Fuzzy Continuous Petri Net-Based Approach for Modeling Immune Systems

The immune system has unique defense mechanisms such as innate, humoral and cellular immunity. These mechanisms are closely related to prevent pathogens from spreading in the host and to clear them effectively. To get a comprehensive understanding of the immune system, it is necessary to integrate the knowledge through modeling. Many immune models have been developed based on differential equations and cellular automata. One of the most difficult problem in modeling the immune system is to find or estimate appropriate kinetic parameters. However, it is relatively easy to get qualitative or linguistic knowledge. To incorporate such knowledge, we present a novel approach, fuzzy continuous Petri nets. A fuzzy continuous Petri net has capability of fuzzy inference by adding new types of places and transitions to continuous Petri nets. The new types of places and transitions are called fuzzy places and fuzzy transitions, which act as kinetic parameters and fuzzy inference systems between input places and output places. The approach is applied to model helper T cell differentiation, which is a critical event in determining the direction of the immune response.