Open Access. Powered by Scholars. Published by Universities.®
Ordinary Differential Equations and Applied Dynamics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Dynamic Systems (4)
- Life Sciences (4)
- Non-linear Dynamics (3)
- Numerical Analysis and Computation (3)
- Analysis (1)
-
- Bioinformatics (1)
- Control Theory (1)
- Data Science (1)
- Disease Modeling (1)
- Diseases (1)
- Ecology and Evolutionary Biology (1)
- Immunology and Infectious Disease (1)
- Mathematics (1)
- Medicine and Health Sciences (1)
- Other Immunology and Infectious Disease (1)
- Population Biology (1)
- Systems Biology (1)
- Virus Diseases (1)
- Keyword
-
- Uniqueness (2)
- Adomian decomposition method (1)
- Allee effect (1)
- Backward bifurcation (1)
- Bacterial spread (1)
-
- Bistability (1)
- Caputo fractional derivative (1)
- Computational efficiency (1)
- Convergence (1)
- Crowley–Martin function (1)
- Daubechies wavelet frames (1)
- Existence (1)
- Fixed point theorems (1)
- Fractional coupled Riccati equations (1)
- Fractional order modelling (1)
- General incidence function (1)
- Global stability (1)
- HIV; incidence; model; parameter estimation; PrEP (1)
- Hopf bifurcation (1)
- Hyers-Ulam stability (1)
- Mathematical model (1)
- Monod-Haldane functional response (1)
- Numerical solutions (1)
- Opioid use disorder (1)
- Optimal control (1)
- Picard method (1)
- Population dynamics (1)
- Positive preserving truncated Euler–Maruyama method (1)
- Sensitivity (1)
- Shigellosis (1)
Articles 1 - 8 of 8
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Dynamical Behavior, Extinction And Persistence In A Stochastic Delayed Two-Strain Epidemic Model With A Generalized Crowley-Martin Incidence Rate, Amina Allali, Dounia Bentaleb, Saida Amine
Dynamical Behavior, Extinction And Persistence In A Stochastic Delayed Two-Strain Epidemic Model With A Generalized Crowley-Martin Incidence Rate, Amina Allali, Dounia Bentaleb, Saida Amine
Mathematical Modelling and Numerical Simulation with Applications
This paper develops and analyzes a novel delayed stochastic SIR epidemic model with two interacting strains and general incidence functions. By establishing the existence and uniqueness of a positive global solution, the well-posedness of the model under stochastic perturbations is ensured. Extinction occurs when the stochastic reproduction number falls below unity, as demonstrated through Itô calculus and martingale convergence theorems, while persistence is guaranteed under the Crowley–Martin incidence when it exceeds one. Numerical experiments based on the Positive Preserving Truncated Euler–Maruyama (PPTEM) scheme confirm the analytical predictions and highlight the influence of time delay and noise intensity on the long-term …
Employing Effective Solution Methods For Caputo-Based Sequential Fractional Models, Eman A. A. Ziada, Mohamed F. Abouelenein, Hijaz Ahmad, Monica Botros
Employing Effective Solution Methods For Caputo-Based Sequential Fractional Models, Eman A. A. Ziada, Mohamed F. Abouelenein, Hijaz Ahmad, Monica Botros
Mathematical Modelling and Numerical Simulation with Applications
This paper investigates a class of nonlinear sequential singular fractional differential equations (FDEs) involving Caputo derivatives. This type of equation has several key advantages that enhance its value, such as capturing memory and hereditary effects. Viscoelastic materials and anomalous diffusion, as well as biological systems, can take advantage of this feature. In addition, fractional derivatives possess a sequential structure that enables the implementation of multiscale processes and hierarchical memory responses. Moreover, it provides an effective and flexible framework for solving differential equations compared to classical differential equations. It can therefore be used to model complex systems in physics, biology, and …
Numerical Simulations And Hyers-Ulam Stability Of A Novel Nonlocal Anthropogenic Cutaneous Leishmaniasis Mathematical Model, Khalid Fanoukh Al Oweidi, Zakirullah -, Kamal Shah, Thabet Abdeljawad
Numerical Simulations And Hyers-Ulam Stability Of A Novel Nonlocal Anthropogenic Cutaneous Leishmaniasis Mathematical Model, Khalid Fanoukh Al Oweidi, Zakirullah -, Kamal Shah, Thabet Abdeljawad
Mathematical Modelling and Numerical Simulation with Applications
In this work, the fractal-fractional Atangana-Baleanu derivative with the Mittag-Leffler kernel is employed to capture the memory and hereditary effects inherent to anthropogenic cutaneous leishmaniasis transmission dynamics. The Banach fixed-point theorem and contraction mapping principle are used to prove the existence and uniqueness of solutions, while Hyers-Ulam stability of the system is analyzed to demonstrate the robustness of solutions with respect to small perturbations. Using a nonlinear least-squares approach, model parameters and fractional order are estimated using epidemiological data from the World Health Organization. The basic reproduction number $R_0 = 0.53$ indicates that the disease is under control after adding …
A Novel Mathematical Model Of Hiv Transmission Incorporating The Effects Of Treatment And Pre-Exposure Prophylaxis: Sensitivity Analysis And Numerical Simulations, Erick Manuel Delgado Moya
A Novel Mathematical Model Of Hiv Transmission Incorporating The Effects Of Treatment And Pre-Exposure Prophylaxis: Sensitivity Analysis And Numerical Simulations, Erick Manuel Delgado Moya
