Influenza and other acute respiratory diseases pose a significant challenge to global health. The complexity of analyzing and mitigating influenza transmission is related to heterogeneity of contact network structures in modern cities. The need for effective public health strategies has driven the development of highly detailed network and agent-based models. To overcome a drawback of modeling multi-agent systems, which is their high demand for computational resources, approximate models can be employed. In our article, we present an approach that allows to convert heterogeneous synthetic populations into an input for the edge-based compartmental SEIR model. We demonstrate the method application by simulating influenza spread in a contact network of the synthetic population of Chelyabinsk, Russia. At a cost of neglecting some details in contact network structure, the proposed algorithm allows to greatly enhance simulation speed compared to multi-agent modeling, and at the same time to preserve population heterogeneity, which makes it a good choice for application in epidemic surveillance.