Contact network models are recent alternatives to equation-based models in epidemiology. In this paper, the spread of disease is modeled on contact networks using bond percolation. The weight of the edges in the contact graphs is determined as a function of several variables in which case the weight is the product of the probabilities of independent events involving each of the variables. In the first experiment, the weight of the edges is computed from a single variable involving the number of passengers on flights between two cities within the United States, and in the second experiment, the weight of the edges is computed as a function of several variables using data from 2012 Kenyan household contact networks. In addition, the paper explored the dynamics and adaptive nature of contact networks. The results from the contact network model outperform the equation-based model in estimating the spread of the 1918 Influenza virus.