Propagation of information over the network of taxpayers in the model of tax auditing

Tax control is one of the most important tools for the administration of the tax system (fiscal, social, regulatory and control). Tax audit enables to increase the revenue of taxes and fees in the state budget. Assume that each taxpayer can declare his income less then his true income level, however total tax audits of the taxpayers´ population is economically unreasonable and even selective tax audits are not always profitable. Though, the tax authority needs to stimulate taxpayers to pay taxes, correspondingly to their true income. One possible way of such stimulation is spreading of information about future tax auditing. In this case the propagation of the information can be viewed as an “infection of the mind”, and its spreading shows an interesting resemblance to that of epidemics. To describe the spreading process we can use a modification of classical Susceptible-Infected-Recovery (SIR) model. We study a model of information spreading in large population of taxpayers and describe the dynamics of the model on complex social networks. We formulate an optimal control problem for the tax auditing policy and analyze the behavior of agents in different subgroups depending on the social connections between their agents.