Journal of Applied Mathematics

Published by Hindawi
Online ISSN: 1687-0042
Print ISSN: 1110-757X
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In this paper, the population dynamics of rabies-infected dogs are studied. The mathematical model is constructed by dividing the dog population into two categories: stray dogs and domestic dogs. On the other hand, the rabies virus is likely to spread in both populations. In the current model, disease-controlling strategies such as vaccination and culling are applied, and their impact is studied. Both subpopulations of susceptible individuals are vaccinated to control disease spread. The current study assumes that stray dogs can transmit rabies to domestic dogs but not the other way around. Because domestic dogs are under the control of their owners, they are well vaccinated. The model is medically and analytically correct because the findings are idealistic and limited. The next-generation matrix technique is used to compute the effective reproductive amount, and also, each parameter is subjected to sensitivity analysis. The equilibrium point free from disease is discovered, demonstrating that it was asymptotically steady locally and globally. A conditionally global asymptotically stable point of endemic equilibrium is also discovered using the Lyapunov function method. The numerical simulation, which makes use of approximations for parameter values, shows that the most efficient method for avoiding rabies transmission is a combination of vaccination and the culling of infected stray dogs. Using MATLAB’s ode45, this numerical simulation investigation was carried out. Our early findings indicated that the annual dog birth rate is a critical factor in influencing the occurrence of rabies. In the body of the paper, the findings and discussion are organized logically.
We introduce the delayed Mittag-Leffler type matrix functions, delayed fractional cosine, and delayed fractional sine and use the Laplace transform to obtain an analytical solution to the IVP for a Hilfer type fractional linear time-delay system D 0 , t μ , ν z t + A z t + Ω z t − h = f t of order 1 < μ < 2 and type 0 ≤ ν ≤ 1 , with nonpermutable matrices A and Ω . Moreover, we study Ulam-Hyers stability of the Hilfer type fractional linear time-delay system. Obtained results extend those for Caputo and Riemann-Liouville type fractional linear time-delay systems with permutable matrices and new even for these fractional delay systems.
In this paper, we study the flow of two immiscible fluids namely, couple stress fluid and Jeffrey fluid in a porous channel. Instead of the classical no-slip conditions on the boundaries, we used slip boundary conditions, which are more realistic and meaningful. In addition, we used inclined magnetic field effects on the fluid flow. The couple stress fluid and Jeffrey fluid are flowing adjacent to each other in the region I and in the region II, respectively, of the horizontal porous channel. The nondimensionalized governing equations are solved analytically by using slip conditions at the lower and upper boundaries and interface conditions at the fluid-fluid interface. The analytical expressions for the velocity components in both regions are obtained in closed form. The effects of slip parameter, Hartmann number, couple stress parameter, Jeffrey parameter, angle of inclination, and Darcy number on velocity components in both regions are investigated. In the absence of slip, couple stress parameter, and Jeffrey parameters, limiting cases are obtained and discussed.
In this article, the effect of electromagnetic force with the chemical and thermal radiation effect on the Oldroyd-B fluid past an exponentially stretched sheet with a heat sink and porous medium was studied. The governing system of nonlinear partial differential equations has transformed into a system of ordinary differential equations using similarity transformations. The system is then solved numerically using a successive linearization method. The numerical results of velocity, temperature, and concentration profiles are represented graphically. Several parameters’ effects are investigated and examined. Local Nusselt number, skin friction coefficient, porosity, Deborah numbers, and local Sherwood number numerical values are listed and analyzed. The results reveal that many parameters have a significant impact on the fluid flow profiles. The concentration profiles were considerably affected by the reaction rate parameter, and the concentration thickness of the boundary layer decreased as the reaction rate parameter increased. The results of the analysis were compared to the results of existing works and found to be in excellent agreement.
We provide sufficient conditions for the existence of periodic solutions for an idealized electrostatic actuator modeled by the Liénard-type equation x ¨ + F D x , x ̇ + x = β V 2 t / 1 − x 2 , x ∈ − ∞ , 1 with β ∈ ℝ + , V ∈ C ℝ / T ℤ , and F D x , x ̇ = κ x ̇ / 1 − x 3 , κ ∈ ℝ + (called squeeze film damping force), or F D x , x ̇ = c x ̇ , c ∈ ℝ + (called linear damping force). If F D is of squeeze film type, we have proven that there exists at least two positive periodic solutions, one of them locally asymptotically stable. Meanwhile, if F D is a linear damping force, we have proven that there are only two positive periodic solutions. One is unstable, and the other is locally exponentially asymptotically stable with rate of decay of c / 2 . Our technique can be applied to a class of Liénard equations that model several microelectromechanical system devices, including the comb-drive finger model and torsional actuators.
Modelling population dynamics in ecological systems reveals properties that are difficult to find by empirical means, such as the probability that a population will go extinct when it is exposed to harvesting. To study these properties, we use an aquatic ecological system containing one fish species and an underlying resource as our models. In particular, we study a class of stage-structured population systems with and without starvation. In these models, we study the resilience, the recovery potential, and the probability of extinction and show how these properties are affected by different harvesting rates, both in a deterministic and stochastic setting. In the stochastic setting, we develop methods for deriving estimates of these properties. We estimate the expected outcome of emergent population properties in our models, as well as measures of dispersion. In particular, two different approaches for estimating the probability of extinction are developed. We also construct a method to determine the recovery potential of a species that is introduced in a virgin environment.
