The immune system provides the host organism with defense mechanisms against invading pathogens and tumor development and it plays an active role in tissue and organ regeneration. Deviations from the normal physiological functioning of the immune system can lead to the development of diseases with various pathologies including autoimmune diseases and cancer. Modern research in immunology is characterized by an unprecedented level of detail that has progressed towards viewing the immune system as numerous components that function together as a whole network. Currently, we are facing significant difficulties in analyzing the data being generated from high-throughput technologies for understanding immune system dynamics and functions, a problem known as the ‘curse of dimensionality’.

As the mainstream research in mathematical immunology is based on low-resolution models, a fundamental question is how complex the mathematical models should be? To respond this challenging issue, we advocate a hypothesis-driven approach to formulate and apply available mathematical modelling technologies for understanding the complexity of the immune system. Moreover, pure empirical analyses of immune system behavior and the system’s response to external perturbations can only produce a static description of the individual components of the immune system and the interactions between them. Shifting our view of the immune system from a static schematic perception to a dynamic multi-level system is a daunting task. It requires the development of appropriate mathematical methodologies for the holistic and quantitative analysis of multi-level molecular and cellular networks. Their coordinated behavior is dynamically controlled via distributed feedback and feedforward mechanisms which altogether orchestrate immune system functions. The molecular regulatory loops inherent to the immune system that mediate cellular behaviors, e.g. exhaustion, suppression, activation and tuning, can be analyzed using mathematical categories such as multi-stability, switches, ultra-sensitivity, distributed system, graph dynamics, or hierarchical control.

The aim of this Research Topic is to collect current state-of-the-art research on using mathematically-driven exploration and development of predictive models to describe the complexity of the immune system. The development of comprehensive mathematical and computational modelling methodologies will open novel avenues for quantifying the controlability of the immune system, for establishing a predictive platform for lymphoid tissue- and organ engineering, and for the model-informed rational design of combination and personalized treatments of immune-related diseases.

We welcome the submission of Original Research, Hypothesis and Theory, Perspective, Methods, Technology Report, Systematic Review, Review, Mini-Review, Opinion articles that cover the following topics:

1. Mathematical modeling of immune cell dynamics in lymphoid organs.
2. Mathematical modeling of immune cell migration.
3. Mathematical modeling of immune system homeostasis.
4. Multi-scale and hybrid modeling of viral and microbial infections.
5. Mathematical modelling of immune cell regulation and the cell fate decisions made under normal and pathogenic conditions.
6. Computational immunology methods and software related to addressing the sub-topics mentioned above.

Important Note: All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.