الفهرس 
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Abstract
The main objective of this work is to discuss the spreading of epidemics on small world networks. These networks are more realistic than the regular ones since they include some long distance effects. The dynamics of spreading epidemics can be modeled by differential equations, difference equations or cellular automata. There are some difficulties facing the use of differential equations in modeling epidemics such as global interacting system and it usually assumes that the population size is constant which may not be true. It assumes that the population is wellmixed which is not valid in reality. Also differences in human susceptibility are difficult to model. For these reasons, Cellular automata as a complete discrete dynamical system is the suitable candidate method for modeling epidemics although it has some defects, for example, it depends on the lattice size and its analytical results still are not enough. In this study direct simulations and mean field approximations are used to determine phase transitions of some epidemic models. Some epidemic models have been investigated and modified to include the small world networks and inhomogeneity. We study Bagnoli et al model using both direct simulation and mean field approximation, the two methods gave the same bifurcation diagram except in a small region. SIRS on small world network with distant neighbors are simulated with direct simulation and the results have been compared with the previous ones. We conclude that the epidemic regions of SIRS models increased by introducing small world network in all cases under study.