الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
In this thesis, we have introduced a brief introduction to the RVT technique then applied this technique to treat two different and important problems; the first problem is the Milne problem which is included in chapter 3, and the second problem is the SIR-epidemiological model that presented in chapter 4. The RVT technique enables us to assume any distribution for the input RVs according to the nature of randomness in the medium. However we considered only Gamma, exponential and Gaussian distributions for the sake of clarification. We have obtained the complete solution represented by closed expressions for the first probability density function and the first statistical moments of the solution and we have studied the effect of randomness in the properties of the medium on some physical quantities of interest like the radiant energy, the reflectivity, transmissivity and the linear extrapolation distance.
In chapter 4, we provided a full probabilistic description of the random SIR model. The obtained results are more general in the sense that all the involved input parameters have been assumed to be RVs having any probability density function. The first probability density function of the solution stochastic process of the governing nonlinear differential equation has been obtained. from this crucial function, the solution is completely characterized for each time An important contribution of this chapter is the determination of the first probability density function of the time until a given proportion of the population remains susceptible or infected. This is very useful from a practical stand point since it permits forecasting the earliest time instant at which the susceptible subpopulation will reach a given threshold. The theoretical study has been completed by providing a stochastic interpretation of a very important parameter in epidemiology, namely, the basic reproductive number.