With the appearance of the COVID-19 virus pandemic, the topic of the spread of the infection became very usual and part of the everyday life of an average man. Modelling the spread of the infection has already aroused great interest in various scientific communities and became an area of multidisciplinary research since it has intrigued mathematicians, physicists, biologists, sociologists, and other scientists. In this thesis, we summarize the most important contributions to epidemiological modelling, the general properties of complex networks, and the most significant contributions to the problem of detecting sources of infection on complex networks. Also, we will consider the characteristics of the average distance of the observed node to all infected ones and its gradient on the example of the SIS model infection spreading on the small-world network. We will prove that the gradient of the average distance of the observed node to all infected ones is the largest for the source of infection, which we will also check on a set of data describing a real network. The SIS model is very similar in its characteristics to the dynamics of coronavirus spread (a recovered patient after some time becomes susceptible to a new infection again). Homogeneous mixing models only approximately describe the disease spread, so in this paper, we observe the SIS model spreading of infection on complex networks, specifically on small-world networks. The peculiarity of complex networks is a possibility of correct representation of the distribution of people and their interactions, where people are the vertices of the graph, and the interactions are the connections between the vertices. This paper deals with the source detection problem in SIS model disease spreading on small-world networks.