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We analyze the propagation of the susceptible–infected–susceptible model on the network, where the partial connection information is known. In order to analyze the spread of network epidemics, the quenched mean-field method requires complete connection information, while the heterogeneous mean-field method requires complete topology information. When only partial connection information is available, the quenched mean-field method may be disabled. In view of this situation, a hybrid model consisting of connection and topology information is proposed. The theoretical results are in good agreement with stochastic simulations on scale-free networks. In addition, as the proportion of connection information in the network increases, model predictions about final epidemic size become more accurate when the effective transmission rate is slightly larger than the simulation threshold. • A hybrid one-vertex model composed of QMF and HMF methods is developed. • A heterogeneous network with partial connection information can be handled by using the hybrid method. • The hybrid model is an improvement on the HMF model especially for scale-free networks. • The dimension reduction method for the QMF model is obtained. [ABSTRACT FROM AUTHOR]