Background Outbreaks of respiratory infectious diseases often take place in crowded places. To understand the spreading pattern of an outbreak of a respiratory infectious disease and provide a theoretical basis for the targeted implementation of scientific prevention and control, we attempted to establish a stochastic model to simulate an outbreak of a respiratory infectious disease at a military camp. This model fits the general pattern of disease transmission and further enriches theories on the transmission dynamics of infectious diseases. Methods We established an enclosed system of 500 people exposed to adenovirus type 7 in a military camp. During the infection period, the patients transmitted the virus randomly to susceptible people. The spread of the epidemic under militarized management mode was simulated using a computer model named “the random collision model”, and the effects of factors such as the basic reproductive number ( R 0 ), time of isolation of the patients (TOI), interval between the onset and isolation (IOI), and immunization rates (IR) on the developmental trend of the epidemic were quantitatively analysed. Results Once the R 0 exceeds 1.5, the median attack rate increases sharply; when R 0 =3, with a delay in the TOI, the attack rate increases gradually and eventually remains stable. If the IOI exceeds 2.3 days, the median attack rate will also increase dramatically. If the IR exceeds 0.5, the median of the attack rate nears zero. The median generation time was 8.26 days (95% CI: 7.84-8.69 days). The partial rank correlation coefficients between the attack rate of the epidemic and the R 0 , TOI, IOI, and IR were 0.61, 0.17, 0.45, and -0.27, respectively. Conclusion The random collision model not only simulates how an epidemic spreads with superior precision but also allows more flexibility in the settings of the exposure population’s activities and different types of infectious diseases, which is conducive to furthering the exploration of the epidemiological characteristics of epidemic outbreaks.