Vector field (10): lengths of arrows indicate the rate at which flow is proceeding toward K=1−I.
Integral curves of the vector field (10) in the invariant region Ω.
Integral curves of (10) in the complement of Ω impinging into different equilibrium points
Quasisimple wave solutions of Euler’s system of equations for ideal gas are investigated under the assumption of spherical and cylindrical symmetries. These solutions are proved to be stabilized into sound wave solutions and cavitation. It is proved that if initial conditions from outside the invariant region approach to transitional solution, then reciprocal of the self-similar parameter goes to infinity. However, when initial conditions stabilize into sound waves or cavitation, then reciprocal of self-similar parameter approaches finite value. Further, it is proved that initial conditions can be parametrized so that some of the initial conditions stabilize into sound wave solutions. The rest of the initial conditions are proved to be stabilized into cavitation. This extends the work of G. I. Taylor to the case of cavitation. It is proved that quasisimple wave solutions exist for the balance laws comprised of Euler’s system of equations in the case of cylindrically and spherically symmetric cases. The description applies to the motion of cylindrical and spherical piston in real life. In particular, self-similar description of appearance of vacuum in the motion of cylindrical and spherical piston is given.
The paper studies the dynamics of a full delay-logistic population model incorporated with a proportionate harvesting function. The study discusses the stability of the model in comparison with the well-known Hutchinson logistic growth equation with harvesting function using the rate of harvesting as a bifurcation parameter to determine sustainable harvesting rate even at a bigger time delay of τ = 3:00. In all cases, the Hutchinson equation with harvesting was forced to converge to equilibrium using an additional and a different time delay parameter, a deficiency previous researchers have failed to address when the Hutchinson model is used for this purpose. The population fluctuations are catered for with this model making the estimated maximum sustainable growth and harvest reflect realities as this model drastically reduces time-delay associated oscillations compared to the well-known Hutchinson delayed logistic models. The numerical simulations were be done using the MatLab Software.
This paper explores the impact of chemical reaction and thermal radiation on time-dependent hydromagnetic thin-film flow of a second-grade fluid across an inclined flat plate embedded in a porous medium. The thermal radiation based on the Rosseland approximation is incorporated in the energy equation. Uniform applied magnetic field and first-order homogenous chemical reaction are included in the momentum and concentration equations, respectively. The novel mathematical flow model is constructed by using a set of partial differential equations (PDEs). The PDEs are then transformed into an equivalent set of ordinary differential equations (ODEs) and solved by applying the Laplace transform method. However, the time domain solutions are obtained by using the INVLAP subroutine of MATLAB. Physical parameters influencing thin-film velocity, temperature, and concentration are illustrated graphically, while those affecting skin friction, heat, and mass transfer rates are presented in a tabular form. It is found that thin-film velocity and temperature boost with increasing values of thermal radiation, but thin-film velocity decreases with increasing values of chemical reaction and magnetic field. The current investigation is to enhance heat and mass transfer in the design of mechanical systems involving the thin film flow of second-grade fluids over an inclined flat plate after applying thermal radiation and chemical reaction.
In this paper, a coupled system of two transport equations is studied. The techniques are a fixed-point and Space-Time Integrated Least Square (STILS) method. The nonstationary advective transport equation is transformed to a “stationary” one by integrating space and time. Using a variational formulation and an adequate Poincare inequality, we prove the existence and the uniqueness of the solution. The transport equation with a nonlinear feedback is solved using a fixed-point method.
The outbreak of the Coronavirus (COVID-19) pandemic around the world has caused many health and socioeconomic problems, and the identification of variants like Delta and Omicron with similar and often even more transmissible modes of transmission has motivated us to do this study. In this article, we have proposed and analyzed a mathematical model in order to study the effect of health precautions and treatment for a disease transmitted by contact in a constant population. We determined the four equilibria of the system of ordinary differential equations representing the model and characterized their existence using exact methods of algebraic geometry and computer algebra. The model is studied using the stability theory for systems of differential equations and the basic reproduction number R 0 . The stability of the equilibria is analyzed using the Lienard-Chipart criterion and Lyapunov functions. The asymptotic or global stability of endemic equilibria is established, and the disease-free equilibrium is globally asymptotically stable if R 0 < 1 . Model simulation is done with Python software to study the effects of health precautions and treatment, and the results are analyzed. It is observed that if the rate of treatment and compliance with health precautions are high, the number of infections decreases in the classes of infectious and is canceled out over time. It is concluded that the high treatment rate accompanied by a suitable rate of compliance with health precautions allows for the control the disease.
In this paper, the transmission dynamics of cotton leaf curl virus (CLCuV) disease in cotton plants was proposed and investigated qualitatively using the stability theory of a nonlinear ordinary differential equations. Cotton and vector populations were both taken into account in the models. Cotton population was categorized as susceptible (A) and infected (B). The vector population was also categorized as susceptible (C) and infected (D). We established that all model solutions are positive and bounded by relevant initial conditions. The existence of unique CLCuV free and endemic equilibrium points, as well as the basic reproduction number, which is computed using the next generation matrix approach, are investigated. The conditions for the local and global asymptotic stability of these equilibrium points are then established. When the basic reproduction number is less than one, the system has locally and globally asymptotically stable CLCuV free equilibrium point, but when the basic reproduction number is more than one, the system has locally and globally asymptotically stable endemic equilibrium point. The numerical simulation findings show that lowering the infection rate of cotton vectors has a significant impact on controlling cotton leaf curl virus (CLCuV) in the time frame given.
