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Delfim F. M. Torres

Publications and source records attributed to Delfim F. M. Torres.

At least 37 records · Page 2Linked to original sources
arXiv2024

Parameters estimation and uncertainty assessment in the transmission dynamics of rabies in humans and dogs

Rabies remains a pressing global public health issue, demanding effective modeling and control strategies. This study focused on developing a mathematical model using ordinary differential equations (ODEs) to estimate parameters and assess uncertainties related to the transmission dynamics of rabies in humans and dogs. To determine model parameters and address uncertainties, next-generation matrices were utilized to calculate the basic reproduction number ${\cal R}_{0}$. Furthermore, the Partial Rank Correlation Coefficient was used to identify parameters that significantly influence model outputs. The analysis of equilibrium states revealed that the rabies-free equilibrium is globally asymptotically stable when $R_0<1$, whereas the endemic equilibrium is globally asymptotically stable when ${\cal R}_{0}\geq 1$. To reduce the severity of rabies and align with the Global Rabies Control (GRC) initiative by 2030, the study recommends implementing control strategies targeting indoor domestic dogs.

q-bio.PE↗
arXiv2024

Exact solution for a discrete-time SIR model

We propose a nonstandard finite difference scheme for the Susceptible-Infected-Removed (SIR) continuous model. We prove that our discretized system is dynamically consistent with its continuous counterpart and we derive its exact solution. We end with the analysis of the long-term behavior of susceptible, infected and removed individuals, illustrating our results with examples. In contrast with the SIR discrete-time model available in the literature, our new model is simultaneously mathematically and biologically sound.

math.DS↗
arXiv2024

Stability analysis and optimal control of the logistic equation

We consider the unexploited/exploited logistic equation and study the stability of equilibrium points through Lyapunov functions. Then, we apply first and second order optimality conditions for the optimal control of the total biomass yield. Finally, we note that the time-scale logistic equation present in the literature lacks biological significance and we propose a new version of a dynamic logistic equation, valid on an arbitrary time scale, for which any trajectory of the system, beginning with a positive initial condition, remains nonnegative.

math.OC↗
arXiv2024

Alternative views on fuzzy numbers and their application to fuzzy differential equations

We consider fuzzy valued functions from two parametric representations of $α$-level sets. New concepts are introduced and compared with available notions. Following the two proposed approaches, we study fuzzy differential equations. Their relation with Zadeh's extension principle and the generalized Hukuhara derivative is discussed. Moreover, we prove existence and uniqueness theorems for fuzzy differential equations. Illustrative examples are given.

math.GM↗
arXiv2024

Mathematical model to assess the impact of contact rate and environment factor on transmission dynamics of rabies in humans and dogs

This paper presents a mathematical model to understand how rabies spreads among humans, free-range, and domestic dogs. By analyzing the model, we discovered that there are equilibrium points representing both disease-free and endemic states. We calculated the basic reproduction number, $\mathcal{R}_{0}$, using the next generation matrix method. When $\mathcal{R}_{0}<1$, the disease-free equilibrium is globally stable, whereas when $\mathcal{R}_{0}>1$, the endemic equilibrium is globally stable. To identify the most influential parameters in disease transmission, we used the normalized forward sensitivity index. Our simulations revealed that the contact rates between the infectious agent and humans, free-range dogs, and domestic dogs have the most significant impact on rabies transmission. The study also examines how periodic changes in transmission rates affect the disease dynamics, emphasizing the importance of transmission frequency and amplitude on the patterns observed in rabies spread. Therefore, the study proposes that to mitigate the factors most strongly linked to disease sensitivity, effective disease control measures should primarily prioritize on reducing the population of both free-range and domestic dogs in open environments.

