This paper presents 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. Our results are a generalization of that Hawkins et al done. Because of the spread of diseases, a technical innovative model should be made to recover their time regions. Many researches tried to solve this problem based on medical dis- ease feature, which suffer from unpredictable ones. Whilst a single infected host might not be significant, a disease that spreads through a large population yields serious health and economic threats. In this sense, mathematical epidemiology is concerned with modeling the spread of infectious disease in a population (see 2). The aim is generally to understand the time course of the disease with the goal of controlling its spread. Traditionally, the majority of existing mathematical models to simulate epidemics are based on ordinary differential equa- tions. These models have serious drawbacks in that they ne- glect the local characteristics of the spreading process and they do not include variable susceptibility of individuals. Spe- cifically, they fail to simulate in a proper way (1) the individ- ual contact processes, (2) the effects of individual behavior, (3) the spatial aspects of the epidemic spreading, and (4) the effects of mixing patterns of the individuals.
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