Intrusion detection is an important problem in sensor networks. Prior works in static sensor environments show that constructing sensor barriers with random sensor deployment can be effective for intrusion detection. In response to the recent surge of interest in mobile sensor applications, this paper studies the intrusion detection problem in a mobile sensor network, where it is believed that mobile sensors can improve barrier coverage. Specifically, we focus on providing $k$-barrier coverage against moving intruders. This problem becomes particularly challenging given that the trajectories of sensors and intruders need to be captured. We first demonstrate that this problem is similar to the classical kinetic theory of gas molecules in physics. We then derive the inherent relationship between barrier coverage performance and a set of crucial system parameters including sensor density, sensing range, and sensor and intruder mobility. We examine the correlations and sensitivity from the system parameters, and we derive the minimum number of mobile sensors that needs to be deployed in order to maintain the $k$ -barrier coverage for a mobile sensor network. Finally, we show that the coverage performance can be improved by an order of magnitude with the same number of sensors when compared to that of the static sensor environment.