الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
This thesis develops the solutions of an interesting class of stochastic differential equations besides their applications in epidemiology and health via the random variable transformation (RVT) technique. This technique is a powerful technique to get the complete solution for the stochastic differential equations and stochastic difference equations represented by the first probability density function(1-PDF) of the solution process. We applied RVT technique to treat three different important problems. The first one is the susceptible-infected-recovery (SIR) epidemiological model, addressed in Chapter 3, and the second is the Leukemia model, presented in chapter 4. The third is the Red Blood Cells (RBCs) model, shown in Chapter 5. In chapter 2 the preliminaries of RVT technique, theories and statistical rules used through the thesis to find the stochastic solutions of the problems that treated in the next chapters are included. Chapter 3 deals with an interesting study in epidemiology that represents susceptible-infected-recovery (SIR) epidemiological model. Firstly, the problem is solved deterministically, then the RVT technique is applied to obtain the 1-PDF of the solution process, from which some parameters that give indication of the spread or decay of the disease are evaluated. These parameters are the basic reproductive number, the replacement number and the contact number. An illustrative example is presented to clear out the advantage of the theoretical probabilistic finding of random SIR model and to study the spread of epidemic diseases. Some specific probability distributions are chosen for the random input parameters which are assumed to be independent random variables. In chapter 4, we presented a probabilistic study for the four compartmental leukemia mathematical model. The leukemia mathematical model is solved at first deterministically depending on the randomized endemic equilibrium state, then the stochastic solution and other related quantities such as the mean and the variance functions for the solution processes are found using the RVT technique. At last, some numerical results are presented to test the validity of the theoretical findings associated to the proposed randomized leukemia model. In chapter 5, we discussed the RBCs mathematical model from deterministic and stochastic point of view. A complete probabilistic solution of this problem is conducted via applying the RVT technique. This is achieved by deriving the first probability density function of the solution processes. The probabilistic behavior of the steady state case (when time tends to infinity) is also studied. Moreover, the fundamental statistical measures, related to the stochastic solutions, such the mean, the variance and the confidence intervals are obtained. Numerical results (for pre-assigned distributions to the model parameters and initial conditions) are presented. Finally, conclusions about the obtained results are presented.