Elimination of danger (e.g. pathogens) is an important activity for organisms. From this viewpoint, the optimization analysis is applicable to study the reaction of immune system.

There are different patterns of defense observed in immune system. Higher vertebrates have both innate immunity and acquired immunity, whilst lower animals don't. Some proteins for defense are stored beforehand, whilst others are produced after infection. It is likely that some advantages lay under the realized patterns of defense. The organisms should prevent pathogen growth, with saving defense cost (e.g. tissue injury). I present the optimal defense pattern using the above criterion.

First, we focus on difference between two defense options, such as delay, cost, effectiveness, and uncertainty of information available. If defense proteins are produced via gene expression after pathogen attack the host (infection), the pathogen abundance increases quickly until the level of defense protein becomes enough. In contrast, if defense proteins are produced and stored before the infection, the host can escape from the disadvantage. However, the storing holds another disadvantage -- stored proteins can be wasteful, because the information available before the infection is limited. Taking these into consideration, I discuss the optimal defense strategy.

Second, I present a model clarifying dynamic defense strategy of the adaptive immune response. "Bang-bang control", to produce "immune activity" is an economical strategy for the host's immune system. The switching 0 and 1 continues just before the end of lifetime. This result suggests that some immune activity can be maintained in the host body even if no risk of re-infection is.