The evolution of mathematical immunology

Abstract

The types of mathematical models used in immunology and their scope have changed drastically in the past 10 years. Classical models were based on ordinary differential equations (ODEs), difference equations, and cellular automata. These models focused on the 'simple' dynamics obtained between a small number of reagent types (e.g. one type of receptor and one type of antigen or two T-cell populations). With the advent of high-throughput methods, genomic data, and unlimited computing power, immunological modeling shifted toward the informatics side. Many current applications of mathematical models in immunology are now focused around the concepts of high-throughput measurements and system immunology (immunomics), as well as the bioinformatics analysis of molecular immunology. The types of models have shifted from mainly ODEs of simple systems to the extensive use of Monte Carlo simulations. The transition to a more molecular and more computer-based attitude is similar to the one occurring over all the fields of complex systems analysis. An interesting additional aspect in theoretical immunology is the transition from an extreme focus on the adaptive immune system (that was considered more interesting from a theoretical point of view) to a more balanced focus taking into account the innate immune system also. We here review the origin and evolution of mathematical modeling in immunology and the contribution of such models to many important immunological concepts.

The role of mathematical models of host–pathogen interactions for livestock health and production – a review

“…Detailed information about various types of models of immune system dynamics published in the immunological and mathematical literature is beyond the scope of this review, but can be found in several excellent reviews (e.g. Morel, 1998;Nowak and May, 2000;Yates et al, 2001;Perelson, 2002;Louzoun, 2007;Kirschner and Linderman, 2009). …”

“…Traditional conceptual approaches are replaced by more data-driven approaches and mathematical systems with few components giving way to large networks. Citing Louzoun (2007), 'mathematical modelling in immunology is becoming more and more molecular'.…”

“…Despite their simplicity, they are able to generate a rich spectrum of complex dynamic patterns (Ganguly et al, 2003;Bauer et al, 2009). Integration of new biological insights into the model rules is relatively straightforward for these types of models compared with the mechanistic DE or stochastic models, which do not lend themselves easily to model extensions (Louzoun, 2007). However, several restrictions apply to CA and ABMs: first, the simulations are often sensitive to parameter changes, so that model validation requires a comprehensive sensitivity analysis (Louzoun, 2007).…”

“…Integration of new biological insights into the model rules is relatively straightforward for these types of models compared with the mechanistic DE or stochastic models, which do not lend themselves easily to model extensions (Louzoun, 2007). However, several restrictions apply to CA and ABMs: first, the simulations are often sensitive to parameter changes, so that model validation requires a comprehensive sensitivity analysis (Louzoun, 2007). As the overall system behaviour emerges from local interactions, it can be difficult to discern whether an unexpected result is the reflection of a programming mistake or a surprising emerging property of the model.…”

“…Bioinformatics and systems biology Growing information with regard to the pathogen genomes and molecular and biochemical pathways involved in the host immune response has shifted the demand of quantitative methods beyond the realm of mathematics towards bioinformatics and systems biology, which are focused on interpreting the large data sets emerging from genomic studies (Louzoun, 2007;Forst, 2010). Bioinformatics and systems biology are closely related.…”