We investigate dynamic public good games in networks consisting of strategic users with interdependent network security. The strategic users can choose their investment strategies to contribute to the basic security of the network. Mimicking the behavior of infection propagation over multi-hop networks which depends on the average degree of the network, we propose a mean-field-type model to capture the effect of the others' control actions on the security state. Using linear-quadratic differential mean-field-type games we propose and analyze two different regimes, examining the equilibria and global optima of each to address. We show that, generically, each user has a unique best response strategy to invest into security. Closed-form expressions are obtained using the recent development of mean-field-type game theory.