731 citations · 12.8k across the 413 of their papers we have counts for
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The Lotka-Volterra Dynamical System and its Discretization
Márcia Lemos-Silva, Delfim F. M. Torres
Dynamical systems are a valuable asset for the study of population dynamics. On this topic, much has been done since Lotka and Volterra presented the very first continuous system t…
A Lotka-Volterra type model analyzed through different techniques
Jorge Pinto, Sandra Vaz, Delfim F. M. Torres
We consider a modified Lotka-Volterra model applied to the predator-prey system that can also be applied to other areas, for instance the bank system. We show that the model is wel…
Three-Species Predator-Prey Stochastic Delayed Model Driven by Lévy Jumps and with Cooperation Among Prey Species
Jaouad Danane, Delfim F. M. Torres
Our study focuses on analyzing the behavior of a stochastic predator-prey model with a time delay and logistic growth of prey, influenced by Lévy noise. Initially, we establish the…
Discrete-Time System of an Intracellular Delayed HIV Model with CTL Immune Response
Sandra Vaz, Delfim F. M. Torres
In [Math. Comput. Sci. 12 (2018), no. 2, 111--127], a delayed model describing the dynamics of the Human Immunodeficiency Virus (HIV) with Cytotoxic T Lymphocytes (CTL) immune resp…
Lyapunov Functions and Stability Analysis of Fractional-Order Systems
Adnane Boukhouima, Houssine Zine, El Mehdi Lotfi +3
This study presents new estimates for fractional derivatives without singular kernels defined by some specific functions. Based on obtained inequalities, we give a useful method to…
Hybrid Method for Simulation of a Fractional COVID-19 Model with Real Case Application
Anwarud Din, Amir Khan, Anwar Zeb +3
In this research, we provide a mathematical analysis for the novel coronavirus responsible for COVID-19, which continues to be a big source of threat for humanity. Our fractional-o…
Mathematical Analysis of a Fractional COVID-19 Model Applied to Wuhan, Spain and Portugal
Faical Ndairou, Delfim F. M. Torres
We propose a qualitative analysis of a recent fractional-order COVID-19 model. We start by showing that the model is mathematically and biologically well posed. Then, we give a pro…
Global stability of a Caputo fractional SIRS model with general incidence rate
Moulay Rchid Sidi Ammi, Mostafa Tahiri, Delfim F. M. Torres
We introduce a fractional order SIRS model with non-linear incidence rate. Existence of a unique positive solution to the model is proved. Stability analysis of the disease free eq…
Parametric identification of the dynamics of inter-sectoral balance: modelling and forecasting
Olena Kostylenko, Helena Sofia Rodrigues, Delfim F. M. Torres
This work is devoted to modelling and identification of the dynamics of the inter-sectoral balance of a macroeconomic system. An approach to the problem of specification and identi…
Modeling TB-HIV syndemic and treatment
Cristiana J. Silva, Delfim F. M. Torres
Tuberculosis (TB) and human immunodeficiency virus (HIV) can be considered a deadly human syndemic. In this article, we formulate a model for TB and HIV transmission dynamics. The…
Noether's Symmetry Theorem for Variational and Optimal Control Problems with Time Delay
Gastao S. F. Frederico, Delfim F. M. Torres
We extend the DuBois-Reymond necessary optimality condition and Noether's symmetry theorem to the time delay variational setting. Both Lagrangian and Hamiltonian versions of Noethe…