Ki Lee, Hosmay Lopez, Gregory R. Foltz, Caihong Wen, Robert West, Jason Dunion
Summary: The Atlantic hurricane activity is influenced by multiple climate modes at seasonal-to-interannual scales. Among them, the Atlantic Nino/Nina is the dominant mode of sea surface temperature variability during the hurricane season. The Atlantic Nino enhances African easterly wave activity and increases the likelihood of powerful hurricanes developing near the Cape Verde islands.
NATURE COMMUNICATIONS
(2023)
Article
Engineering, Electrical & Electronic
Daniel Vazquez Pombo, Ha Thi Nguyen, Leila Chebbo, Dominique A. Sorensen
Summary: Reference systems are crucial platforms for evaluating and comparing different methods and technologies in the context of energy transition. The proposed reference system based on Cape Verde islands captures the behavior of modern grids and accommodates diverse technological mix. It is suitable for a range of traditional and modern studies and offers off-the-shelf usage advantages.
IEEE TRANSACTIONS ON SMART GRID
(2022)
Article
Engineering, Multidisciplinary
Sanjoy Basu, R. Prem Kumar, P. K. Santra, G. S. Mahapatra, A. A. Elsadany
Summary: This study presents an optimal control strategy through a mathematical model to analyze the effect of lock-down and treatment controls on the Covid-19 outbreak. The results predict the fate of India's second wave situation and evaluate the effectiveness of the controls in terms of the exposed phase, infective phase, and recovery phase. This model provides insights on the total number of infected and active cases, deaths, and recoveries, as well as the effects of vaccines and treatment controls.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Mathematics, Applied
Xiaoguang Li, Liming Cai, Mohammad Murshed, Jin Wang
Summary: In this paper, a new mathematical model is proposed to study the transmission dynamics of dengue. The model incorporates an age-structured system of differential and integral equations that couple host and mosquito populations, and includes both symptomatic and asymptomatic infections. The basic reproduction number is derived and the local and global stabilities of the disease-free steady state are rigorously analyzed. The existence of endemic steady states and conditions that could lead to a backward bifurcation are also studied. In addition, the weak and strong uniform persistence properties of the system are established.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Interdisciplinary Applications
Xinjie Fu, JinRong Wang
Summary: We developed a complex network-based model for infectious diseases and analyzed its stability. The results show that when considering three control measures including isolation and vaccination, the scale and cost of the disease are minimized.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Engineering, Mechanical
Sayooj Aby Jose, R. Raja, B. Omede, Ravi P. Agarwal, J. Alzabut, J. Cao, V. E. Balas
Summary: In this paper, a deterministic mathematical model for the transmission dynamics of co-infection of Dengue Fever and Zika virus is formulated and analyzed. It is found that each disease undergoes backward bifurcation when the reproduction number of the sub-models is less than one. Simulation of the full model provides a clear visualization of disease transmission, and the numerical solution of the model is provided in detail.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Mayowa M. Ojo, Olumuyiwa James Peter, Emile Franc Doungmo Goufo, Hasan S. Panigoro, Festus Abiodun Oguntolu
Summary: Tuberculosis, an infectious disease caused by bacteria, poses a significant threat to the health of populations, particularly in sub-Saharan African countries. This study investigates the impact of vaccination on the dynamics of tuberculosis, using a mathematical model. Results show that reducing contact with infected individuals and increasing the vaccination rate of susceptible individuals with effective vaccines can alleviate the burden of tuberculosis in the population.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2023)
Article
Computer Science, Interdisciplinary Applications
F. M. M. Pereira, P. H. T. Schimit
Summary: This paper explores the spatial dynamics of dengue fever and analyzes the variations of the basic reproduction number. By simulating the spatial distribution of vector breeding places, the results show that the more spread out these places, the easier the disease spreads. The findings have important implications for the prevention and control of dengue fever.
COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE
(2022)
Article
Mathematics, Interdisciplinary Applications
Xue Yang, Yongmei Su, Liangli Yang, Xinjian Zhuo
Summary: In this paper, a Caputo fractional order HBV humoral and CTL immunity model with more general mass action incidences is established, and the existence and uniqueness of positive solutions are proved. The relationship between five different basic reproductive numbers and their corresponding five equilibria is derived, and the general form of Lyapunov functions for the fractional order model is also derived. The global stability of the five equilibria is analyzed by constructing Lyapunov function, and numerical simulation is conducted to test the theory.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
Tchule Nguiwa, Gabriel Guilsou Kolaye, Mibaile Justin, Djaouda Moussa, Gambo Betchewe, Alidou Mohamadou
Summary: The study investigates a mathematical fractional-order cholera model, deriving the basic reproduction number and stability conditions of equilibrium points, emphasizing the importance of vaccination in controlling the spread of cholera.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Fereshte Gazori, Mahmoud Hesaaraki
Summary: In this paper, a mathematical model of dengue transmission with different subclasses of infected and exposed populations in humans and mosquitoes is considered. The local dengue propagation in small regions is studied by ignoring human movement. The basic reproduction number, R-0, is obtained using the next-generation approach. It is shown that the disease-free equilibrium is globally asymptotically stable when R-0 < 1, and a unique endemic equilibrium emerges and is locally asymptotically stable when R-0 > 1. The minimum speed of traveling wave solutions, c*, is investigated when R-0 > 1, and an approximation of c* for the proposed model is sought. The existence of traveling wave solutions is verified through numerical simulations.
COMPUTATIONAL & APPLIED MATHEMATICS
(2023)
Article
Public, Environmental & Occupational Health
Katsuma Hayashi, Marie Fujimoto, Hiroshi Nishiura
Summary: This study quantitatively assessed the future risk of dengue in Japan using climate change scenarios and found that the risk of transmission may extend to late spring and autumn due to increasing temperatures. The study emphasizes the importance of developing adaptation policies to prevent dengue transmission, such as eliminating mosquito breeding sites and distributing insecticides.
FRONTIERS IN PUBLIC HEALTH
(2022)
Editorial Material
Physics, Mathematical
Delfim F. M. Torres
Summary: The validity of Noether's theorem and the conclusions of Anerot et al. in the Journal of Mathematical Physics (2020, 61(11), 113502) are discussed.
JOURNAL OF MATHEMATICAL PHYSICS
(2023)
Article
Mathematics, Applied
Adelaide Freitas, Helena Sofia Rodrigues, Natalia Martins, Adela Iutis, Michael A. A. Robert, Demian Herrera, Manuel Colome-Hidalgo
Summary: This study investigates the associations between meteorological variables and dengue transmission in the Dominican Republic in 2019. The findings suggest that temperature and rainfall have a delayed impact of 2-5 weeks on the development of dengue outbreaks, creating breeding conditions for mosquitoes.
Article
Mathematics, Interdisciplinary Applications
Om Kalthoum Wanassi, Delfim F. M. Torres
Summary: This study investigates a fractional differential equation with an order ranging from 2 to 3, where a Caputo fractional derivative is involved. The equation includes initial conditions on the function and its first derivative, as well as an integral boundary condition dependent on the unknown function. In application, the population growth of the world is examined. The researchers found an optimal order and function that better describe the given real data compared to existing models.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Jose Vanterler da C. Sousa, Daniela S. Oliveira, Gastao S. F. Frederico, Delfim F. M. Torres
Summary: We present a new version of ?-Hilfer fractional derivative on arbitrary time scales and investigate its fundamental properties. We derive an integration by parts formula and propose a ?-Riemann-Liouville fractional integral using Laplace transform. We demonstrate the applicability of these new operators by studying a fractional initial value problem and prove the existence, uniqueness, and controllability of solutions in a suitable Banach space. The obtained results are interesting and nontrivial, suggesting new directions for further research. The article concludes with comments and future work.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics
Ashish Rayal, Bhagawati Prasad Joshi, Mukesh Pandey, Delfim F. M. Torres
Summary: This article presents an approximation technique using fractional order Bernstein wavelets for numerical simulations of fractional oscillation equations with variable order. The equations describe electrical circuits exhibiting various nonlinear dynamical behaviors. The proposed variable order model has current interest in engineering and applied sciences. To analyze the behavior of the equations under variable-order fractional operator, the proposed model is converted into nonlinear algebraic equations using collocation nodes. Different cases of the model are examined to demonstrate the precision and performance of the method. The results confirm the simplicity and efficiency of the scheme for studying nonlinear random order fractional models in engineering and science.
Article
Mathematics
Silverio Rosa, Delfim F. M. Torres
Summary: In this article, a simple mathematical code is developed using GNU Octave/MATLAB for simulating mathematical models governed by fractional-order differential equations and resolving fractional-order optimal control problems. The code is applied to a fractional-order model for respiratory syncytial virus (RSV) infection. Both the initial value problem and the fractional optimal control problem are numerically solved using the implemented algorithms. The code is available on GitHub and compatible with MATLAB.
