Bacterial immune systems (CRISPR-Cas and restriction-modification systems) defend bacterial cells against invasion by viruses or plasmids. CRISPR-Cas has also found major biotechnology applications, but to optimally exploit them, it is necessary to understand native function of this system in bacteria. CRISPR-Cas is typically silent under normal conditions, and one of the main questions in understanding CRISPR-Cas functioning is how this normally silent system is induced, which is very hard to directly experimentally observe. Consequently, CRISPR-Cas induction mechanism is currently unknown, and the main goal of this work is to use computational modeling to understand the role of the key features in CRISPR-Cas activation, and to propose a realistic experimental model for CRISPR-Cas induction. To address these questions, we use thermodynamical modeling of the system transcription regulation, and dynamical modeling of the relevant molecular species (RNA and proteins). Furthermore, much more rudimental bacterial immune systems (restriction-modification) exhibit similar features in their transcription regulation as CRISPR-Cas, and likely face similar dynamical constraints in their functioning. Consequently, we also model regulation of bacterial restriction-modification systems with different architectures, and propose that the same design principles may be behind regulation of both bacterial immune systems. Finding the same design principles behind mechanistically otherwise different systems (in this case CRISPR-Cas and restriction-modification systems) is also a major goal of systems biology.