### فهرست مطالب

• سال دهم شماره 4 (Autumn 2020)
• تاریخ انتشار: 1400/04/22
• تعداد عناوین: 6
|
• Mathematical Model of Herpes Simplex Virus – II (HSV-II) with Global Stability Analysis
Eshetu Gurmu *, Boka Bole, Purnachandra Koya Page 1

In 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_0

Keywords: HSV, reproductive number, Stability Analysis, Sensitivity
• Mathematical Model of HIV and Cholera Co-infection in the Presence of Treatment
Kumama Cheneke *, Geremew Edessa, Purnachandra Koya Page 4

In 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.

Keywords: well-posedness, Basic reproduction number, Stability Analysis, Co-infection, and Sensitivity Analysis
• Ahmed Al Gonah * Pages 265-279

In this paper, we introduce a new extension of generalized Laguerre polynomialsof two variable by using the extended Beta function. Some properties of theseextension polynomials such as generating functions, integral representation, recurrencerelations and summation formulae are obtained.

Keywords: Beta function, generalized Laguerre polynomials, generating functions, summation formulae
• Manochehr Kazemi *, Vali Torkashvand, Einollah Fathizade Pages 281-294

In 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.

Keywords: Integral equations, Haar wavelet, Lipschitz condition, Successive approximations