Article
Mathematics
Jaouad Danane, Delfim F. M. Torres
Summary: Our study focuses on the behavior analysis of a stochastic predator-prey model with a time delay and logistic growth of prey under the influence of Levy noise. We establish the existence, uniqueness, and boundedness of a positive solution that spans globally. We explore the conditions for extinction and identify criteria for persistence. Numerical simulations validate our theoretical findings and illustrate the dynamics of the stochastic delayed predator-prey model based on different criteria.
Article
Operations Research & Management Science
Sakine Esmaili, M. R. Eslahchi, Delfim F. M. Torres
Summary: This study investigates the optimal control problem for a stochastic model of tumour growth with drug application. The model consists of three stochastic hyperbolic equations for the tumour cells' evolution, and two stochastic parabolic equations for the diffusions of nutrient and drug concentrations. Stochastic terms are added to account for uncertainties, and control variables are added to control the drug and nutrient concentrations. The study proves the existence of unique optimal controls, derives necessary conditions using stochastic adjoint equations, and transforms the stochastic model and adjoint equations into deterministic ones to prove the existence and uniqueness of the optimal control.
Article
Multidisciplinary Sciences
Amal S. Alali, Shahbaz Ali, Muhammad Adnan, Delfim F. M. Torres
Summary: The metric dimension of a graph refers to the smallest set of vertices needed to differentiate or categorize every other vertex. This concept has applications in various domains, and the paper proposes two specific types of graphs and discusses their metric dimension upper bounds.
Article
Mathematics
Faical Ndairou, Delfim F. M. Torres
Summary: This paper introduces a new optimal control problem involving a controlled dynamical system with multi-order fractional differential equations. The continuity and differentiability of the state solutions are established with respect to perturbed trajectories. A Pontryagin maximum principle for incommensurate Caputo fractional optimal control problems is stated and proven. An example is provided to illustrate the applicability of the Pontryagin maximum principle.
Article
Mathematics, Applied
Mohamed A. Zaitri, Cristiana J. Silva, Delfim F. M. Torres
Summary: In this study, an analytical solution for the time-optimal control problem in the induction phase of anesthesia is obtained and compared with the conventional shooting method. The results show that the proposed analytical method aligns numerically with the shooting method. This method has advantages in solving the minimum-time problem in the induction phase of anesthesia.
Article
Tropical Medicine
Michael A. Robert, Helena Sofia Rodrigues, Demian Herrera, Juan de Mata Donado Campos, Fernando Morilla, Javier Del Aguila Mejia, Maria Elena Guardado, Ronald Skewes, Manuel Colome-Hidalgo
Summary: Dengue has become more widespread globally in the past two decades, with many endemic areas seeing an increase in cases. The Dominican Republic experienced its largest outbreaks in 2015 and 2019, highlighting the need to develop tools for healthcare systems and mosquito control. This paper focuses on understanding the relationship between climate variables and dengue transmission in the country.
TROPICAL MEDICINE AND HEALTH
(2023)
Article
Mathematics, Interdisciplinary Applications
Naima Hakkar, Rajesh Dhayal, Amar Debbouche, Delfim F. M. Torres
Summary: We present a new class of impulsive fractional stochastic differential systems driven by mixed fractional Brownian motions with infinite delay and Hurst parameter H<^>& ISIN;(1/2,1). Using fixed point techniques, a q-resolvent family, and fractional calculus, we investigate the existence of a piecewise continuous mild solution for the proposed system. Additionally, we study the approximate controllability of the considered system under appropriate conditions. The main results are illustrated with a demonstrative example.
FRACTAL AND FRACTIONAL
(2023)
Article
Biology
Mohamed Abdelaziz Zaitri, Hanaa Zitane, Delfim F. M. Torres
Summary: This paper presents a novel Pharmacokinetic/Pharmacodynamic (PK/PD) model for the induction phase of anesthesia, incorporating the Psi-Caputo fractional derivative. Numerical analysis and simulations in MATLAB are performed to explore the effects of Psi functions and fractional orders on the model. The results suggest that Psi functions and fractional differentiation play an important role in modeling individual-specific characteristics.
COMPUTERS IN BIOLOGY AND MEDICINE
(2023)
Article
Mathematics
Dafang Zhao, Xuexiao You, Delfim f. m. Torres
Summary: In this paper, we introduce the forward (backward) gH-difference operator of interval sequences and establish new inequalities for interval-valued functions. We also generalize classical discrete Opial type inequalities and provide examples to illustrate our results.
MATHEMATICAL INEQUALITIES & APPLICATIONS
(2023)
