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- Allee effect (1)
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Articles 1 - 15 of 15
Full-Text Articles in Dynamic Systems
Exact Solution Structure And Dynamic Preservation In A Nonstandard Finite-Difference Formulation Of The Sir Model, Ramsha Shafqat, Wutiphol Sintunavarat
Exact Solution Structure And Dynamic Preservation In A Nonstandard Finite-Difference Formulation Of The Sir Model, Ramsha Shafqat, Wutiphol Sintunavarat
Mathematical Modelling and Numerical Simulation with Applications
A new nonstandard finite difference method is developed for discretizing the classical Susceptible--Infected--Removed (SIR) epidemic model. In the proposed approach, the first derivatives in the continuous SIR system are replaced by two carefully constructed nonstandard denominator functions, yielding a dynamically consistent discrete model with improved numerical stability while preserving consistency with the original continuous system. It is proved that the proposed scheme preserves the fundamental dynamical properties and qualitative behavior of the continuous SIR model, including positivity and the long-term dynamics of the population classes. Moreover, the resulting discrete system admits explicit analytical solutions, providing further insight into the model …
Neural Network-Based Analysis Of Heroin Epidemic Models With Modified Fractional Operators, M. A. El-Shorbagy, Sedat Pak, Mati Ur Rahman, Hossam A. Nabwey
Neural Network-Based Analysis Of Heroin Epidemic Models With Modified Fractional Operators, M. A. El-Shorbagy, Sedat Pak, Mati Ur Rahman, Hossam A. Nabwey
Mathematical Modelling and Numerical Simulation with Applications
Heroin and synthetic narcotic abuse have become a major global concern, posing challenges to individuals, families, and communities. Their widespread availability and low cost have intensified the crisis. This study investigates a heroin transmission model using the modified Atangana--Baleanu--Caputo (mABC) fractional operator, with emphasis on non-zero solutions. Series solutions are derived by combining the Laplace transform with the Adomian decomposition method to address nonlinear components. Qualitative analysis is conducted through fixed-point theory, while stability is assessed using the T-Picard method. Numerical simulations explore the effects of different fractional orders and transmission parameters on the system. The study incorporates a deep …
Pattern Formation And Diffusion-Driven Instability Of A Modified Lengyel-Epstein Model, Müge Meyvacı, Hüseyin Merdan, Yafia Radouane
Pattern Formation And Diffusion-Driven Instability Of A Modified Lengyel-Epstein Model, Müge Meyvacı, Hüseyin Merdan, Yafia Radouane
Mathematical Modelling and Numerical Simulation with Applications
We consider a modified Lengyel-Epstein model that is covered by a system of reaction-diffusion equations and investigate the sufficient conditions on parameters of the model at which the diffusion-driven instability occurs. We perform numerical simulations to support and extend the theoretical findings. Analytical results and numerical simulations show that the modified Lengyel-Epstein system with positive initial and non-flux boundary conditions presents Turing patterns under some conditions on its parameters.
Bifurcation Dynamics Of A Harvested Predator-Prey Model, Hala H. Emam, Mohamed F. Abouelenein, Mona Anis, M. Y. Hamada, F. A. Atia, H. El-Metwally
Bifurcation Dynamics Of A Harvested Predator-Prey Model, Hala H. Emam, Mohamed F. Abouelenein, Mona Anis, M. Y. Hamada, F. A. Atia, H. El-Metwally
Mathematical Modelling and Numerical Simulation with Applications
In ecosystems, the harvesting effect is essential to preserving the relationships between prey and predator. This work examines a model of predator-prey in discrete time with harvesting. The Jacobian matrix's eigenvalues are calculated for the associated fixed points. We examine the dynamical and qualitative analysis of this model, look into the criteria for stability and bifurcation, and analyze analytical results that show the rich dynamics and complexity of this model. We give sufficient circumstances for the Period-doubling at the interior equilibrium point by employing the harvesting effect. The discrete system's chaos control is carried out, and the outcomes are supported …
A Mathematical Model For Managing Diphtheria Outbreaks In Nigeria Via Vaccination, Enhanced Surveillance, Effective Quarantine, And Social Distancing Measures, Hycienth Ortser Orapine, Nyiutya Cephas Ine, Dekera Jacob Washachi, Ali Audu Baidu, Lubem Matthew Kwaghkor
A Mathematical Model For Managing Diphtheria Outbreaks In Nigeria Via Vaccination, Enhanced Surveillance, Effective Quarantine, And Social Distancing Measures, Hycienth Ortser Orapine, Nyiutya Cephas Ine, Dekera Jacob Washachi, Ali Audu Baidu, Lubem Matthew Kwaghkor
Mathematical Modelling and Numerical Simulation with Applications
Diphtheria is a highly infectious respiratory and skin disease that poses a significant threat to global public health. In Nigeria, children and adults with low immunity remain at high risk due to recurring annual outbreaks in the last decade, with a death rate of as high as 68.8\%. This paper presents a deterministic compartmental model to evaluate the effectiveness of interventions implemented by the Nigerian government. The model's mathematical and epidemiological validity is established through proofs of non-negativity and boundedness. The basic reproduction number ($R_0$) is derived, and stability analysis confirms that the diphtheria-free equilibrium is locally and globally asymptotically …
Modelling Of Dust Devil Flow Dynamics: Effects Of The Sharpness Parameter On Velocity And Pressure, Deepanshu Kumar, Hossein Jafari
Modelling Of Dust Devil Flow Dynamics: Effects Of The Sharpness Parameter On Velocity And Pressure, Deepanshu Kumar, Hossein Jafari
Mathematical Modelling and Numerical Simulation with Applications
