9 citations · 30 across the 14 of their papers we have counts for
15 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 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…
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…
Identifying Memory Effects in Epidemics via a Fractional SEIRD Model and Physics-Informed Neural Networks
Achraf Zinihi
We develop a physics-informed neural network (PINN) framework for parameter estimation in fractional-order SEIRD epidemic models. By embedding the Caputo fractional derivative into…
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.…
Fractional differential equations of a reaction-diffusion SIR model involving the Caputo-fractional time-derivative and a nonlinear diffusion operator
Achraf Zinihi, Moulay Rchid Sidi Ammi, Delfim F. M. Torres
The main aim of this study is to analyze a fractional parabolic SIR epidemic model of a reaction-diffusion, by using the nonlocal Caputo fractional time-fractional derivative and e…
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…
Stability Analysis of a Diffusive SVIR Epidemic Model with Distributed Delay, Imperfect Vaccine and General Incidence Rate
Achraf Zinihi, Mostafa Tahiri, Moulay Rchid Sidi Ammi
In this chapter, we consider a reaction-diffusion SVIR infection model with dis-tributed delay and nonlinear incidence rate. The wellposedness of the proposed model is proved. By m…
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…