This study is focused on the construction and analysis of a complex epidemiological practical model built on the basis of the Susceptible-Infected-Removed (SIR) model. The examples illustrate the behavior of the practical model in various scenarios and also compare this model and a similar model, taking into account migration. The nature of the behavior of the model is determined by parameters such as the rate of spread of infection, the coefficients of recovery, mortality, the intergroup transition and others with different values of influence.
We construct and study a continuous model that describes the conflict interaction of two complex systems with non-trivial internal structures. External conflict interaction is modeled by the additional influence of chance. The dynamics of internal conflict are similar to the Lotka-Volterra model, namely the model of information warfare. We interpret the new model of information warfare as the influence of rare events that rapidly change certain ideas of a large number of people. As a result, the number of supporters of different ideas make stochastic jumps that we can see using the Levy approximation scheme. We suggest that such a model could be more natural, as important news now has a quick and wonderful impact on audiences through television and the Internet.