AIDS stands for acquired immunodefciency syndrome , a disease that makes it difficult for the body to fight off infectious diseases . The human immunodefciency virus known as HIV causes AIDS by infecting and damaging the CD4+T-cells , which are a type of white blood cells in the body's immune system that is supposed to fight off invading germs . In a normal healthy individual's peripheral blood , the level of CD4+T-cells is between 800 and 1200 / mm3 and once this number reaches 200 or below in an HIV infected patient , the person is This model reproduce the three phase pattern observed in CD4+T-cell and virus counts of infected patients , namely , the primary response , the clinical latency period , and the onset of AIDS . In the beginning we'll give some requirement mathematical concepts . Also we will define cellular automata as a discrete dynamical system . We de?ne and discuss the dynamics of cellular automata with the property that at each site in the lattice , or at each coordinate of a point in the domain of the map , a random choice among ?nitely many local rules is made . We call these stochastic CA’s and we set up a mathematical framework for them and provide simple examples . We also use techniques from topological dynamics and ergodic theory to understand and generalize the model which was presented in Zorzenon dos Santos and Coutinho with minimal mathematical explanation and we prove statements about related models and parameter changes . Then we will build model by previous content and compare the results with the biological observations . We give some justi?cation for choices of constants . We also try to separate the biological statements from the mathematical analysis to the extent possible . We conclude this section with a preliminary analysis of how and why the model behaves as it does and we combine the mathematical and biological statements . We also give an explanation for the timing in the model supported by some numerical observations . Thereafter we will investigate properties and mathematical results for the proposed model . We define a Markov cellular automata that models the spread of viruses that often progress to a chronic condition , such as HIV . We show that the complex dynamical system often produces a Markov process at the later stages , whose eigenvectors corresponding to the eigenvalue 1 have physical significance for the longterm prognosis of the virus and finally discuss about modification of the proposed model and influence of drugs on the manner of the spread of virus .