math.DS↗
arXiv2024

Universe-inspired algorithms for Control Engineering: A review

Control algorithms have been proposed based on knowledge related to nature-inspired mechanisms, including those based on the behavior of living beings. This paper presents a review focused on major breakthroughs carried out in the scope of applied control inspired by the gravitational attraction between bodies. A control approach focused on Artificial Potential Fields was identified, as well as four optimization metaheuristics: Gravitational Search Algorithm, Black-Hole algorithm, Multi-Verse Optimizer, and Galactic Swarm Optimization. A thorough analysis of ninety-one relevant papers was carried out to highlight their performance and to identify the gravitational and attraction foundations, as well as the universe laws supporting them. Included are their standard formulations, as well as their improved, modified, hybrid, cascade, fuzzy, chaotic and adaptive versions. Moreover, this review also deeply delves into the impact of universe-inspired algorithms on control problems of dynamic systems, providing an extensive list of control-related applications, and their inherent advantages and limitations. Strong evidence suggests that gravitation-inspired and black-hole dynamic-driven algorithms can outperform other well-known algorithms in control engineering, even though they have not been designed according to realistic astrophysical phenomena and formulated according to astrophysics laws. Even so, they support future research directions towards the development of high-sophisticated control laws inspired by Newtonian/Einsteinian physics, such that effective control-astrophysics bridges can be established and applied in a wide range of applications.

math.OC↗
arXiv2024

Modelling the dynamics of online food delivery services on the spread of food-borne diseases

We propose and analyze a deterministic mathematical model for the transmission of food-borne diseases in a population consisting of humans and flies. We employ the Caputo operator to examine the impact of governmental actions and online food delivery services on the transmission of food-borne diseases. The proposed model investigates important aspects such as positivity, boundedness, disease-free equilibrium, basic reproduction number and sensitivity analysis. The existence and uniqueness of a solution for the initial value problem is established using Banach and Schauder type fixed point theorems. Functional techniques are employed to demonstrate the stability of the proposed model under the Hyers-Ulam condition. For an approximate solution, the iterative fractional order Predictor-Corrector scheme is utilized. The simulation of this scheme is conducted using Matlab as the numeric computing environment, with various fractional order values ranging from 0.75 to 1. Over time, all compartments demonstrate convergence and stability. The numerical simulations highlight the necessity for the government to implement the most effective food safety control interventions. These measures could involve food safety awareness and training campaigns targeting restaurant managers, staff members involved in online food delivery, as well as food delivery personnel.

math.DS↗
arXiv2024

Stability criteria of nonlinear generalized proportional fractional delayed systems

This work deals with the finite time stability of generalized proportional fractional systems with time delay. First, based on the generalized proportional Grönwall inequality, we derive an explicit criterion that enables the system trajectories to stay within a priori given sets during a pre-specified time interval, in terms of the Mittag-Leffler function. Then, we investigate the finite time stability of nonlinear nonhomogeneous delayed systems by means of an approach based on Hölder's and Jensen's inequalities. Numerical applications are presented to illustrate the validity and feasibility of the developed results.

math.OC↗
arXiv2024

Modeling the dynamics of the Hepatitis B virus via a variable-order discrete system

We investigate the dynamics of the hepatitis B virus by integrating variable-order calculus and discrete analysis. Specifically, we utilize the Caputo variable-order difference operator in this study. To establish the existence and uniqueness results of the model, we employ a fixed-point technique. Furthermore, we prove that the model exhibits bounded and positive solutions. Additionally, we explore the local stability of the proposed model by determining the basic reproduction number. Finally, we present several numerical simulations to illustrate the richness of our results.

q-bio.PE↗
arXiv2024

The Duality Theory of Fractional Calculus and a New Fractional Calculus of Variations Involving Left Operators Only

Through duality it is possible to transform left fractional operators into right fractional operators and vice versa. In contrast to existing literature, we establish integration by parts formulas that exclusively involve either left or right operators. The emergence of these novel fractional integration by parts formulas inspires the introduction of a new calculus of variations, where only one type of fractional derivative (left or right) is present. This applies to both the problem formulation and the corresponding necessary optimality conditions. As a practical application, we present a new Lagrangian that relies solely on left-hand side fractional derivatives. The fractional variational principle derived from this Lagrangian leads us to the equation of motion for a dissipative/damped system.

math.OC↗
arXiv2024

Permanence and Uniform Asymptotic Stability of Positive Solutions of SAIQH Models on Time Scales

A susceptible, asymptomatic, infectious, quarantined, and hospitalized (SAIQH) compartmental model on time scales is introduced and a suitable Lyapunov function is defined. Main results include: the proof that the system is permanent; proof of existence of solution; and sufficient conditions implying the dynamic system to have a unique almost periodic solution that is uniformly asymptotically stable. An example is presented supporting the obtained results.

math.DS↗
arXiv2024

Dynamics of a Model of Polluted Lakes via Fractal-Fractional Operators with Two Different Numerical Algorithms