In this paper, we apply Markov chain techniques to select the best financial stocks listed on the Ghana Stock Exchange based on the mean recurrent times and steady-state distribution for investment and portfolio construction. Weekly stock prices from Ghana Stock Exchange spanning January 2017 to December 2020 was used for the study. A three-state Markov chain was used to estimate the transition matrix, long-run probabilities, and mean recurrent times for stock price movements from one state to another. Generally, the results revealed that the long-run distribution of the stock prices showed that the constant state recorded the highest probabilities as compared to the point loss and point gain states. However, the results showed that the mean recurrent time to the point gain state ranges from three weeks to thirty-five weeks approximately. Finally, Standard Chartered Bank, GCB, Ecobank, and Cal Bank emerged as the top best performing stocks with respect to the mean recurrent times and steady-state distribution, and therefore, these equities should be considered when constructing asset portfolios for higher returns.
An irreversible conversion process is a dynamic process on a graph where a one-way change of state (from state 0 to state 1) is applied on the vertices if they satisfy a conversion rule that is determined at the beginning of the study. The irreversible k -threshold conversion process on a graph G = V , E is an iterative process which begins by choosing a set S 0 ⊆ V , and for each step t t = 1 , 2 , ⋯ , , S t is obtained from S t − 1 by adjoining all vertices that have at least k neighbors in S t − 1 . S 0 is called the seed set of the k -threshold conversion process, and if S t = V G for some t ≥ 0 , then S 0 is an irreversible k -threshold conversion set (IkCS) of G . The k -threshold conversion number of G (denoted by ( C k G ) is the minimum cardinality of all the IkCSs of G . In this paper, we determine C 2 G for the circulant graph C n 1 , r when r is arbitrary; we also find C 3 C n 1 , r when r = 2 , 3 . We also introduce an upper bound for C 3 C n 1 , 4 . Finally, we suggest an upper bound for C 3 C n 1 , r if n ≥ 2 r + 1 and n ≡ 0 mod 2 r + 1 .
In this paper, a high security color image encryption algorithm is proposed by 2D Sin-Cos-Hénon (2D-SCH) system. A new two-dimensional chaotic system which is 2D-SCH. This system is hyperchaotic. The use of the 2D-SCH, a color image encryption algorithm based on random scrambling and localization diffusion, is proposed. First, the secret key is generated by SHA512 through plaintext. As the initial value of the 2D-SCH system, the secret key is used to generate chaotic sequences. Then, the random scrambling is designed based on chaotic sequences. Finally, a pair of initial points is generated by the secret key; the image diffuses around this point. The ciphertext is obtained by a double encryption. Different from the traditional encryption algorithm, this paper encrypts three channels of color image simultaneously, which greatly improves the security of the algorithm. Simulation results show that the algorithm can resist various attacks.
Plots of modified Merton value function and the value function in the three regions with λ=0.5. μ1=0.02,μ2=0.2,σ1=0.25,σ2=0.5,r1=0.09,ρ=3,p=0.5, and β=0.2. Then, the portfolio becomes θ=0.8286.
Plots of modified Merton value function and the value function in the three regions with λ=0.5. μ1=0.02,μ2=0.2,σ1=0.25,σ2=0.5,r1=0.09,ρ=3,p=0.5, and β=0.2. Then, the portfolio becomes θ=0.8286.
We consider a problem of maximizing the utility of an agent who invests in a stock and a money market account incorporating proportional transaction costs λ > 0 and foreign exchange rate fluctuations. Assuming a HARA utility function U c = c p / p for all c ≥ 0 , p < 1 , p ≠ 0 , we suggest an approach of determining the value function. Contrary to fears associated with exchange rate fluctuations, our results show that these fluctuations can bring about tangible benefits in one’s wealth. We quantify the level of these benefits. We also present an example which illustrates an investment strategy of our agent.
In this paper, we construct and analyze a theoretical, deterministic 5 D mathematical model of Limnothrissa miodon with nutrients, phytoplankton, zooplankton, and Hydrocynus vittatus predation. Local stability analysis results agree with the numerical simulations in that the coexistence equilibrium is locally stable provided that certain conditions are satisfied. The coexistence equilibrium is globally stable if certain conditions are met. Existence, stability, and direction of Hopf bifurcations are derived for some parameters. Bifurcation analysis shows that the model undergoes Hopf bifurcation at the coexistence point for the zooplankton growth rate with periodic doubling leading to chaos.
