African Conference on Research in Computer Science and Applied Mathematics

We consider the problem on additive model building for spatial functional regression, where a scalar response is related to the components of a square-integrable spatial functional process. We propose a methodology that leads to the minimisation of a spatially weighted \(\ell _2\)-error norm with a group LASSO type penalty, which constitutes our selection criterion. The originality of this proposed method is that we consider spatially dependent functional data as covariates. A simulation study highlights the importance of the choice of the spatial weight matrix as well as the appreciable asymptotic behaviour of the estimators. Precisely, our method selects better in the case of strong spatial dependency than in the independent data case and increasing the sample size clearly improves the number of selected components using the proposed criterion for this study with probability converging to 1.

In this study, we propose an new approach for solving a quadratic programming problem with diagonally dominant M-matrix and box constraints. This approach is based on the preprocessing technique, as well as an algorithm inspired by a method of Voglis and Lagaris. The principle of this approach is to apply a preprocessing technique initially to reduce the size of the original problem. The preprocessing step allows to identify certain active and inactive indices at the optimum, in order to fix in advance the corresponding values of certain variables, and put the others in the support set \(J_S\). In order to solve the resulting reduced problem, we then developed an approach inspired on the method of Voglis and Lagaris which falls into the category of exterior point and active set techniques (Kunish and Rendl). Using the notion of support for an objective function developed by Gabasov et al., our approach leads to a more general condition which allows to have an initial pseudo-solution, related to a coordinator support and close to the optimal solution.

This work considers the availability probability density function estimation based on beta prime kernel of a repairable series system, in the case of identical components operating independently, in the context of non negative data. We have obtained certain properties of the estimator such as bias, variance, optimal convergence rate for mean squared error (MSE) and integrated mean squared error (MISE). In addition, for the bandwidth selection method, we use cross-validation and rule-of-thumb approaches and compare their performances. Finally, a simulation study, sensitivity analysis and a real data application are presented to illustrate the results.

Among imperfect maintenance models, hybrid ones give interesting results when modeling the effect of replacing one or several components on the behavior of a multi-component systems, whatever their configurations. The herein paper, which concerns series systems, aims at studying the effect of the replacement time and the number of replaced components on the imperfect maintenance hybrid model with three parameters (i.e. geometric and arithmetic adjustment of failure rate parameters and virtual age adjustment parameter). A mathematical model is then fitted for each hybrid model parameter. This will allow a realistic modeling and planning of maintenance tasks of series systems.

A Web service designates a new type of software component having the capacity to publish its functions on the Internet in the form of services, and to make these services easily invocable and to make them available to clients through standard Internet protocols. However, Web services as they are presented are limited to simple functionalities, so the task of composing existing Web services is essential in order to satisfy a complex request of clients. In this work, we proposed a model for the performance evaluation of a Web services system based on an open tandem queue network, with three stations, taking into account client requests. An analysis and modeling of this system with a Jackson network is reported. We calculated the average response time in the system, the average number of clients in the system, the average number of clients waiting in the system, and the average waiting time as a function of \(\lambda \).

We have data on the follow-up of 260 Covid’19 patients at major hospital in Madagascar. According to specialists, the patient’s daily oxygen saturation and requirement allow us to characterize the form of the patient’s case in free different states: mild form, moderate form, severe form. We propose a semi-Markovian model with five states (Mild form, Moderate form, Sever form, Cured and Deceased) to analyze the time scales of recovery and death as well as the probability of recovery and death as a function of patient status. The model was also used to measure the dynamic reliability of care up to hospital discharge, i.e. the probability of not being severely ill as a function of hospitalization time.

We propose an algorithm to generate refined descriptive samples from dependent random variables for estimation of expectations of functions of output variables using the Iman and Conover algorithm to transform the dependent variables to independent ones. Hence, the asymptotic variance of such an estimate in case of dependent input random variables is proved, using a result from to be less than that obtained using simple random sampling.

The predator-prey equations are widely used to model the complex dynamics of interacting species in ecological systems. This paper investigates the synchronization of coupled Caputo fractional-order predator-prey equations, incorporating group defense mechanisms and Michaelis-Menten type harvesting to enhance the model’s realism. We design a linear controller to facilitate synchronization, offering advantages in cost and simplicity. A suitable Lyapunov fonction is employed to analyze the stability of the error system. Numerical simulations demonstrate the applicability of the proposed synchronization scheme. This investigation provides valuable insights into the synchronization dynamics of ecological networks and their potential management implications.

