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pp. 271-282 | DOI:10.5890/JAND.2022.06.001
K. Madhusudhan Reddy, K. Kaladhar, D. Srinivasacharya
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In this paper, we investigate the effects of an inclined magnetic field, Hall current, and radiation on an incompressible mixed convection laminar flow through an inclined channel with slip conditions. Dimensionless governing equations are derived by using the suitable transformations, and the resulting system of ordinary differential equations are solved by using the spectral quasilinearization method (SQLM). The influence of emerging parameters on fluid flow velocities and temperature are presented graphically.
pp. 283-295 | DOI:10.5890/JAND.2022.06.002
M. Fardi, J. Tenreiro Machado
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The efficiency of convective straight fins with temperature dependent thermal conductivity is determined by means of the reproducing kernel (RK) method. The RK space $W^3 [0,\lambda-1]$ is constructed so that every function satisfies the boundary conditions of the problem. The representation of the exact solution is given in the form of a series and the approximation is obtained by its truncation. The paper (i) derives the error estimates, (ii) proves the convergence and (iii) develops an iterative algorithm for obtaining the solution in the space $W^3 [0,\lambda -1]$. The results obtained by the proposed method are compared with those given by schemes in previous works demonstrating a fast convergence and high precision.
pp. 297-308 | DOI: 10.5890/JAND.2022.06.003
Kenneth Dukuza
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In this paper, we construct and analyse a discrete cancer mathematical model. Essential dynamic properties such as positivity and boundedness of solutions are discussed. Using the Lyapunov stability theorem, we prove that one of the tumor-free equilibria is globally asymptotically stable. Furthermore, the discrete model exhibits chaos for certain parameter values and this is supported by the existence of a positive Lyapunov exponent. Numerical simulations are performed to demonstrate our analytical results.
pp. 309-321 | DOI: 10.5890/JAND.2022.06.004
Hiba Abouatia, Amar Guesmia, Khaled Zennir
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The main aim of this article is to study the decay rate of a system of three semilinear wave equations with strong external forces in Rn, including damping terms of memory type with past history which is very important problem from the point of view of application in sciences and engineering. We work in a weighted phase spaces where the problem is well defined and deduce a decay result depending on the relaxation functions. Using the Faedo-Galerkin method and some energy estimates, we prove the existence of global solution owing to to the weighted function. By imposing a new appropriate conditions, which are not used in the literature, with the help of some special estimates and generalized Poincar´e’s inequality, we obtain an unusual decay rate for the energy function. It is a generalization of similar results in [1] and [2] for a single equation and [3] for coupled system to the case of a system of three equations. The work is relevant in the sense that the problem is more complex than what can be found in the literature. However, the techniques involved in order to study this generalization is a combination of the techniques used in [1] in order to deal with the memory and weighted spaces with standard techniques in order to deal with coupled system with nonlinearities.
pp. 323-341 | DOI: 10.5890/JAND.2022.06.005
Van-Tu Nguyen, Xuan-Dai Nguyen
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Metallic yield damper has been considered a reliable solution for the seismic-resistant design and widely applied in recent years for construction engineering. The U-shaped device is one of the most commonly used metal yielding devices in practice, based on its benefits such as low-cost, flexible application, and high-efficiency. However, the large plastic deformation during loading making it is difficult to predict its behavior and assess its seismic performance, especially in the practical design, where a suitable estimated behavior of the device is needed. This paper aims to investigate the seismic performance of the U-shaped damper subjected to the cyclic loading in different operating directions and gives approximate formulas to estimate its nonlinear behavior for its selection and sizing in the preliminary design. Analytical procedures and 3D finite element analyses are carried out to determine the variability of the device parameters with various effects, including geometrical parameters, displacement amplitudes, and operating directions. The results present a high seismic performance of the U-shaped damper based on its great plastic deformation capacity. The best efficiency of the device corresponds to the in-plane operation. Furthermore, an approximate prediction of the nonlinear behavior of U-shaped dampers is proposed for the two orthogonal operating directions of the device by the equivalent bilinear hysteresis. The material properties, geometrical parameters, and deformation rates are considered the key parameters to predict the hysteretic behavior of the U-shaped device.