In this paper, we propose a continuous mathematical model that describes the spread of multistrains COVID-19 virus among humans: susceptible, exposed, infected, quarantined, hospitalized, and recovered individuals. The positivity and boundedness of the system solution are provided in order to get the well posedness of the proposed model. Secondly, three controls are considered in our model to minimize the multistrain spread of the disease, namely, vaccination, security campaigns, social distancing measures, and diagnosis. Furthermore, the optimal control problem and related optimality conditions of the Pontryagin type are discussed with the objective to minimize the number of infected individuals. Finally, numerical simulations are performed in the case of two strains of COVID-19 and with four control strategies. By using the incremental cost-effectiveness ratio (ICER) method, we show that combining vaccination with diagnosis provides the most cost-effective strategy
Faces are widely used in information recognition and other fields. Due to the openness of the Internet, ensuring that face information is not stolen by criminals is a hot issue. The traditional encryption method only encrypts the whole area of the image and ignores some features of the face. This paper proposes a double-encrypted face image encryption algorithm. The contour features of the face are extracted, followed by two rounds of encryption. The first round of encryption algorithm encrypts the identified face image, and the second round of encryption algorithm encrypts the entire image. The encryption algorithm used is scrambling and diffusion at the same time, and the keystream of the cryptosystem is generated by 2D SF-SIMM. The design structure of this cryptosystem increases security, and the attacker needs to crack two rounds of the algorithm to get the original face image.
The bare rudiments of the principle of mathematical induction as a method of proof date back to ancient times. In the contemporary university milieu, the demonstrative scheme is taught as part of a course in discrete mathematics, set theory, number theory, graph theory, group theory, game theory, linear algebra, logic, and combinatorics. In theoretical computer science, it bears the pivotal role of developing the appropriate cognitive skills necessary for the effective design and implementation of algorithms, assessing for both their correctness and complexity. Pure mathematics and computer science aside, the scope of its utility in the physical sciences remains limited. Following an outline of some elementary concepts from vector algebra and phasor analysis, the proofs by induction of a couple of salient results in multiple-slit interferometry are presented, viz., the fringe intensity distribution formula and the upper bound of the total fringe count. These specific optical instantiations serve to illustrate the versatility and power of the principle at tackling real-world problems. It thereby makes a welcome departure from the popular view of induction as a mere last resort for proving abstract mathematical statements.
Nonlinear heat equation solved by the barycentric rational collocation method (BRCM) is presented. Direct linearization method and Newton linearization method are presented to transform the nonlinear heat conduction equation into linear equations. The matrix form of nonlinear heat conduction equation is also obtained. Several numerical examples are provided to valid our schemes.
In this paper, we present a new method to establish the oscillation of advanced second-order difference equations of the form Δ(η(ℓ)Δυ(ℓ))+ρ(ℓ)υ(σ(ℓ))=0, using the ordinary difference equation Δ(η(ℓ)Δυ(ℓ))+q(ℓ)υ(ℓ+1)=0. The obtained results are new and improve the existing criteria. We provide examples to illustrate the main results.
We study the triangular equilibrium points in the framework of Yukawa correction to Newtonian potential in the circular restricted three-body problem. The effects of α and λ on the mean-motion of the primaries and on the existence and stability of triangular equilibrium points are analyzed, where α ∈ − 1 , 1 is the coupling constant of Yukawa force to gravitational force, and λ ∈ 0 , ∞ is the range of Yukawa force. It is observed that as λ ⟶ ∞ , the mean-motion of the primaries n ⟶ 1 + α 1 / 2 and as λ ⟶ 0 , n ⟶ 1 . Further, it is observed that the mean-motion is unity, i.e., n = 1 for α = 0 , n > 1 if α > 0 and n < 1 when α < 0 . The triangular equilibria are not affected by α and λ and remain the same as in the classical case of restricted three-body problem. But, α and λ affect the stability of these triangular equilibria in linear sense. It is found that the triangular equilibria are stable for a critical mass parameter μ c = μ 0 + f α , λ , where μ 0 = 0.0385209 ⋯ is the value of critical mass parameter in the classical case of restricted three-body problem. It is also observed that μ c = μ 0 either for α = 0 or λ = 0.618034 , and the critical mass parameter μ c possesses maximum ( μ c max ) and minimum ( μ c min ) values in the intervals − 1 < α < 0 and 0 < α < 1 , respectively, for λ = 1 / 3 .
This article addresses the hydrodynamic boundary layer flow of a chemically reactive fluid over an exponentially stretching vertical surface with transverse magnetic field in an unsteady porous medium. The flow problem is modelled as time depended dimensional partial differential equations which are transformed to dimensionless equations and solved by means of approximate analytic method. The results are illustrated graphically and numerically and compared with previously published results which shown a good agreement. Physically increasing Eckert number of a fluid amplifies the kinetic energy of the fluid, and as a novelty, the Eckert number under the influence of chemically reactive magnetic field is effective in controlling the kinematics of hydrodynamic boundary layer flow in porous medium. Interestingly, whilst the Eckert number amplifies the thermal boundary layer thickness and velocity as well as the concentration of the fluid, the presence of the magnetic field and the strength of the chemical reaction have a retarding effect on the flow. Also, the chemical reaction parameter and permeability of porous medium are effective in reducing skin friction in chemically reactive magnetic porous medium and are relevant in practice because reduced skin friction enhances the efficiency of a system. The results of the current study are useful in solar energy collector systems and materials processing.
Compartment model for COVID-19.
Dynamical simulation of St,Et, and Qt for the deterministic system (1) and stochastic system (2) with the parameter’s value presented in Table 1 and noise parameter values: σ1=0.6, σ2=0.7, σ3=0.6, σ4=0.6, σ5=0.6, π1α=0.01, π2α=0.1, π3α=0.04, π4α=0.01, and π5α=0.01.