We employ Mittag-Leffler type kernels to solve a system of fractional differential equations using fractal-fractional (FF) operators with two fractal and fractional orders. Using the notion of FF-derivatives with nonsingular and nonlocal fading memory, a model of three polluted lakes with one source of pollution is investigated. The properties of a non-decreasing and compact mapping are used in order to prove the existence of a solution for the FF-model of polluted lake system. For this purpose, the Leray-Schauder theorem is used. After exploring stability requirements in four versions, the proposed model of polluted lakes system is then simulated using two new numerical techniques based on Adams-Bashforth and Newton polynomials methods. The effect of fractal-fractional differentiation is illustrated numerically. Moreover, the effect of the FF-derivatives is shown under three specific input models of the pollutant: linear, exponentially decaying, and periodic.

math.DS↗
arXiv2024

Modeling Blood Alcohol Concentration Using Fractional Differential Equations Based on the $ψ$-Caputo Derivative

We propose a novel dynamical model for blood alcohol concentration that incorporates $ψ$-Caputo fractional derivatives. Using the generalized Laplace transform technique, we successfully derive an analytic solution for both the alcohol concentration in the stomach and the alcohol concentration in the blood of an individual. These analytical formulas provide us a straightforward numerical scheme, which demonstrates the efficacy of the $ψ$-Caputo derivative operator in achieving a better fit to real experimental data on blood alcohol levels available in the literature. In comparison to existing classical and fractional models found in the literature, our model outperforms them significantly. Indeed, by employing a simple yet non-standard kernel function $ψ(t)$, we are able to reduce the error by more than half, resulting in an impressive gain improvement of 59 percent.

physics.med-ph↗
arXiv2024

Existence and Uniqueness of Weak Solutions to Frictionless-Antiplane Contact Problems

We investigate a quasi-static-antiplane contact problem, examining a thermo-electro-visco-elastic material with a friction law dependent on the slip rate, assuming that the foundation is electrically conductive. The mechanical problem is represented by a system of partial differential equations, and establishing its solution involves several key steps. Initially, we obtain a variational formulation of the model, which comprises three systems: a hemivariational inequality, an elliptic equation, and a parabolic equation. Subsequently, we demonstrate the existence of a unique weak solution to the model. The proof relies on various arguments, including those related to evolutionary inequalities, techniques for decoupling unknowns, and certain results from differential equations.

math.AP↗
arXiv2024

Boundary Controllability of Riemann-Liouville Fractional Semilinear Equations

We study the boundary regional controllability of a class of Riemann-Liouville fractional semilinear sub-diffusion systems with boundary Neumann conditions. The result is obtained by using semi-group theory, the fractional Hilbert uniqueness method, and Schauder's fixed point theorem. Conditions on the order of the derivative, internal region, and on the nonlinear part are obtained. Furthermore, we present appropriate sufficient conditions for the considered fractional system to be regionally controllable and, therefore, boundary regionally controllable. An example of a population density system with diffusion is given to illustrate the obtained theoretical results. Numerical simulations show that the proposed method provides satisfying results regarding two cases of the control operator.

math.OC↗
arXiv2024

Boundary Regional Controllability of Semilinear Systems Involving Caputo Time Fractional Derivatives

We study boundary regional controllability problems for a class of semilinear fractional systems. Sufficient conditions for regional boundary controllability are proved by assuming that the associated linear system is approximately regionally boundary controllable. The main result is obtained by using fractional powers of an operator and the fixed point technique under the approximate controllability of the corresponding linear system in a suitable subregion of the space domain. An algorithm is also proposed and some numerical simulations performed to illustrate the effectiveness of the obtained theoretical results.

math.OC↗
arXiv2023

A Necessary Optimality Condition for Extended Weighted Generalized Fractional Optimal Control Problems

Using the recent weighted generalized fractional order operators of Hattaf, a general fractional optimal control problem without constraints on the values of the control functions is formulated and a corresponding (weak) version of Pontryagin's maximum principle is proved. As corollaries, necessary optimality conditions for Caputo-Fabrizio, Atangana-Baleanu and weighted Atangana-Baleanu fractional dynamic optimization problems are trivially obtained. As an application, the weighted generalized fractional problem of the calculus of variations is investigated and a new more general fractional Euler-Lagrange equation is given.

math.OC↗