The goal of this work is to derive and study a Cholera model using fractional-order derivative in the sense of Atangana-Baleanu. After the model formulation, we compute the basic reproduction number and perform stability of the disease-free equilibrium whenever the basic reproduction number is less than unity. We then prove existence and uniqueness of solutions. Using Euler scheme, we perform numerical simulations to validate our theoretical results.

This work deals with the mathematical modelling of Typhoid fever disease dynamics using Caputo type fractional derivative. After the formulation of the model, we compute the basic reproduction number \(R_0\) and prove the local and global stability of the Typhoid-free equilibrium whenever \(R_0<1\). For \(R_0>1\), we prove that there exists only one endemic equilibrium which is globally asymptotically stable. Then, we prove existence and uniqueness of solution as well as its global stability using the Ulam-Hyers criterion. We finally perform numerical simulation to validate our theoretical results.

In this paper we consider a competition model between plasmid-bearing and plasmid-free organisms in a chemostat that incorporates both general response functions, distinct yields and distinct removal rates. The model with identical removal rates and identical yields was studied in the existing literature. The object of this paper is to provide the local analysis of the model in the case of different removal rates and distinct yields. In this case the conservation law fails. The operating diagram giving the asymptotic behaviour of the model with respect of the operating parameters is also presented.

A singularly perturbed model emerges when we combine a SEIRS epidemiological model whose time scale is the day, with a juvenile/adult demographic model whose time scale is the year. In this article, the combined model is used to describe the dynamics of the corona virus COVID-19, taking into account the rhythm of the start of this epidemic, which seemed to affect only adults. The 5 dimension model is reduced, by applying Tikhonov’s Theorem for slow-fast systems, to a linear or affine planar model, depending on the initial conditions, whose solutions provide an approximation of the initial solutions in their slow phases, for arbitrarily large times.

The main objective of this paper is the study of the global asymptotic stability of an interior equilibrium for a general prey-predator model with a variable mortality rate. Knowing the local asymptotic stability conditions, we give various other conditions for globality, using Lyapunov’s direct method or showing the non-existence of limit cycles by Dulac’s criterion. We also provide applications for specific models.

This paper investigates the dynamics of a chemostat model incorporating two populations of one bacterial species: susceptible and virus-infected. Through the two operating parameters of the model, represented by the input concentration of the nutrient and the dilution rate of the chemostat, we analyze the existence and stability conditions of all possible equilibria, and then describe the operating diagram of the model, which is the bifurcation diagram giving its behavior with respect to those operating parameters, that visually depicts the various regions of stability of those equilibria. This diagram gives a better understanding of the complex interplay between bacterial populations growth, viral infection and environmental factors, in a controlled environment.

Being able to predict the different transitions of vegetation mosaics in humid environments is one of the main objectives in the study of vegetation dynamics. This work attempts to model the capacity of the forest in humid tropical ecosystems, to replace grassland in landscape mosaics if no appropriate management plan is implemented. We build in one spatial dimension, a reaction-dispersion model with nonlocal dispersion and we study the long-term dynamics of forest-grassland mosaic by the mean of the traveling wave solution setting. Precisely, we prove the existence of a traveling wave that connects the forest homogeneous steady state to the grassland homogeneous steady state. We also characterise the minimal wave speed of the aforementioned forest-grassland traveling wave. Moreover, we provide numerical simulations that depict how some parameters of the model may shape variations of the minimal speed.

Let \( \varOmega \subset \mathbb {R}^N \) be a smooth bounded domain with \( 0 \in \varOmega \), \( N \ge 3 \), \( 0 \le s < 2 \), and define the critical Hardy-Sobolev exponent by \( 2^*(s) \triangleq \frac{2(N-s)}{N-2} \). In this paper, We establish the existence of positive weak solutions of the singular critical problem with Dirichlet boundary conditions on \( \varOmega \), where \( \lambda \) and \( \mu \) are positive parameters.

Anti-plane problems of elasticity theory occupy an important place in the mechanics of deformable solids, which is connected with their role in modeling of various engineering problems. This work is devoted to solving of the anti-plane problem of the elasticity theory for a strip weakened by a crack, the construction of an analytical solution of the problem through the application of the integral Fourier transform, the reduction of the original problem to one-dimensional problem and by its solving through the Green’s function. The final results are derived by the solving of the singular integral equation by the orthogonal polynomials method. The numerical solution of the problem consists in the application of reduction method and deriving the unknown jump function in the form of a series of Chebyshev polynomials. The study of displacements and stresses is made through the construction of graphic calculations for the area and the calculation of stress intensity factors for this problem under specified loads and for specific parameters of materials and crack locations.