pp. 343-358 | DOI: 10.5890/JAND.2022.06.006
Abdelkarim Kelleche, Nasser-eddine Tatar
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This paper addresses the stabilization question for a nonlinear model of an axially moving string. The string is tensioned and is subject to spatiotemporary varying disturbances. The Hamilton principle of changing mass is employed to formulate mathematically the problem. By means of the Faedo{Galerkin method, we establish the well-posedness. A boundary control with a time-varying delay is designed to stabilize uniformly the string. Then, we derive a decay rate of the solution under the condition that the retarded term be dominated by the damping one. Some examples are given to clarify when the rate is exponential or polynomial.
pp. 359-374 | DOI: 10.5890/JAND.2022.06.007
Abdelatif Boutiara, Maamar Benbachir, Kaddour Guerbati
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In this paper, we study the existence and uniqueness of solutions for a nonlinear fractional boundary value problem with Caputo-adamard derivative. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using scheafer’s and krasnoselskii’s fixed point theorems. At the end, some illustrative examples are presented.
pp. 375-386 | DOI: 10.5890/JAND.2022.06.008
Fatiha Mesdoui, Nabil Shawagfeh, Adel Ouannas
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This study considers the problem of control-synchronization for chaotic systems involving fractional derivatives with a non-singular kernel. Using an extension of the Lyapunov Theorem for systems with Atangana-Baleanu-Caputo (ABC) derivative, a suitable control scheme is designed to achieve matrix projective synchronization (MP) between nonidentical ABC systems with different dimensions. The results are exemplified by the ABC version of the Lorenz system, Bloch system, and Liu system. To show the effectiveness of the proposed results, numerical simulations are performed based on the Adams-Bashforth-Mounlton numerical algorithm.
pp. 387-400 | DOI: 10.5890/JAND.2022.06.009
Matthew O. Adewole, Akindele Onifade, Ahmad Izani Md Ismail, Taye Faniran, Farah A. Abdullah
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Cholera affects populations living with poor sanitary conditions and has caused enormous morbidity and mortality. A mathematical model is presented for the spread of cholera with focus on three human populations; susceptible human, infected human and recovered human. The infected human population was subdivided into two groups - symptomatic individuals and asymptomatic individuals. We obtain the reproductive number and a sensitivity analysis of model parameters is conducted. The sensitivity analysis reveals key parameters which can be used to propose intervention strategies. Our analysis indicates that a single intervention strategy is insufficient for the eradication of the disease. Optimal control strategy is incorporated to find effective solutions for time-dependent controls for eradicating cholera epidemics. We use numerical simulations to explore various optimal control solutions involving single and multiple controls. Our results show that, as in related previous studies, the costs of controls have a direct effect on the duration and strength of each control in an optimal strategy. It is also established that a combination of multiple intervention strategies attains better results than a single-pronged approach since the strength of each control strategy is limited by available resources and social factors.
pp. 401-414 | DOI: 10.5890/JAND.2022.06.010
Driss Kiouach, Yassine Sabbar
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This paper considers the classical SIR epidemic model driven by a multidimensional Levy jump process. We consecrate to develop a mathematical method to obtain the asymptotic properties of the perturbed model. Our method differs from previous approaches by the use of the comparison theorem, mutually exclusive possibilities lemma, and some new techniques of the stochastic differential systems. In this framework, we derive the threshold which can determine the existence of a unique ergodic stationary distribution or the extinction of the epidemic. Numerical simulations about different perturbations are realized to confirm the obtained theoretical results.
pp. 415-425 | DOI: 10.5890/JAND.2022.06.011
Eihab B. M. Bashier, Hasim A. Obaid
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In this paper, the problem of controlling the transmission dynamics of HBV epidemics is formulated as an optimal control problem governed by a system of nonlinear differential equations. To reduce the HBV infection, we formulate two controls representing the increase of effort to immunize the new born individuals and isolating the infection carriers. The first order necessary conditions for optimal control are derived. The numerical simulations considered many scenarios and the controls are shown to be effective in reducing the number of infectious individuals. They showed that reducing the numbers of infected carriers can be achieved by applying the maximum controls for long periods of times and the immunization of new born individuals is more effective than isolating the infected individuals.
pp. 427-457 | DOI: 10.5890/JAND.2022.06.012
Subhashis Das, Prasenjit Mahato, Sanat Kumar Mahato, Debkumar Pal
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Background & objectives: Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2) is a highly infectious virus which causes the severe respiratory disease for human also known as Coronavirus Disease (COVID) emerged in China in December 2019 that spread rapidly all over the world. As there is no proper medicine or vaccine against the virus SARS-CoV-2 or COVID-19 to control the spread of the virus, all the countries are taking many steps as preventive measures, like lockdown, stay-at-home, social distancing, sanitization, use of mask, etc. For almost three months of lockdown many countries are relaxing the lockdown period and the movement of people. The objective of this study is to develop a new mathematical model, called the SEIQRS model in imprecise environment and to find out the essentiality of quarantine, stay-at-home orders, lockdown as precautionary measures to protect the human community.
