Hybrid disease modeling is a perspective area of research that allows using detailed individual-based models for the outbreak onset phase and lightweight compartmental models to capture the general trend of the disease progression. In such a way, the method of hybrid modeling provides a good trade-off between the simulation speed and the accuracy of reproducing disease dynamics. One of the problems related to this approach is how to switch properly between the two models. That included detecting the right time moment to finish simulations with the detailed model and calculating correctly the input parameters for the compartmental model. In this paper, we propose an implementation of switching which relies on evaluation and prediction of disease transmission rate. Using an example with a network-based model and a discrete compartmental model, we demonstrate several methods of disease transmission prediction based on statistical models and machine learning approaches and analyze their advantages and disadvantages. The developed methods can be generalized to hybrid modeling of highly detailed demographic processes and propagation processes in general.