الفهرس 
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Abstract
The main objective of this thesis is to show some of the results of our probabilistic cellular automaton (PCA) based epidemic model. It is shown that PCA performs better than deterministic ones. We consider two possible ways of interaction that relies on a two-way split rules either horizontal or vertical interaction with 2 different probabilities causing more of the best possible choices for the behavior of the disease.
The thesis contains four chapters.
Chapter 1: Gives a survey about the previous studies on disease spreading including both approaches, deterministic and probabilistic one. The deterministic side concerns with Ordinary Differential equations (ODE) and Partial Differential Equations (PDE). The probabilistic side concerns with Cellular Automata. We also gave a brief idea about the advantages and disadvantages of each of them which resulting from previous studies.
Chapter 2: In this chapter, some basic notions of Cellular Automata are included. A brief history about interesting aspects of Cellular Automata and some of its application are studied.
Chapter 3: Deals with Probabilistic Cellular Automata (PCA) and its mathematical formulation. In the rest of this chapter we mentioned a brief summary about the two researches: [1, 4] which were the backbone and the starting point of our work.
Chapter 4: Introduces a modified method of reducing the impact of an epidemic by considering two possible ways of interaction. This method relies on a two-way split rules either horizontal or vertical interaction with 2 different probabilities causing more of the best possible choices for the behavior of the disease.