iosr-Jm   Volume-15 ~ Issue-4 ~ July-August 2019

Abstract: In this article it is formulated and analyzed an unconditionally stable nonstandard finite difference method for the general nonlinear first order dynamic differential equation. This work manages with the relationship between a continuous dynamical system and numerical methods for its computer simulations, viewed as discrete dynamical systems. The term 'dynamic consistency' of a numerical scheme with the associated continuous system is usually loosely defined, meaning that the numerical solution replicate some of the properties of the solutions of the continuous system.

Key Word: Non linear first order dynamic equation; Non-standard finite difference method; Stability.

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[3]. Z. Lu and W. Wang. Permanence and global attractivity for Lotka-volterra difference systems. J.Math. biol., 1999, 39, pp. 269 – 282.
[4]. L. J. S. Allen. Some discrete-time SI, SIR, and SIS epidemic models. Mathematical Biosciences, 1994, 124, pp. 83 -105.

[5]. Ronald E. Mickens and Talitha M. Washington, A note on an nonstandard finite difference scheme for mathematical model of respiratory virus transmission, arxiv:1008.2314V1.[q.bio.PE].13Aug2010.

Abstract: Measles virus is a member paramyxoviridae within the genus of morbillivirus. Its genome consist of approximately 16,000 bases of non-segmented single stranded negative sense RNA. This means that the virus is transcribed immediately upon entry into the cell. The virus spreads from person to person through the release of the aerosol droplets. In this paper, we investigate the transmission of measles virus using the five compartments of susceptible, vaccinated, exposed, infectious and recovered individuals with demographic factors. We give the mathematical.......

Key Word: Measles virus, basic reproduction number, vaccine efficacy. Mathematics subject classification: 97M60, 00A71, 46N70

[1]. Momoh A.A., Ibrahim M.O., Uwanta J.I., and Manga S.B. Mathematical model for control of measles epidemiology. International Journal of Pure and Applied Mathematics, 87(5):707–718, 2013.
[2]. Mose Ongau Fred, Johana K. Sigey, Jeconiah A. Okello, M. Okwoyo James, and Giterere J. Kang'ethe. Mathematical modeling on the control of measles by vaccination: Case study of KISII County, Kenya. The SIJ Transactions on Computer Science Engineering and its Applications (CSEA), 2(3), 2014.
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[5]. Christopher Obumneke, Ibrahim Isa Adamu, and Shamaki Timothy Ado. Mathematical model for the dynamics of measles under the combined effect of vaccination and measles therapy. International Journal of Science and Technology, 6(6):862–874, 2017..

Abstract: Computer aided geometric design (CAGD) is concerned with the approximation and representation of curves and surfaces when they are subjected to computer processing. CAGD is a relatively new field. The idea in CAGD is to find representations of curves and surfaces which are easy to treat on a computer, and to render on a graphical device such as a computer screen. The work in this field was started in the mid-1960s. Barnhill and Riesenfeld established the field of CAGD in 1974 when they organized a conference on the topic at the University of Utah in the United.........

[1]. Abbas, M., Majid, A. A. and Ali, J. (2014). Positivity-preserving rational bi-cubic spline interpolation for 3D positive data, Applied Mathematics and Computation 234:460–476.
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Abstract: In this paper, the study seeks to introduce the concept of statistical order convergence and statistically relatively uniform convergence in Riesz spaces of double sequences. Which is an extension of that of recently introduced for single sequences. We shall also give the analogous definitions of statistical order convergence, statistically relatively uniform convergence and norm statistical convergence of double sequences. Finally, we shall explore and establish some inclusion relations among these concepts........

Keywords and phrases: Statistical convergence, Riesz space, double sequence, relatively uniform ,order convergence.

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Abstract: In this work we considered nonlinear ordinary differential equations to study the dynamics of hepatitis B virus (HBV) epidemics within the host. We proved that the invariant and bounded ness of the solution of the dynamical system. We used a nonlinear stability analysis method for proving the local and global stability of the existing equilibrium points. We found that the diseases free equilibrium point and endemic equilibrium point exist for some conditions.We proved that the disease free equilibrium point is locally asymptotically stable and also globally asymptotically stable. We found that the basic reproduction number for the system is...........