Dynamical simulation of Et for the deterministic system (1) and stochastic system (2) with the parameter’s value presented in Table 1 and noise parameter values: σ1=0.2, σ2=0.2, σ3=0.1, σ4=0.1, σ5=0.1, π1α=0.01, π2α=0.1, π3α=0.04, π4α=0.01, and π5α=0.01.
At the end of 2019, the world knew the propagation of a new pandemic named COVID-19. This disease harmed the exercises of humankind and changed our way of life. For modeling and studying infectious illness transmission, mathematical models are helpful tools. Thus, in this paper, taking into account the effect of the intensity of the noises, we define a threshold value Π s of the model, which determines the extinction and persistence of the COVID-19 pandemic. We give numerical simulations to illustrate the analytical results.
In recent times, all world banks have been threatened by the liquidity risk problem. This phenomenon represents a devastating financial threat to banks and may lead to irrecoverable consequences in case of negligence or underestimation. In this article, we study a mathematical model that describes the contagion of liquidity risk in the banking system based on the SIR epidemic model simulation. The model consists of three ordinary differential equations illustrating the interaction between banks susceptible or affected by liquidity risk and tending towards bankruptcy. We have demonstrated the bornness and positivity of the solutions, and we have mathematically analyzed this system to demonstrate how to control the banking system’s stability. Numerical simulations have been illustrated by using real data to support the analytical results and prove the effects of different system parameters studied on the contagion of liquidity risk.
This paper demonstrates the applicability of the large parameter spectral perturbation method (LSPM) to a coupled system of partial differential equations that cannot be solved exactly. The LSPM is a numerical method that employs the Chebyshev spectral collocation method in the solution of a sequence of ordinary differential equations (ODEs) that are derived from decomposing coupled systems of nonlinear partial differential equations (PDEs) using series expansion about a large parameter. The validity of the LSPM is applied to the problem of boundary layer flow and heat transfer in a micropolar fluid past a permeable flat plate in the presence of heat generation and thermal radiation. The coupled nature of the PDEs that define the problem under investigation precludes the option of using series-based methods that seek to generate analytical solutions even in the presence of small or large parameters. The present study demonstrates that the LSPM can easily overcome this limitation while giving very accurate results in a computationally efficient manner. For qualitative validation of the results and the numerical method used, calculations were carried out to graphically obtain the velocity, microrotation, and temperature profiles for selected physical parameter values. The results obtained were found to correlate with the results from a published literature. For quantitative confirmation of our findings, the LSPM numerical solutions were again validated against known results from the literature and against results obtained using the multidomain bivariate spectral quasilinearisation method (MD-BSQLM), and the results were observed to be in perfect agreement. Further accuracy validation is displayed by using residual error and solution error analysis on the governing PDEs and their underlying solutions. This study’s findings indicate that the heat generation and thermal radiation parameters have related effects on the temperature profile, enhancing both the fluid temperature and the thermal boundary layer thickness.
Maximum 1/cosθBo/Oh for monotone rise.
Maximum b to maintain monotone rise for water at 20°C and the corresponding equilibrium height.
In this note, the dimensions of elliptic and semielliptic tubes in which the capillary rise starts oscillating about its Jurin’s height are determined. Comparisons with the capillary rise in the classical circular and in semicircular tubes are made.
Minimizing a sum of Euclidean norms (MSEN) is a classic minimization problem widely used in several applications, including the determination of single and multifacility locations. The objective of the MSEN problem is to find a vector x such that it minimizes a sum of Euclidean norms of systems of equations. In this paper, we propose a modification of the MSEN problem, which we call the problem of minimizing a sum of squared Euclidean norms with rank constraint, or simply the MSSEN-RC problem. The objective of the MSSEN-RC problem is to obtain a vector x and rank-constrained matrices A 1 , ⋯ , A p such that they minimize a sum of squared Euclidean norms of systems of equations. Additionally, we present an algorithm based on the regularized alternating least-squares (RALS) method for solving the MSSEN-RC problem. We show that given the existence of critical points of the alternating least-squares method, the limit points of the converging sequences of the RALS are the critical points of the objective function. Finally, we show numerical experiments that demonstrate the efficiency of the RALS method.
Hepatitis B and HIV/AIDS coinfections are common globally due to their similar mode of transmission. Since HIV infection modifies the course of HBV infection by increasing the rate of chronicity, prolonging HBV viremia, and increasing liver disease-associated deaths, individuals with coinfection of both diseases have a higher tendency of developing cirrhosis of the liver, higher levels of HBV DNA, reduced rate of clearance of the hepatitis B e antigen (HBeAg), and more likely to die than an individual with a single infection. This nature of HBV-HIV/AIDS coinfection motivated us to conduct this study. In this paper, we proposed and rigorously analyzed a deterministic mathematical model with the aim of investigating the effect of vaccination against hepatitis B virus and treatment for all infections on the transmission dynamics of HBV-HIV/AIDS coinfection in a population. We proved that the solutions of the submodels and the coinfection model are positive and bounded. The models are studied qualitatively using the stability theory of differential equations, and the effective reproduction numbers of the models are derived using the next generation matrix method. Stability of the equilibria of the submodels and the coinfection model is analyzed using Routh-Hurwitz criteria. The disease-free and endemic equilibria of the submodels and the coinfection model are computed, and both local and global asymptotic stability conditions for those equilibria are discussed. We performed a sensitivity analysis to illustrate the influence of different parameters on the effective reproduction number of HBV-HIV/AIDS coinfection model, and we identified the most sensitive parameters are ωB and ωH, which are the effective contact rates for HBV and HIV transmission, respectively. The numerical simulation of the model is done using MATLAB, and the findings from the simulations are discussed. It is observed that if the vaccination and treatment rates are increased, then the number of individuals susceptible to both infections and HBV-HIV/AIDS coinfection decreases and even falls to zero over time. Hence, it is concluded that vaccination against hepatitis B virus infection, treatment of hepatitis B and HIV/AIDS infections, and HBV-HIV/AIDS infection at the highest possible rate is very essential to control the spread of HBV-HIV/AIDS coinfection as an important public health problem.
