# Tumour-immune dynamics models

Source: https://onco.cc/technologies/immune-tumour-dynamics-models/  
OnCo record `immune-tumour-dynamics-models` (Technology). Data CC BY-NC 4.0, attribute "Data from OnCo (onco.cc)"; commercial use needs a licence.

## TL;DR

Predator-prey style equations describe how immune cells hunt tumour cells, and they reproduce dormancy, escape and the delayed, sometimes explosive, responses seen with immunotherapy; they now help design combination and scheduling trials.

## Summary

Kuznetsov and colleagues' 1994 model treated effector immune cells and tumour cells as interacting populations, reproducing dormancy, sneaking-through and oscillations. Later models added checkpoints, exhaustion, antigen presentation and cytokines, and have been used to explain pseudoprogression and hyperprogression under PD-1 blockade, to propose sequencing of radiotherapy and immunotherapy, and to simulate CAR-T expansion and cytokine release. Quantitative systems pharmacology models of checkpoint blockade are increasingly used by developers to choose doses and combinations.

## Fields

- Kind: Technology
- Status: emerging
- Last checked: 2026-09-17
- Tags: mathematical-model
- Principle: Coupled ordinary differential equations for tumour and immune populations with recruitment, killing, exhaustion and suppression terms, whose equilibria correspond to dormancy, escape or elimination.
- Since: 1994
- Strengths: Explains non-linear immunotherapy responses; Guides sequencing with radiotherapy and chemotherapy; Extends to CAR-T kinetics
- Limitations: Immune parameters are poorly identifiable; Spatial and antigen heterogeneity simplified; Predictions rarely validated prospectively

## Sources

- Kuznetsov and colleagues 1994, Bulletin of Mathematical Biology: https://doi.org/10.1007/BF02460644

## Connected records

- fronts: [AI & Computation](https://onco.cc/fronts/ai-computation/), [Drug Discovery Platforms](https://onco.cc/fronts/drug-discovery/)
- technologies: [CAR-T cell therapy](https://onco.cc/technologies/car-t/), [Immune checkpoint inhibitors](https://onco.cc/technologies/checkpoint-inhibitor/), [Quantitative systems pharmacology (QSP)](https://onco.cc/technologies/quantitative-systems-pharmacology/)

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