5 citations · 21 across the 15 of their papers we have counts for
16 papers
Structure-Preserving Neural ODEs via Nonstandard Finite Difference Discretization
Achraf Zinihi, Matthias Ehrhardt, Moulay Rchid Sidi Ammi
Although neural ordinary differential equations (NODEs) are a powerful framework for learning continuous-time dynamics, they generally do not preserve essential qualitative propert…
A Nonstandard Finite Difference Scheme for a Nonlinear Parabolic Equation with p-Laplacian-Type Diffusion
Achraf Zinihi, Matthias Ehrhardt, Moulay Rchid Sidi Ammi
We propose and analyze a nonstandard finite difference (NSFD) scheme for nonlinear parabolic equations involving a p-Laplacian-type diffusion operator in one- and two-dimensional s…
A Fractional-Memory Physics-Informed Neural Network with Fast History Compression for Tempered Fractional Coupled Phase-Field Systems
Shubham Kumar, Himanshu Kumar Dwivedi, Matthias Ehrhardt +1
Tempered time-fractional coupled phase-field (tTFCP) systems are used to model interfacial phenomena involving memory-dependent transport and relaxation mechanisms. Numerical solut…
Structure-Preserving Schemes for a Fractional SVIR Epidemic Model with a Hybrid Mittag-Leffler-Caputo-Fabrizio Operator
Seham M. Al-Mekhlafi, Ahmed Boudaoui, Matthias Ehrhardt
This paper proposes and analyzes a fractional-order SVIR epidemic model based on a hybrid Mittag-Leffler-Caputo-Fabrizio (MLCF) fractional operator with a nonsingular kernel. This…
A Koopman-PINN Framework for Epidemic Models: Parameter Inference and Forecasting
Achraf Zinihi, Matthias Ehrhardt, Moulay Rchid Sidi Ammi
We propose a Koopman-enhanced physics-informed neural network (K--PINN) framework for parameter inference and forecasting in nonlinear epidemic models. This method combines Koopman…
A Generalized Hacker Dynamics Model with Nonlinear Incidence: Analysis and Positivity-Preserving Numerical Simulation
Manh Tuan Hoang, Hoai Thu Pham, Matthias Ehrhardt
We propose and analyze a generalized compartment model for hacker dynamics in cybersecurity systems. This model is an extension of a recently introduced framework, replacing the bi…
Constraint-Aware Physics-Informed Neural Networks for SEIR Reaction-Diffusion Epidemic Models with Vital Dynamics
Achraf Zinihi, Matthias Ehrhardt
Reaction-diffusion epidemic models with vital dynamics are an important framework for describing the spatial and temporal spread of infectious diseases. In this work, we present a…
A Nonstandard Finite Difference Scheme for an SEIQR Epidemiological PDE Model
Achraf Zinihi, Matthias Ehrhardt, Moulay Rchid Sidi Ammi
This paper introduces a nonstandard finite difference (NSFD) approach to a reaction-diffusion SEIQR epidemiological model, which captures the spatiotemporal dynamics of infectious…
A Koopman Operator Framework for Nonlinear Epidemic Dynamics: Application to an SIRSD Model
Achraf Zinihi, Matthias Ehrhardt, Moulay Rchid Sidi Ammi
We develop and analyze an SIRSD epidemic model, which extends the classical SIR framework by incorporating waning immunity and disease-induced mortality. A rigorous well-posedness…
Actuarial Analysis of an Infectious Disease Insurance based on an SEIARD Epidemiological Model
Achraf Zinihi, Matthias Ehrhardt, Moulay Rchid Sidi Ammi
The growing number of infectious disease outbreaks, like the one caused by the SARS-CoV-2 virus, underscores the necessity of actuarial models that can adapt to epidemic-driven ris…
Spatiotemporal SEIQR Epidemic Modeling with Optimal Control for Vaccination, Treatment, and Social Measures
Achraf Zinihi, Matthias Ehrhardt, Moulay Rchid Sidi Ammi
This paper introduces a spatiotemporal SEIQR epidemic model governed by a system of reaction-diffusion partial differential equations that incorporates optimal control strategies.…
Square Root Operators and the Well-Posedness of Pseudodifferential Parabolic Models of Wave Phenomena
Matthias Ehrhardt, Jochen Glück, Pavel Petrov +1
Pseudodifferential parabolic equations with an operator square root arise in wave propagation problems as a one-way counterpart of the Helmholtz equation. The expression under the…
Dynamical Analysis of a Cocaine-Heroin Epidemiological Model with Spatial Distributions
Achraf Zinihi, Moulay Rchid Sidi Ammi, Matthias Ehrhardt +1
This article conducts an in-depth investigation of a new spatio-temporal model for the cocaine-heroin epidemiological model with vital dynamics, incorporating the Laplacian operato…
Dynamical Behavior of a Stochastic Epidemiological Model: Stationary Distribution and Extinction of a SIRS Model with Stochastic Perturbations
Achraf Zinihi, Moulay Rchid Sidi Ammi, Matthias Ehrhardt
This paper deals with a new epidemiological model of SIRS with stochastic perturbations. The primary objective is to establish the existence of a unique non-negative nonlocal solut…
Optimal Control of a Diffusive Epidemiological Model Involving the Caputo-Fabrizio Fractional Time-Derivative
Achraf Zinihi, Moulay Rchid Sidi Ammi, Matthias Ehrhardt
In this work we study a fractional SEIR biological model of a reaction-diffusion, using the non-singular kernel Caputo-Fabrizio fractional derivative in the Caputo sense and employ…
Mathematical Modeling and Hyers-Ulam Stability for a Nonlinear Epidemiological Model with Operator and Mittag-Leffler Kernel
Achraf Zinihi, Moulay Rchid Sidi Ammi, Matthias Ehrhardt
This paper investigates a novel nonlinear singular fractional SI model with the operator and the Mittag-Leffler kernel. The initial investigation includes the existence, uniq…