Motivated by the need to include the different characteristics of individuals and the damping effect in predictions of epidemic spreading, we build a model with variant coefficients and white Gaussian noise based on the traditional SIR model. The analytic and simulation results predicted by the model are presented and discussed. The simulations show that using the variant coefficients results in a higher percentage of susceptible individuals and a lower percentage of removed individuals. When the noise is included in the model, the percentage of infected individuals has a wider peak and more fluctuations than that predicted using the traditional SIR model. The history of Homo sapiens is always closely interrelated with the study of diseases. Whether it be the Black Death in Europe in the fourteenth century or the superbug that recently spread across the globe like wildfire [1,2], scientists have always looked at diseases with great interest [3][4][5][6][7][8][9][10]. In the well-known theoretical SIS model, the population is divided into two disjoint classes, susceptible individuals and infected individuals, for which the percentages at time t are denoted by s(t) and i(t), respectively [11][12][13][14]. However, this model is not suitable for describing diseases like flu or malaria. The subsequent has a third class with percentages denoted by r(t). They are the recovered individuals who are immune to the infection. This is a simple model commonly used for many infectious diseases like measles, mumps and rubella. In these two models, the spread of an infectious disease in a population depends mainly on the character of the disease. The most suitable model can be chosen according to the particular case. However, these models do not work well for some special cases. For example, in the spreading of SARS, although an individual cannot develop lasting immunity, there is only a very tiny chance of being infected again. By mean field theory, the course of an epidemic spreading is determined by the contact rates among susceptible, infected and removed individuals, which are assumed to be proportional to the number of encounters among susceptible, infected and removed individuals. Each individual is treated in the same way, even at different times. A more realistic and interesting model of infectious diseases should take into account a change in the environment and the variety of characteristics of individuals [21]. Along with the spreading process, the preventive effect should become stronger because people could find useful methods such as taking pills and avoiding close contacts with infected individuals to prevent the disease from spreading [22,23]. Moreover, how easy or difficult it is for an individual to be infected by others depends on their own characteristic, such as age, nutritional status, sex and so on. Therefore, each individual should be distinguished by different transmission coefficients and recovery coefficients. Furthermore, the part of the model that measures the coefficient of infection during the w...