  The main aim to build models capable of simulating the spreading of
infectious diseases is to control them. And along this way, the key to find the
optimal strategy for disease control is to obtain a large number of simulations
of disease transitions under different scenarios. Therefore, the models that
can simulate the spreading of diseases under scenarios closer to the reality
and are with high efficiency are preferred. In the realistic social networks,
the random contact, including contacts between people in the public places and
the public transits, becomes the important access for the spreading of
infectious diseases. In this paper, a model can efficiently simulate the
spreading of infectious diseases under random contacts is proposed. In this
approach, the random contact between people is characterized by the random
matrix with elements randomly generated and the spread of the diseases is
simulated by the Markov process. We report an interesting property of the
proposed model: the main indicators of the spreading of the diseases such as
the death rate are invariant of the size of the population. Therefore,
representative simulations can be conducted on models consist of small number
of populations. The main advantage of this model is that it can easily simulate
the spreading of diseases under more realistic scenarios and thus is able to
give a large number of simulations needed for the searching of the optimal
control strategy. Based on this work, the reinforcement learning will be
introduced to give the optimal control strategy in the following work.