Methods: In this study, after developing the COVID-19 SEIQRS model, the SEIQRS fuzzy model and the SEIQRS interval model are constructed by taking parameters as triangular fuzzy numbers and interval numbers respectively. Solution curves are drawn for two imprecise models by using MATLAB R2014a software package and the sensitivity analysis is also performed with respect to the control parameters. The next generation matrix approach is adopted to calculate the basic reproduction number $(R_0)$ from the SEIQRS model to assess the transmissibility of the SARS-CoV-2.
Results: The basic reproduction number $(R_0)$ is calculated for this model and to get the stability and disease free equilibrium the value of the basic reproduction number must be less than 1. Also, we find the solution curves in different uncertain environments and sensitivity studies show the importance of newly added population (α), rate of spreading asymptomatic infection (β ), rate of developing symptoms of infection (λ ), proportion of infected population in quarantine (γ ).
Interpretation & conclusions: Our model shows that quarantine, lockdown are essential to control the spread of the disease as at present there is no such medicine or vaccine to combat COVID-19. Once the virus establishes transmission within the community, it will very difficult to stop the infection. As a measure of public health, healthcare and community preparedness, it would be serious to control any impending outbreak of COVID-19 in the country.
pp. 459-471 | DOI: 10.5890/JAND.2022.06.013
S. ElFadily, A. Kaddar, K. Najib
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The relationship between demographic change and economic growth is a topical subject that has always attracted the interest of researchers. Given the fluctuations in economic and demographic variables, studing and analysing the direct relationship (cause and effect relationship) between economic growth and population is complex one. In the same line, the present paper aims at analising this relationships by increasing the dynamic of the Solow economic growth model with three demographic variables and considering two time delays. The study investigates the stability of positives equilibria and the existence of limit cycles by using Hopf bifurcation theorem. The role of the time delays in the variables of the proposed model and possible links between them at various phases (stability, limit cycle and instability) are also examined in this study. Finally, to illustrate our analytical results, some numerical simulations are presented.
pp. 473-485 | DOI: 10.5890/JAND.2022.06.014
Alborz Niknam, Kambiz Farhang
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A well-known 2-DOF mass-on-belt model is used to investigate friction-induced vibration. By employing a Kelvin-Voigt de nition to simulate viscoelastic contact interface, e ects of contact modeling on the stability of a linearized system and sustain vibrations of the nonlinear system, such as stick-slip and contact detachment are studied. In addition, the e ect of a hardening nonlinear contact stiffness on transient and steady-state system responses has been discussed. Horizontal friction force is a function of vertical displacement and velocity through viscoelastic de nition of contact. Contact detachment, where friction force disappears, is another source of nonlinearity and considered in governing equations. Eigenvalue analysis is performed to show the e ect of viscoelastic/nonlinear contact on the stability of a linearized system. Numerical analysis is employed to solve Filippov systems of equations of motion with di erent possible phases in a cycle, i.e. slip, stick and separation. Results show that viscoelasticity at the contact interface plays a crucial role in the local stability of the linearized system and vertical sustained oscillation.
pp. 487-497 | DOI: 10.5890/JAND.2022.06.015
Eric Donald Dongmo, Kayode Stephen Ojo, Paul Woafo, Abdulahi Ndzi Njah
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This paper investigates a new synchronization Difference-Difference Synchronization (DDS), based on drive response configuration via the active backstepping technique. In this new synchronization scheme, the difference between the state variables of two master systems synchronizes with the difference between the state variables of two response systems. The proposed DDS scheme is investigated using four chaotic systems and four hyperchaotic systems evolving from different initial conditions. The analytical and numerical simulations show the feasibility and the effectiveness of the proposed synchronization scheme.