Encounter-based network is a frequently-disconnected wireless ad-hoc network requiring immediate neighbors to store and forward aggregated data for information disseminations. Using traditional approaches such as gateways or firewalls for deterring worm propagation in encounter-based networks is inappropriate. We propose the worm interaction approach that relies upon automated beneficial worm generation aiming to alleviate problems of worm propagations in such networks. To understand the dynamic of worm interactions and its performance, we mathematically model worm interactions based on major worm interaction factors including worm interaction types, network characteristics, and node characteristics using ordinary differential equations and analyze their effects on our proposed metrics. We validate our proposed model using extensive synthetic and trace-driven simulations. We find that, all worm interaction factors significantly affect the pattern of worm propagations. For example, immunization linearly decreases the infection of susceptible nodes while on-off behavior only impacts the duration of infection. Using realistic mobile network measurements, we find that encounters are bursty, multi-group and non-uniform. The trends from the trace-driven simulations are consistent with the model, in general. Immunization and timely deployment seem to be the most effective to counter the worm attacks in such scenarios while cooperation may help in a specific case. These findings provide insight that we hope would aid to develop counter-worm protocols in future encounter-based networks.