This study explores the application of fractional calculus in enhancing the dynamics of differential system models, focusing on the time-fractional version of the Degn-Harrison model. By employing a linear controller, global synchronization of the model is achieved, showcasing the efficacy of fractional calculus in control theory. The findings are validated through numerical simulations, providing empirical evidence for the proposed approach’s effectiveness in understanding and manipulating complex dynamical systems.

A new wave of curiosity has recently focused on fractional calculus, a branch of mathematics concerned with integrals and derivatives of non-integer order. Control theory, signal processing, engineering, and physics are just a few of the areas that have benefited from its use. New control algorithms and methods have been developed thanks to the application of fractional calculus in control theory. These methods and algorithms offer advantages when dealing with complicated and non-linear systems. By incorporating a fractional order integrator and differentiator into the classical feedback adaptive PID controller, this study demonstrates how to optimize a fractional adaptive PID controller using a genetic algorithm to enhance aircraft performance in four key areas: rise time, setting time, overshoot, and mean absolute error. Research comparing the classical adaptive PID controller to the suggested genetic algorithm-optimized fractional-order adaptive PID controller has been conducted in order to substantiate the claims. In order to confirm the optimal controller, numerical simulations and analyses are provided. When comparing settling time, rising time, overshoot, and mean absolute error, the fractional order adaptive PID performs the best. To enhance the performance and noise rejection of various fractional and integer systems, this approach can also be applied generally.

In this work, we propose a new heuristic aimed at finding feasible solutions for bounded integer linear programming problems with a positive constraint matrix and right-hand side. The heuristic involves bound reduction and rounding using an auxiliary problem. Both the bound reduction and rounding steps rely on the optimal solution of the continuous relaxation. The efficiency of the proposed heuristic, in terms of execution time and solution accuracy, is demonstrated through numerical experiments.

This paper addresses the Multi-Objective Stochastic Traveling Salesman Problem (MO-STSP), where travel distances and times are modeled as stochastic variables following a uniform distribution. To manage the inherent uncertainty, the problem is first transformed into a deterministic form using the expected values of these stochastic parameters. Subsequently, heuristic methods are applied to solve the deterministic version. Specifically, two approaches are proposed: the 2-Opt local search algorithm, which iteratively refines local solutions through edge rearrangement, and Monte Carlo simulations, which explore the solution space via random sampling. Both methods were selected for their effectiveness in managing the complexities and uncertainties associated with the MO-STSP. Implemented in Python and tested on random instances, these methods provide robust solutions that balance travel distance and time. The study includes a comparative analysis of the two heuristics, highlighting their strengths and trade-offs, and suggests practical applications in logistics and transportation. This research contributes to the field of stochastic optimization by demonstrating the effectiveness of using expected values and heuristic techniques to address the MO-STSP and proposes future research directions, including the integration of advanced metaheuristics.

In order to establish chaos synchronisation with other chaotic maps, we generalize, in this study, an integer-order system proposed in 1995 to introduce a new fractional-order map. Using phase portrait, and bifurcation diagram, we establish the occurrence of chaos. The study then suggests a linear controller in order to bring two fractional-order systems into linear synchronisation. The one-dimensional and linear nature of the developed controller makes them affordable and simple to use.

The dual support method is developed by Gabasov and Kirillova for solving Linear Programming (LP) problems with finite-bounded variables. In this work, we present a version of the dual support method for solving LP problems with nonnegative variables. In order to initialize this algorithm, we propose a technique for finding a dual feasible solution, then we present a numerical example to illustrate the proposed approach.

Estimating Value-at-Risk (VaR) on time series data with potentially heteroscedastic dynamics is a complex challenge. This task often involves dealing with limited data and a high degree of non-linearity, which poses difficulties for both traditional and machine learning estimation methods. In this paper, we introduce a new Value-at-Risk estimator that leverages a long short-term memory (LSTM) neural network provides more accurate predictions of the VaR of each of the Tunindex, ADI, MASI and TASI indices. A number of previous studies have confirmed the predictive ability of a classical feedforward neural network compared to traditional statistical models. To this end, our study uses an LSMT neural network to produce forecasts of future returns which are then used to calculate the VaR through the Bootstrap Historical Simulation (BHS). The model is evaluated using the MAE. The empirical results indicate that the VaR forecasting is reassuring in the case of ADI index for the 99% or 95% VaR, but not at all in others indexes cases.