Tax system accomplishes several significant functions, concerned with different fields of its activities, such as fiscal, social, regulatory, distributive, incentive and control. The correctness of work of fiscal system depends on tax control; in turn, the most important part of tax control is tax audit. However, the previous studies have shown that the implementation of tax audits with an optimal probability is an expensive procedure. Due to the restricted budget of the tax authorities, such audits are not always feasible. Therefore, to increase tax collection, it is necessary to apply additional ways to stimulate taxpayers to fair tax payments. In this paper, we investigate a model of tax control taking into account the dissemination information about possible audits over the population of taxpayers as a tool to stimulate tax collection. We use an evolutionary approach to describe the behavior of taxpayers in total population, where each taxpayer has one of three different risk statuses: risk-loving, risk-neutral, and risk-avoiding. The idea of disseminating information in a population has been studied based on the Markov process in networks with different structures. We estimate the influence of the propagated information on the final distribution of risk statuses and the evasions of taxpayers. We design a series of numerical simulations with the different topology of the network and artificial centers of influence which can be included or not included in the network of contacts to corroborate our theoretical arguments. As well as we present a comparative analysis of the received numerical simulations.