Mathematical Modelling and Numerical Simulation with Applications
Human immunodeficiency virus (HIV) continues to be a public health problem in many countries of the world, and Pre-exposure prophylaxis (PrEP) is a preventive method for HIV, which has shown great efficacy and is in use worldwide. This work presents a new mathematical model for HIV transmission incorporating PrEP use and evaluates the impact of PrEP along with its increasing use in a population. The construction of the model takes into account three forms of diagnosis: diagnosis of individuals in risky sexual contact, diagnosis after risky contact (diagnosis in the undiagnosed infected compartment), and diagnosis associated with attempting to enter …
Construction And Data-Driven Analysis Of A Stochastic, Individual-Based Opioid Epidemiology Network Model, Leigh Bennett Pearcy, Owen Queen, Vincent Jodoin, Suzanne Lenhart, Christopher Strickland
Construction And Data-Driven Analysis Of A Stochastic, Individual-Based Opioid Epidemiology Network Model, Leigh Bennett Pearcy, Owen Queen, Vincent Jodoin, Suzanne Lenhart, Christopher Strickland
Mathematical Modelling and Numerical Simulation with Applications
While substance use epidemiology has been an active area of mathematical research in recent years, the social and mental processes that are involved in the development of substance use disorders have presented challenges to advancing the epidemiological theory and how they differ from the contraction of pathogenic disease. Such distinction is especially pertinent in the context of the current United States opioid epidemic and its intersection with the recent COVID-19 pandemic, as both prescription drugs and social influence play major roles in the development of opioid use disorder. In this paper, we construct a stochastic network model capturing how individual …
High-Order Adaptive Solutions For Coupled Fractional Riccati Equations Via Daubechies Redundant Frames, Mutaz Mohammad, Alexander Trounev
High-Order Adaptive Solutions For Coupled Fractional Riccati Equations Via Daubechies Redundant Frames, Mutaz Mohammad, Alexander Trounev
Mathematical Modelling and Numerical Simulation with Applications
Coupled fractional Riccati equations play a fundamental role in modeling complex systems with memory effects and anomalous diffusion, frequently arising in engineering, control theory, finance, and quantum mechanics. Their analytical and numerical treatment remains highly challenging due to the nonlocal nature of fractional-order derivatives and the presence of nonlinear coupling terms. This study introduces an adaptive numerical framework that combines the Caputo fractional derivative with redundant Daubechies wavelet frames. The method leverages multi-resolution analysis, compact support, and controlled redundancy to achieve accurate approximation of both localized and global solution features, particularly in scenarios characterized by singular behavior and long-range memory …
Global Stability And Bifurcation Analysis Of A Predator-Prey Model Involving Allee Effect And Monod-Haldane Functional Response, Resmawan Resmawan, Agus Suryanto, Isnani Darti, Hasan S. Panigoro
Global Stability And Bifurcation Analysis Of A Predator-Prey Model Involving Allee Effect And Monod-Haldane Functional Response, Resmawan Resmawan, Agus Suryanto, Isnani Darti, Hasan S. Panigoro
Mathematical Modelling and Numerical Simulation with Applications
In this paper, the complexity of the dynamic behavior of the interaction between prey and predator is studied. The predator-prey relationship involves Allee effects and Monod-Haldane functional response. The constructed model has been shown to have validity in several respects, including the existence and uniqueness of the solution, as well as its non-negativity and boundedness. Three equilibrium points, namely trivial, axial, and coexistence points, are found, including their global dynamics using the Lyapunov function together with the LaSalle's invariance principle. The effect of the predation conversion rate causes changes in the dynamic behavior of predators and prey, which is characterized …
Dynamics And Optimal Intervention Strategies In A Shigellosis Transmission Model, Mehmet Gümüs, Shewafera Wondimagegnhu Teklu, Kemal Türk
Dynamics And Optimal Intervention Strategies In A Shigellosis Transmission Model, Mehmet Gümüs, Shewafera Wondimagegnhu Teklu, Kemal Türk
Mathematical Modelling and Numerical Simulation with Applications
This research explores how water treatment contributes to limiting the transmission of Shigellosis, an infection caused by bacteria from the Shigella genus. A mathematical framework is formulated to evaluate the influence of protective strategies and water purification on the spread of the disease. To confirm the model's biological relevance, its well-posedness is investigated. The basic reproduction number $(\mathfrak{R}_0)$, a critical indicator of disease behavior, is derived using the matrix operator method. Findings indicate that if $\mathfrak{R}_01$, the infection persists, with the endemic equilibrium exhibiting local asymptotic stability. A comprehensive cost-effectiveness analysis reveals that combining environmental protection with water treatment represents …