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Wireless sensor networks present a feasible and economic solution to some of the most challenging problems such as intrusion detection. In this paper, we establish relationship between node density, sensing range, and the possible intrusion distance before the intruder is detected by any of the sensors. We also extend our model to the multi-sensor joint detection case where an event can only be detected by k (k > 1) sensors simultaneously. Furthermore, we consider the effect of node heterogeneity on the intrusion detection in wireless sensor network, where two types of sensors with different sensing ranges are deployed. All the analytical results are validated via simulations. Our analysis can provide very useful insights in choosing network design parameters of sensor networks so that specified performance requirements can be met, thereby enhancing the acceptance of sensor networks.