As one of the most important aspects of spreading dynamics on networks, propagation of rumor, which includes the process of rumor diffusing and elimination, plays an important role in the understanding of information dissemination within social networks. However, the current understanding of rumor propagation within networks is far from clear, especially the full analysis of the process of rumor diffusing and elimination is lacking. Here, with the rumor elimination process supplemented to the susceptible-infective-refractory (SIR) rumor spreading model, a modified rumor spreading model is established and defined as spreader-ignorant-eliminater-Rstifler-Estifler (SIERsEs) model. The developed mean-field equations of SIERsEs model, with the diffussing and elimination thresholds calculated, could describe the theory of steady-state dynamics of the rumor propagation. Simulation analysis is performed to assess the interaction between the diffussing and elimination process, and estimate the influences of diffusing rate, estimation rate, and averaged degree of the network, on the rumor spreading. The results show whether low or high value of average network degree would accompany a low level of the influence of rumor propagation. In addition, the shortcomings of the traditional immunization strategies, such as targeted immunization and acquaintances immunization, are pointed out. Based on this understanding, we propose two optimized immunization strategies, defined as active immunization and passive immunization, and we further evaluate how different parameters (forgetting rate of spreader, forgetting rate of eliminater and the starting time of immunization) affect the suppression effectiveness of the newly developed active and passive immunization strategies. Importantly, some so-called rumor-inhibition strategies actually could not inhibit but enhance the rumor propagation instead. These obtained findings in the present study could not only elaborate our understandings in spreading dynamics within network, but also provide an insight into the developing effective strategies of inhibiting rumor propagation.