This paper deals with an initial-boundary value problem in a quarter-plane for the nonlinear one-dimensional Kawahara equation. For reasonable boundary conditions we prove the existence and uniqueness of a global regular solution. We also show that the rate of decay of the obtained solution as x → ∞ does not depend on time-variable and is the same as one of the initial data. Mathematics Subject Classification numbers: 35M20, 35Q72
Approximate solutions and its corresponding absolute errors at different degrees of approximation m.
Approximate solution for Example 2 and its absolute errors.
Approximate solutions and its absolute errors.
The approximate solution for Example 4 and its absolute errors at different values of m.
In this paper, perturbed Galerkin method is proposed to find numerical solution of an integro-differential equations using fourth kind shifted Chebyshev polynomials as basis functions which transform the integro-differential equation into a system of linear equations. The systems of linear equations are then solved to obtain the approximate solution. Examples to justify the effectiveness and accuracy of the method are presented and their numerical results are compared with Galerkin’s method, Taylor’s series method, and Tau’s method which provide validation for the proposed approach. The errors obtained justify the effectiveness and accuracy of the method.
Rainfall intensity prediction or forecast is vital in designing hydraulic structures and flood and erosion control structures. In this work, meteorological data were obtained from the National Aeronautics and Space Administration's (NASA) website. Models estimating maximum rainfall intensities were derived, and some meteorological factors' effects on the models were tested. The meteorological factors considered include annual relative humidity averages, specific humidity, temperature range at 2 m, maximum temperature, and minimum temperature. This research was aimed at developing a model for estimating maximum rainfall intensities, and the effects of various meteorological factors on the models were investigated. The exponentiated standardized half logistic distribution (ESLD) was used to model the effects of the factors and return periods on 35 years' (1984-2018) annual maxima monthly rainfall intensities for Port Harcourt metropolis, Nigeria. The model parameters were estimated using the maximum likelihood estimation method. Compared with the results from the five standard distributions, three criteria were used to determine the best-performed distribution. These indicated that the ESLD performed considerably better than the other five compared distributions. Only the return period had significant effects on the model for the rainfall intensity prediction since p < 0:05, while the effects of the meteorological factors are insignificant.
Fractured porous media modeling and simulation has seen significant development in the past decade but still pose a great challenge and difficulty due to the multiscale nature of fractures, domain heterogeneity, and the nonlinear flow fields due to the high flow velocity and permeability resulting from the presence of fractures. Therefore, modeling fluid transport that is influenced by both advection and diffusion in fractured porous media studies becomes a generic problem, which this study seeks to address. In this paper, we present a study on non-Darcian fluid transport in multiscale naturally fractured reservoirs via an upscaling technique. An averaged macroscopic equation representing pressure distribution in a three-phase multiscale fractured porous medium was developed, consisting of the matrix and a 2-scale fractured network of length-scales ℓ m and ℓ M . The resulting macroscopic model has cross-advective and diffusive terms that account for induced fluxes between the interacting domains, as well as a mass transfer function that is dependent on both physical and geometric properties of the domain, with both advective and diffusive properties. This model also has effective diffusive and advective coefficients that account for reservoir properties such as viscosity, fluid density, and flow velocity. From the numerical simulation, a radial, a horizontal-linear flow behavior, and a transient and quasi-steady-state flow regime that is typical of naturally fractured porous media was observed. The findings of this study will provide researchers a reliable tool to study fractured porous media and can also help for better understanding of the dynamics of flow in fractured reservoirs.
Tuberculosis (TB) and coronavirus (COVID-19) are both infectious diseases that globally continue affecting millions of people every year. They have similar symptoms such as cough, fever, and difficulty breathing but differ in incubation periods. This paper introduces a mathematical model for the transmission dynamics of TB and COVID-19 coinfection using a system of nonlinear ordinary differential equations. The well-posedness of the proposed coinfection model is then analytically studied by showing properties such as the existence, boundedness, and positivity of the solutions. The stability analysis of the equilibrium points of submodels is also discussed separately after computing the basic reproduction numbers. In each case, the disease-free equilibrium points of the submodels are proved to be both locally and globally stable if the reproduction numbers are less than unity. Besides, the coinfection disease-free equilibrium point is proved to be conditionally stable. The sensitivity and bifurcation analysis are also studied. Different simulation cases were performed to supplement the analytical results.