Key words:-Hepatitis B virus (HBV), local stability, global stability, reproduction number, sensitivity, 𝐶𝐷8+ 𝑇 cells, numerical simulation

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Abstract: This article considers nonlinear dynamical system to study the dynamics of tuberculosis through vaccination and dual treatments. By dual treatments we studychemoprophylaxis and therapeuticstreatments of latent and active tuberculosis respectively. The total population is divided in to ten compartments. We found the dynamical system has disease free equilibrium point and endemic equilibrium point. We also found that the basic reproduction number of the considered dynamical system is..........

Keywords: Nonlinear dynamical system, Vaccination, Dual treatments, Stability Analysis, Sensitivity Analysis.

[1] AgagwalatuChiedozie Ferdinand;Mathematical Model for the Dynamics of Tuberculosis Disease with Vaccination. Pacific Journal of Science and Technology,2015, –234– http://www.akamaiuniversity.us/PJST.htm,
[2] Anatole Temgouay, Global properties of a tuberculosis model with lost sight and multi-compartment of latents, Journal of Mathematical Modeling, 2018, Vol. 6, No. 1, pp. 47-76
[3] C. E. Madubueze, Bifurcation and Stability Analysis of the Dynamics of Cholera Model with Controls, International Journal of Mathematical and Computational Sciences, 2015, Vol:9, No:11
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Abstract: In this paper we considered a nonlinear deterministic dynamical system to study the effect of post exposure vaccination on fast and slow latent infection stages. We found that there are two equilibrium points exist. These are disease free equilibrium point and endemic equilibrium point. Their local stability and global stability analysis investigated using nonlinear stability methods. We also found that the dynamical system has basic reproduction number........

Keywords: Nonlinear dynamical system, TB Post exposure vaccination, Stability analysis, Numerical simulation, Sensitivity analysis.

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Abstract: In this work we considered a nonlinear deterministic dynamical system to study dynamics of HIV/AIDS with different mode of transmissions. We found that the diseases free equilibrium point and endemic equilibrium point exist and we perform their local stability and global stability analysis using nonlinear stability methods. We found the reproduction number.......

Keywords : Nonlinear dynamical system, HIV/AIDS dynamics, Stability analysis, Numerical simulation, Sensitivity analysis.

[1]. AbdulsamadEngidaSado, PurnachandraRaoKoya. Application of Brody Growth Function to Describe Dynamics of Breast Cancer Cells. American Journal of Applied Mathematics(AJAM).Vol.3,No.3,2015,pp. 138-145. Doi:10.11648/j.ajam.20150303.20.
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Abstract: In this work, we have considered a nonlinear dynamical system. We divide the total population of Debre Berhan town into four compartments:Susceptible class𝑆, Exposed class 𝐸 , Infected class𝐼 andRecovered class 𝑅. We found two equilibrium points, the disease free equilibrium point and the endemic equilibrium point. We also found the basic reproduction number of the dynamical system is𝑅0=𝛽 𝛼+𝑝𝜇 𝜇+𝛼 𝜇+𝑑+𝛾 which depends on six parameters. The numerical value of the reproduction number based on real data collected from Debre Berhan town is𝑅0=1.051448663>1. This shows that Pneumonia disease spread in the community of Debre Berhan town. We also proved that........

Keywords :Pneumonia, Sensitivity, reproduction number, stability

[1]. Abdulkarim, A. A., Ibraheem, R. M., Adegboye, A. O., Johnson, W. B. R., &Adeboye, M. A. N. (2013). Childhood pneumonia at the University of Ilorin Teaching Hospital, Ilorin Nigeria. Nigerian Journal of Paediatrics, 40(3), 284-289.

[2]. Al-Sayouri, S. (2014). Predictive analytics of hospital readmissions using an integrated data mining framework. State University of New York at Binghamton.
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[4]. Barbara Boldin, Deterministic structured population epidemic models, 2003. University of Ljubljana, Slovenia.
[5]. Charles Patrick Davis, MD, PhD. (2017). Is Pneumonia Contagious?