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

To Simulate the Spread of Infectious Diseases by the Random Matrix