We present a computational framework for the parallel implementation of a local-scale air quality model described by an advection-diffusion-reaction partial differential equation, the so-called equation of reactive dispersion. The temporal discretization of the model is carried out using the forward Euler scheme. The spatial discretization is achieved using the finite element method. The strategy used for the parallel implementation is based on the distributed-memory approach using the message-passing library MPI. The simulations are focused on two road traffic-related air pollutants, namely particulate matters PM2.5 and PM10. The efficiency and the scalability of the parallel implementation are illustrated by numerical experiments performed using up to 128 processor cores of a cluster computing system.
In this paper, we analyze an M/G/1 priority queueing model with finite and infinite buffers under the N,n-preemptive priority discipline, under which preemption decisions are made based on the number of high-priority customers. This priority queueing model can be used for the performance analysis of communication systems accommodating delay- and loss-sensitive packets simultaneously. To analyze the proposed model, we extend the method of delay cycle analysis and develop a queue length version of it for finite-buffer queues. Throughout our analysis, we demonstrate that by the proposed method the analysis of the complex priority queueing model can be reduced to that of simple delay cycles, so two different preemption modes of the queueing model can be dealt with in a unified way. The numerical study reveals that adjusting the decision variables N and n allows us to fine-tune system performance for different classes of customers, and N operates as a primary control variable, regardless of the preemption mode and service-time distributions.
Velocity field, respectively, for g=1 and g=4.
Velocity field, respectively, for g=1 and g=4.
L2-error estimate, respectively, for mesh size h and time step k.
L2-error estimate, respectively, for mesh size h and time step k.
This paper is devoted to the study of numerical approximation for a class of two-dimensional Navier-Stokes equations with slip boundary conditions of friction type. The objective is to establish the well-posedness and stability of the numerical scheme in L 2 -norm and H 1 -norm for all positive time using the Crank-Nicholson scheme in time and the finite element approximation in space. The resulting variational structure dealing with is in the form of inequality, and obtaining H 1 -estimate is more involved because of the presence of the nondifferentiable term appearing at the boundary where slip occurs. We prove that the numerical scheme is stable in L 2 and H 1 -norms with the aid of different versions of discrete Grownwall lemmas, under a CFL-type condition. Finally, some numerical simulations are presented to illustrate our theoretical analysis.
The box plots for the volatilities obtained from the three methods.
Time series plots of exchange rates by country. Source: FRED, 2000-2020.
Time series plot of growth rates by country. Source: FRED, 2000-2020.
Trend analysis plots of the moving volatilities in exchange rate by country. Source: FRED, 2000-2020.
Trend analysis plots of moving volatilities of growth rate by country. Source: FRED, 2000-2020.
The main objective of this study is to propose a method of analysing the volatility of a seemingly random walk time series with correlated errors without transforming the series as performed traditionally. The proposed method involves the computation of moving volatilities based on sliding and cumulative data matrices. Our method rests on the assumption that the number of subperiods for which the series is available is the same for all periods and on the assumption that the series observations in each subperiod for all the periods under consideration are a random sample from a particular distribution. The method was successfully implemented on a simulated dataset. A paired sample t-test, Wilcoxon signed rank test, repeated measures (ANOVA), and Friedman tests were used to compare the volatilities of the traditional method and the proposed method under both sliding and cumulative data matrices. It was found that the differences among the average volatilities of the traditional method and sliding and cumulative matrix methods were insignificant for the simulated series that follow the random walk theorem. The implementation of the method on exchange rates for Canada, China, South Africa, and Switzerland resulted in adjudging South Africa to have the highest fluctuating exchange rates and hence the most unstable economy.
In this paper, by the use of a new fixed point theorem and the Green function of BVPs, the existence of at least one positive solution for the third-order boundary value problem with the integral boundary conditions is considered,where there is a nonnegative continuous function. Finally, an example which to illustrate the main conclusions of this paper is given.
The problems of polynomial interpolation with several variables present more difficulties than those of one-dimensional interpolation. The first problem is to study the regularity of the interpolation schemes. In fact, it is well-known that, in contrast to the univariate case, there is no universal space of polynomials which admits unique Lagrange interpolation for all point sets of a given cardinality, and so the interpolation space will depend on the set Z of interpolation points. Techniques of univariate Newton interpolating polynomials are extended to multivariate data points by different generalizations and practical algorithms. The Newton basis format, with divided-difference algorithm for coefficients, generalizes in a straightforward way when interpolating at nodes on a grid within certain schemes. In this work, we propose a random algorithm for computing several interpolating multivariate Lagrange polynomials, called RLMVPIA (Random Lagrange Multivariate Polynomial Interpolation Algorithm), for any finite interpolation set. We will use a Newton-type polynomials basis, and we will introduce a new concept called Z , z -partition. All the given algorithms are tested on examples. RLMVPIA is easy to implement and requires no storage.
Let M and M ∗ be two timelike surfaces in Minkowski 3-space ℝ 1 3 . If there exists a spacelike (timelike) Darboux line congruence between each point of M and M ∗ , then the surfaces are timelike Weingarten surfaces. It turns out their Tschebyscheff angles are solutions of the Sinh-Gordon equation, and the surfaces are related to each other by Backlund’s transformation. Finally, a method to construct new timelike Weingarten surface has been found.