This work discusses the development of a straightforward model of dust devils, demonstrating a method for estimating wind speed and pressure. The current model incorporates momentum equations and the mass conservation equation for steady, axisymmetric, inviscid, and incompressible flow. In this model, the radial velocity is first considered, which is restricted in both the radial and axial directions. The sharpness parameter is also incorporated into the radial velocity formulation, as described by Vatistas model. Using the radial velocity as a foundation, we derive the azimuthal and axial velocities. The study further evaluates the pressure. Notably, for large values of the …
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 …
Tumor–Immune Dynamics With Memory And Time Delay: A Fractional-Order Model With Ctla-4 Regulation, Mutaz Mohammad, Mohyeedden Sweidan, Alexander Trounev, Fathalla Rihan
Tumor–Immune Dynamics With Memory And Time Delay: A Fractional-Order Model With Ctla-4 Regulation, Mutaz Mohammad, Mohyeedden Sweidan, Alexander Trounev, Fathalla Rihan
Mathematical Modelling and Numerical Simulation with Applications
This study develops a fractional-order tumor-immune interaction model incorporating Caputo memory effects, delayed immune activation, and CTLA-4 checkpoint regulation. The model describes the coupled dynamics of tumor cells, CD4$^{+}$ T cells, IFN-$\gamma$, and CTLA-4, and extends classical integer-order tumor-immune models by accounting for hereditary immune responses and biologically motivated latency effects. Theoretical properties, including positivity, boundedness, equilibrium structure, and fractional-order stability, are examined to establish the biological and mathematical consistency of the model. The delayed fractional system is then investigated computationally by comparing several numerical methods, including finite difference discretization, Daubechies wavelet collocation, Euler wavelet collocation, and a predictor-corrector scheme. …
Stochastic Analysis Of Epidemic Size And Peak Infection In An Svir Model With Imperfect Vaccine And External Source Of Infection, María Gamboa Pérez
Stochastic Analysis Of Epidemic Size And Peak Infection In An Svir Model With Imperfect Vaccine And External Source Of Infection, María Gamboa Pérez
Mathematical Modelling and Numerical Simulation with Applications
The dynamics of an infectious disease outbreak are studied under a stochastic framework in a closed population where individuals are homogeneously mixed. A vaccination program is implemented in the community prior to the start of the epidemic. The administered vaccine is imperfect, meaning that vaccinated individuals may still become infected upon contact with infected individuals. The mathematical Susceptible-Vaccinated-Infected-Recovered (SVIR) model describing the evolution of the epidemic is formulated as an absorbing, continuous-time, three-dimensional Markov chain with compartments for vaccinated, susceptible, infected and recovered individuals. The aim of this study is to characterize two fundamental epidemiological quantities: the maximum number of …
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 …
Markov-Modulated Queueing Network For Mobile Traffic Aggregation With Threshold-Controlled Buffers, Anton A. Esin, Elmira Yu. Kalimulina
Markov-Modulated Queueing Network For Mobile Traffic Aggregation With Threshold-Controlled Buffers, Anton A. Esin, Elmira Yu. Kalimulina
Mathematical Modelling and Numerical Simulation with Applications
We study the problem of data transmission from mobile platforms operating in high-speed transit between cellular base stations, under conditions of unstable and intermittent connectivity. Conventional queueing and connectivity models often fail to capture the combined effects of rapidly changing signal conditions, finite buffer capacity, and dynamic topology. We aim to develop a tractable yet expressive model that integrates stochastic link availability, queue dynamics, and buffer control. We propose a mathematical framework based on queues whose service intensities are modulated by a continuous-time Markov chain (CTMC) representing signal conditions along a high-speed trajectory. The core subsystem is a two-stage (aggregation …
Measuring Market Risk Through Entropic Var, Dragomir Nedeltchev, Tsvetelin Zaevski
Measuring Market Risk Through Entropic Var, Dragomir Nedeltchev, Tsvetelin Zaevski
Mathematical Modelling and Numerical Simulation with Applications
The article aims to measure the market risk beyond the basic risk measures like the Value-at-Risk (VaR) and the Expected Shortfall (ES). The Entropic Value-at-Risk is selected among the available measures based on its advantages -- it is the coherent upper bound of the VaR and ES. This risk measure is applied to the classical Black-Scholes model as well as to some more realistic ones, such as the exponential tempered stable model (the log-returns are presented by a tempered stable L\'evy process), the stochastic volatility model of Heston, its jump extension of Bates, and another stochastic volatility model but with …
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 …
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 …
Synergistic Modeling Of Hydrogel Gelation Via Time-Delay Dynamics And Machine Learning Algorithms, Mine Babaoglu, Dipesh ., Pankaj Kumar, Jagjit Singh Dhatterwal, Mansoor Alsulami
Synergistic Modeling Of Hydrogel Gelation Via Time-Delay Dynamics And Machine Learning Algorithms, Mine Babaoglu, Dipesh ., Pankaj Kumar, Jagjit Singh Dhatterwal, Mansoor Alsulami
Mathematical Modelling and Numerical Simulation with Applications
This paper presents an integrated framework in which delay differential equation (DDE) modeling and machine learning (ML) approaches are coupled to study hydrogel formation kinetics, with emphasis on delayed crosslinker addition. Conventional mechanistic models disclose many physical and kinetic complexities of reacting mixtures; they seldom depict the nonlinear and time-evolving complexities inherent in developing polymer networks. To address this, a mathematical model is developed that examines how the insertion of crosslinkers affects system stability and equilibrium. Analytical and numerical results show that delays nearing critical levels cause bifurcation behavior with substantial implications on gelation kinetics. Sophisticated machine learning systems, including …