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.

Heat equation is a partial differential equation used to describe the temperature distribution in a heat-conducting body. The implementation of a numerical solution method for heat equation can vary with the geometry of the body. In this study, a three-dimensional transient heat conduction equation was solved by approximating second-order spatial derivatives by five-point central differences in cylindrical coordinates. The stability condition of the numerical method was discussed. A MATLAB code was developed to implement the numerical method. An example was provided in order to demonstrate the method. The numerical solution by the method was in a good agreement with the exact solution for the example considered. The accuracy of the five-point central difference method was compared with that of the three-point central difference method in solving the heat equation in cylindrical coordinates. The solutions obtained by the numerical method in cylindrical coordinates were displayed in the Cartesian coordinate system graphically. The method requires relatively very small time steps for a given mesh spacing to avoid computational instability. The result of this study can provide insights to use appropriate coordinates and more accurate computational methods in solving physical problems described by partial differential equations.

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.

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.

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 $\Delta$-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.

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 $A_1,\cdots ,A_p$ 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 ${\omega }_B$ and ${\omega }_H$, 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.

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 ${\ell }_m$ and ${\ell }_M$. 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.

In this paper, we analyze an M/G/1 priority queueing model with finite and infinite buffers under the $\left(N,n\right)$-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.

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.

Let $M$ and $M^{\ast }$ 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 $M^{\ast }$, 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.

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 $\left(R_0\right)$ is computed using the next-generation matrix method. The analysis shows that corruption-free equilibrium is locally and globally asymptotically stable whenever $R_0<1$. Also, the endemic equilibrium point is locally and globally asymptotically stable whenever $R_0>1$. 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.

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 $\left(Z,z\right)$-partition. All the given algorithms are tested on examples. RLMVPIA is easy to implement and requires no storage.

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.

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, $u_1\left(t\right)$ and $u_2\left(t\right)$, 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, $u_1\left(t\right)$ and $u_2\left(t\right)$, 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, $u_1\left(t\right)$ and $u_2\left(t\right)$, are applied together. Whereas application of control option $u_1\left(t\right)$ implies increasing the level of protection to the susceptible population by implementing public health education campaign; the control option $u_2\left(t\right)$ 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 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.

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.

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.

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.