An optimal control theory is applied to a system of ordinary differential equations representing the dynamics of health-related risks associated with alcoholism in the community with active religious beliefs. Two nonautonomous control variables are proposed to reduce the health risks associated with alcoholism in the community. Consequently, three control strategies are presented using Pontryagin’s maximum principle (PMP), and the necessary conditions for the existence of the optimal controls are obtained. The simulation results revealed that the health risks associated with alcoholism behaviors may be effectively eradicated when both controls, u1t and u2t, are applied in a combination. On the other hand, the cost–effective analysis of the three different strategies confirmed that the desired cost–effective results may be attained when both controls, u1t and u2t, are applied together. Based on these results, this study concludes that, health risks associated with alcoholism behaviors may be efficiently and cost–effectively eradicated from the community when both controls, u1t and u2t, are applied together. Whereas application of control option u1t implies increasing the level of protection to the susceptible population by implementing public health education campaign; the control option u2t implies increasing the removal rate of the moderate risky individuals into recovered population. The control strategy in which the two options are featured in a combination is presented in this study as Strategy C exhibiting the least ICER value and more cost–effective than the rest of strategies presented.
We propose a method of defining absorbing boundary conditions for use in finite element modeling of mechanoacoustic systems. The finite element model of an elastic body is expanded by a water domain, bounded by an axisymmetric surface, to which boundary conditions are applied. The boundary conditions are formed using the method of equivalent sources, so the integral relations for the pressure and its gradient are derived. The method retains its validity for the modeling of radiation in the low-frequency range, as it provides not only the absorption of outgoing waves but also the modeling of the added mass of vibrating elastic bodies.
Irrespective of whether the test for homogeneity is significant or not, most researchers assume time-homogeneity in analysing Markov chains due to scanty literature on the analysis of time-inhomogeneous Markov chains. Based on the assumption that, for each point in time in the future, a stochastic process will be subjected to a randomly selected transition matrix from an ergodic set of transition matrices the process was subjected to in the recent past, a methodology was proposed for analysing the long-run behaviours of time-inhomogeneous Markov chains. The proposed model was implemented to historical data consisting of the exchange rate of cedi-dollar, cedi-pound, and cedi-euro spanning over 6 years (January 2012 to December 2017). The results show that under certain “closeness” conditions, the long-run behaviours of the time-inhomogeneous case are almost identical to those of the time-homogeneous case. The paper asserted that even if the Markov chain exhibit time-inhomogeneity, analysing the Markov chain under the assumption of time-homogeneity is a step in the right direction under certain “closeness” conditions; otherwise, the proposed method is recommended. It was also found that investing in dollars yields better returns than the other currencies in Ghana.
A maximum dynamic multicommodity flow problem concerns with the transportation of several different commodities through the specific source-sink path of an underlying capacity network with the objective of maximizing the sum of commodity flows within a given time horizon. Motivated by the uneven road condition of transportation network topology, we introduce the dynamic multicommodity contraflow problem with asymmetric transit times on arcs that increase the outbound lane capacities by reverting the orientation of lanes towards the demand nodes. Moreover, a pseudo-polynomial time algorithm by using a time-expanded graph and an FPTAS by using a Δ-condensed time-expanded network are presented.
In this paper, a fishery model for African catfish and Nile tilapia is formulated. This model is used to compare financial profit and biomass outtakes in a two-species system versus single species systems. We consider a stage-structured fish population model consisting of the aforementioned fish species together with two food resources. The model dynamics include cannibalism, predator-prey, feeding, reproduction, maturation, development, mortality, and harvesting. We prove consistency of the model in the sense that the solutions will stay bounded and nonnegative over time. Conditions for local stability of fish-free equilibrium point are established. The simulation results reveal asymptotically stable solutions with coexistence of African catfish, Nile tilapia, and two food resources. The major conclusion from our findings is that fisheries should culture both species to maximize the biomass outtake and financial profit.
In this study, a deterministic mathematical model that explains the transmission dynamics of corruption is proposed and analyzed by considering social influence on honest individuals. Positivity and boundedness of solution of the model are proved and basic reproduction number R0 is computed using the next-generation matrix method. The analysis shows that corruption-free equilibrium is locally and globally asymptotically stable whenever R0<1. Also, the endemic equilibrium point is locally and globally asymptotically stable whenever R0>1. Then, the model was extended to optimal control, and some numerical simulations with and without optimal control are also performed to verify the theoretical analysis using MATLAB. Numerical simulation of optimal control model shows that the prevention and punishment strategy is the most effective strategy to reduce the dynamic transmission of corruption.
Edge detection consists of a set of mathematical methods which identifies the points in a digital image where image brightness changes sharply. In the traditional edge detection methods such as the first-order derivative filters, it is easy to lose image information details and the second-order derivative filters are more sensitive to noise. To overcome these problems, the methods based on the fractional differential-order filters have been proposed in the literature. This paper presents the construction and implementation of the Prewitt fractional differential filter in the Asumu definition sense for SARS-COV2 image edge detection. The experiments show that these filters can avoid noise and detect rich edge details. The experimental comparison show that the proposed method outperforms some edge detection methods. In the next paper, we are planning to improve and combine the proposed filters with artificial intelligence algorithm in order to program a training system for SARS-COV2 image classification with the aim of having a supplemental medical diagnostic.
Top-cited authors
Hans Joachim Haubold
  • United Nations Organization
Arak Mathai Mathai
  • McGill University
R. Saxena
  • Jai Narain Vyas University
Aderemi Adewumi
  • University of KwaZulu-Natal
Ayodele Ariyo Adebiyi
  • Landmark University