Islamic Azad University, Central tehran BranchInternational Journal of Mathematical Modelling & Computations2228-6225104 (Fall)20201201Mathematical Model of HIV and Cholera Co-infection in the Presence of Treatment679832ENKumama RegassaChenekeWollega UniversityGeremew KenassaEdessaWollega UniversityPurnachandra RaoKoyaWollega UniversityJournal Article20200205In the current study, a deterministic mathematical model of HIV and Cholera co-infection is developed to analyze the impact of treatments in the presence of diseases in the population. The model consists of nine classes of the human population and one class of bacteria population. The formulated model is mathematically well-posed and biologically meaningful. The reproduction number is employed to analyze the extinction or spreading of the disease in the population. it is observed that cholera has a positive impact on HIV patients and HIV also has a positive impact on cholera patients. A separate analysis of each infection model and co-infection model is presented. Further, the stability analysis of equilibrium points is included. Finally, numerical simulations are performed using Matlab software. The result of numerical simulations shows that early treatment is very powerful for clearing or controlling cholera within a specified period of time and supports HIV/AIDS patients to live more years.Islamic Azad University, Central tehran BranchInternational Journal of Mathematical Modelling & Computations2228-6225104 (Fall)20201201Mathematical Model of Herpes Simplex Virus – II (HSV-II) with Global Stability Analysis679833ENEshetuGurmuMathematics, Natural Science,Wollega University,Nekemte, Ethiopia0000-0003-3209-5844Boka KumsaBoleMathematics, Natural Science, Wollega University, Nekemte, EthiopiaPurnachandra RaoKoyaMathematics, Natural Science, Wollega University, Nekemte, EthiopiaJournal Article20200613In this paper, a nonlinear deterministic mathematical model of ordinary differential equations has been formulated to describe the transmission dynamics of HSV-II. The well-posedness of the formulated model equations was proved and the equilibrium points of the model have been identified. In addition, the basic reproduction number that governs the disease transmission was obtained from the largest eigenvalue of the next-generation matrix. Both local and global stability of the disease-free equilibrium and endemic equilibrium point of the model equation was established using the basic reproduction number. The results show that, if the basic reproduction is less than one then the solution converges to the disease-free steady-state and the disease-free equilibrium is locally asymptotically stable. On the other hand, if the basic reproduction number is greater than one the solution converges to endemic equilibrium point and the endemic equilibrium is locally asymptotically stable. Also, sensitivity analysis of the model equation was performed on the key parameters to find out their relative significance and potential impact on the transmission dynamics of HSV-II. Finally, numerical simulations of the model equations are carried out using the software DE Discover 2.6.4 and MATLAB R2015b with ODE45 solver. The results of simulation show that treatment minimizes the risk of HSV-II transmission from the community and the stability of disease-free equilibrium is achievable when R_0Islamic Azad University, Central tehran BranchInternational Journal of Mathematical Modelling & Computations2228-6225104 (Fall)20201218On extension of generalized Laguerre polynomials of two variable679834ENAhmed AliAl-GonahDepartment of mathematics
Aden University
Aden. YenenJournal Article20200630In this paper, we introduce a new extension of generalized Laguerre polynomials<br />of two variable by using the extended Beta function. Some properties of these<br />extension polynomials such as generating functions, integral representation, recurrence<br />relations and summation formulae are obtained.Islamic Azad University, Central tehran BranchInternational Journal of Mathematical Modelling & Computations2228-6225104 (Fall)20201218A new iterative method of successive approximation to solve nonlinear Urysohn integral equations by Haar wavelet679836ENManochehrKazemiDepartment of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran0000-0001-8392-6690ValiTorkashvandDepartment of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, IranEinollahFathizadeDepartment of Mathematics, Karaj Branch, Islamic Azad University, Karaj, IranJournal Article20200701In this paper, a new method for calculating the numerical approximation of the nonlinear Urysohn integral equations is proposed based on Haar wavelets. Also, the convergence analysis and numerical stability of these method are discussed. Conducting numerical experiments conﬁrm the theoretical results of the applied method and endorse the accuracy of the method.Islamic Azad University, Central tehran BranchInternational Journal of Mathematical Modelling & Computations2228-6225104 (Fall)20201218An Optimum Line Search for Unconstrained Non-Polynomial Test Functions using Nonlinear Conjugate Gradient Methods679837ENAdam AjimotiIshaqDepartment of Physical Sciences, Alhikmah University, Ilorin, NigeriaTolulopeLatundeDepartment of Mathematics, Federal University Oye-Ekiti, Oye-Ekiti,Nigeria0000-0003-3502-3344Folashade MisturaJimohDepartment of Physical Sciences, Alhikmah University, Ilorin, NigeriaJournal Article20200804The nonlinear conjugate gradient method solves issues of the frame: <br /> minimizef(▁x),▁x∈R<br /> employing an iterative plot, ▁x^((k+1))=▁x^((k))+α_k ▁d^((k)), where f is a non-polynomial function.<br />We utilized two variants of the optimum line search namely, direct and indirect methods, to compute the step-length in this paper. Both line searches yielded a great outcome when employed to a few unconstrained non-polynomial test functions.Islamic Azad University, Central tehran BranchInternational Journal of Mathematical Modelling & Computations2228-6225104 (Fall)20201218Modelling the impact of trapping blackfly vectors on the transmission of onchocerciasis679838ENJuliusTumwiineDepartment of Mathematics, Mbarara University of Science and Technology, Mbarara, Uganda0000-0002-7904-6698RaymondMuhumuzaDepartment of Mathematics, Mbarara University of SCience and Technolog. Mbarara, UgandaJournal Article20200730Onchocerciasis, usually referred to as river blindness, a skin and eye parasitic infestation is caused by the filarial nematode Onchocerca volvulus. Current control and eradication efforts are being frustrated by the continued existence and thriving of blackflies which are the disease transmitting vectors that breed along the banks of fast flowing and highly oxygenated rivers and streams. This study aims at assessing the effect of using vector traps on the transmission and control of onchocerciasis. A host-vector deterministic model which incorporates vector trapping by use of a system of ordinary differential equations is developed. The model is analysed for steady states and the basic reproduction number is obtained using the next generation method. It is found that the disease free steady state is stable if the basic reproduction number R0 < 1. There exists a unique endemic equilibrium which is locally and globally asymptotically stable if R0 > 1. Numerical simulations show that trapping the blackfly vectors has an effect on the spread and control of the disease. However, it is discovered that using traps alone is not a sufficient strategy and needs to be combined with other methods if the disease is to be completely wiped out of the population.