Mathematical Analysis of Varicella Zoster Virus Model
Anebi Elisha,
Terhemen Aboiyar,
Anande Richard Kimbir
Issue:
Volume 6, Issue 2, December 2021
Pages:
23-37
Received:
9 July 2021
Accepted:
29 July 2021
Published:
12 October 2021
Abstract: Chicken Pox (also called Varicella) is a disease caused by a virus known as Varicella Zoster Virus (VZV) also known as human herpes virus 3 (HHV -3). Varicella Zoster Virus (VZV) is a DNA virus of the Herpes group, transmitted by direct contact with infective individuals. In this work, a deterministic mathematical model for transmission dynamics of Varicella Zoster Virus (VZV) with vaccination strategy was solved, using Adomian Decomposition Method (ADM) and Fourth-Fifth Rungekutta Felhberg Method and Approximate solutions were realized. ADM, yields analytical solution in terms of rapidly convergent infinite power series with easily computed terms. This solution was realized by applying Adomian polynomials to the nonlinear terms in the system. Similarly, fourth-fifth-order Runge-Kutta Felberg method with degree four interpolant (RK45F) was used to compute a numerical solution that was used as a reference solution to compare with the semi-analytical approximations. The main advantage of the ADM is that it yields an approximate series solution in close form with accelerated convergence. The effect of Varicella was considered in five compartments: The Susceptible, the Vaccinated, the Exposed, the Infective and the Recovered class. The Varicella Zoster virus model which is a nonlinear system can only be solved conveniently using powerful semi-analytic tool such as the ADM. Numerical simulations of the model show that, the combination of vaccination and treatment is the most effective way to combat the epidemiology of VZV in the community.
Abstract: Chicken Pox (also called Varicella) is a disease caused by a virus known as Varicella Zoster Virus (VZV) also known as human herpes virus 3 (HHV -3). Varicella Zoster Virus (VZV) is a DNA virus of the Herpes group, transmitted by direct contact with infective individuals. In this work, a deterministic mathematical model for transmission dynamics of...
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Statistical Perspective Approach to Selection of Sample
Basavarajaiah Doddagangavadi Mariyappa,
Bhamidipati Narasimha Murthy,
Kyathanahalli Basavanthappa Vedamurthy
Issue:
Volume 6, Issue 2, December 2021
Pages:
38-44
Received:
4 March 2019
Accepted:
13 April 2019
Published:
28 October 2021
Abstract: Any research starts with the selection of a problem. Many characteristics or attributes may look for their problems of research viz novelty, interesting, importance, feasibility availability of data and hypothesis testing etc. In the essence of biological research we should make a formulated hypothesis at greater accuracy and precise level of significance ‘’. The research hypothesis is a presumptive statement of a proportion or a reasonable guess based upon the available evidences or attributes, which the researcher seeks to prove through his course of study. It is also driven from deductive reasoning from a scientific theory. The researcher may begin his study by selecting the sample size is very important dogma in his own area of interest. After selecting the particular theory, the researcher proceeds to derive the hypothesis from his theory. The required sample numerals (size of the sample) is very much concern for success of the research pedagogy and also how much data will require to make a correct decision about the population parameters. If we have accurate sampled data sets, then our decision will be more accurate and there will be less standard error of the parameters estimates of research concern. In this accord the present research paper address the basic principles adopted for sample size determination with respect to biological field.
Abstract: Any research starts with the selection of a problem. Many characteristics or attributes may look for their problems of research viz novelty, interesting, importance, feasibility availability of data and hypothesis testing etc. In the essence of biological research we should make a formulated hypothesis at greater accuracy and precise level of signi...
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On the Investigation of the Methods of Parameter Estimation of the Best Probability Model for Wind Speed Data
Obanla Olakunle James,
Awariefe Christopher,
Ilo Hammed Owolabi
Issue:
Volume 6, Issue 2, December 2021
Pages:
45-51
Received:
29 May 2021
Accepted:
12 July 2021
Published:
23 November 2021
Abstract: The focus of this paper is to estimate parameters of the best distribution for modelling wind speed data, real-life data sets of wind speed of Maiduguri, the biggest city in the North Eastern, Nigeria were adopted for application purposes. Six (6) probability density functions, specifically, Weibull, Gamma, Lognormal, Pareto, Burr and Log-Logistic are considered for modelling the wind speed data. In selecting the model of best fit for the variability of the wind speed data, five (5) methods of estimating parameter, such as; Maximum Likelihood Estimation (MLE), Matching Quantiles Estimation (MQE), The Cramer-von Mises Minimum Distance Estimators (CvM), Anderson-Darling Minimum Distance Estimation and Kolmogorov-Smirnov Minimum Distance Estimation (K-S)) were further applied to obtain the best estimates for the best model among compared ones. We discovered in our investigation that Weibull distribution best fitted the wind data per Goodness-of-fit tests, since it has the smallest p-value for K-S (0.03179314), CvM (0.03137888) and AD (0.23725978) revealing the curve is fairly close to our data and the maximum likelihood estimators with the smallest AIC (972.7990) and BIC (980.3105) estimates for Weibull parameters, proved to be the best as compared with other methods of estimation.
Abstract: The focus of this paper is to estimate parameters of the best distribution for modelling wind speed data, real-life data sets of wind speed of Maiduguri, the biggest city in the North Eastern, Nigeria were adopted for application purposes. Six (6) probability density functions, specifically, Weibull, Gamma, Lognormal, Pareto, Burr and Log-Logistic ...
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