{"entity":{"id":"mathematical-oncology","kind":"technology","name":"Mathematical models of cancer (mathematical oncology)","aka":["mathematical models","mathematical model","mathematical oncology","biophysical models","computational models of cancer","tumour modelling","in silico oncology","cancer modelling"],"tldr":"Mathematical oncology writes down how tumours grow, evolve, respond to treatment and interact with the immune system as equations or simulations, then uses them to design doses, schedules and trials. This page gathers every model OnCo covers.","summary":"Mathematical oncology is the use of equations, statistical models and computer simulations to describe cancer and to test treatment ideas before, or alongside, clinical trials. The oldest models describe growth: the Gompertz curve, the log-kill hypothesis and the Norton-Simon hypothesis shaped how chemotherapy is dosed and scheduled. Radiotherapy rests on the linear-quadratic model, fractionation and repopulation models, and tumour control probability. Evolutionary models, adaptive therapy dynamics and clonal evolution describe how resistance emerges and how to delay it.\n\nA second family simulates rather than solves: reaction-diffusion models of glioma spread, agent-based and multicellular simulations, immune-tumour dynamics, tumour mechanics and metastasis seeding models. Pharmacokinetic and pharmacodynamic models link dose to exposure and effect, and minimal residual disease kinetics turn blood tests into forecasts. Digital twin patient models aim to combine all of these for one person.\n\nEach model on this page names its originators, the equation or rule at its core, what it predicted well and where it fails. The models table lists them next to the foundation models and datasets, and the data sources page records the public model repositories, such as BioModels and PhysiCell, that OnCo draws on.","status":"established","asOf":"2026-09-17","links":[{"label":"Wikipedia","url":"https://en.wikipedia.org/wiki/Mathematical_oncology"},{"label":"OnCo models table","url":"https://onco.cc/models/"},{"label":"Society for Mathematical Biology, mathematical oncology subgroup","url":"https://www.smb.org/mathematical-oncology/"}],"tags":["mathematical-model"],"related":["gompertzian-growth-model","log-kill-hypothesis","norton-simon-hypothesis","goldie-coldman-model","drug-resistance-dynamics","adaptive-therapy-dynamics","evolutionary-game-theory-cancer","clonal-evolution-models","reaction-diffusion-glioma-model","agent-based-tumour-models","immune-tumour-dynamics-models","quantitative-systems-pharmacology","pkpd-modelling","body-surface-area-dosing","tumour-control-probability-models","fractionation-repopulation-models","tumour-doubling-time","angiogenesis-models","tumour-mechanics-models","metastasis-seeding-models","mrd-kinetics-models","digital-twin-patient-models"],"cancers":[],"sections":["ai-computation","drug-discovery"],"technologies":[],"targets":[],"drugs":[],"companies":[],"institutions":[],"pathways":[],"terms":[],"trials":[],"people":[],"bottlenecks":[],"keyPapers":[],"journals":[],"dependsOn":[],"notes":[],"principle":"Describe the tumour, the treatment and the host as variables that change over time; fit the model to data; use it to predict what a different dose, schedule or combination would do.","strengths":["Turns scattered observations into testable predictions","Cheap to run compared with trials","Explains why regimens work, not only that they do"],"limitations":["Parameters are hard to measure in one patient","Models can fit the past and still mispredict the future","Few have been validated prospectively"],"since":1964},"route":"/technologies/mathematical-oncology/","neighbours":{"technology":[{"id":"adaptive-therapy-dynamics","kind":"technology","name":"Adaptive therapy (evolution-based dosing)","route":"/technologies/adaptive-therapy-dynamics/"},{"id":"agent-based-tumour-models","kind":"technology","name":"Agent-based and multicellular simulations","route":"/technologies/agent-based-tumour-models/"},{"id":"angiogenesis-models","kind":"technology","name":"Angiogenesis and vascular normalisation models","route":"/technologies/angiogenesis-models/"},{"id":"body-surface-area-dosing","kind":"technology","name":"Body-surface-area dosing","route":"/technologies/body-surface-area-dosing/"},{"id":"clonal-evolution-models","kind":"technology","name":"Clonal evolution and branching models","route":"/technologies/clonal-evolution-models/"},{"id":"digital-twins-trials","kind":"technology","name":"Digital twins and virtual control arms","route":"/technologies/digital-twins-trials/"},{"id":"drug-resistance-dynamics","kind":"technology","name":"Evolutionary dynamics of drug resistance","route":"/technologies/drug-resistance-dynamics/"},{"id":"evolutionary-game-theory-cancer","kind":"technology","name":"Evolutionary game theory in cancer","route":"/technologies/evolutionary-game-theory-cancer/"},{"id":"goldie-coldman-model","kind":"technology","name":"Goldie-Coldman model of resistance","route":"/technologies/goldie-coldman-model/"},{"id":"gompertzian-growth-model","kind":"technology","name":"Gompertzian tumour growth","route":"/technologies/gompertzian-growth-model/"},{"id":"log-kill-hypothesis","kind":"technology","name":"Log-kill hypothesis (Skipper)","route":"/technologies/log-kill-hypothesis/"},{"id":"metastasis-seeding-models","kind":"technology","name":"Metastatic seeding and dormancy models","route":"/technologies/metastasis-seeding-models/"},{"id":"norton-simon-hypothesis","kind":"technology","name":"Norton-Simon hypothesis and dose-dense chemotherapy","route":"/technologies/norton-simon-hypothesis/"},{"id":"digital-twin-patient-models","kind":"technology","name":"Patient digital twins","route":"/technologies/digital-twin-patient-models/"},{"id":"pkpd-modelling","kind":"technology","name":"Pharmacokinetic and pharmacodynamic modelling","route":"/technologies/pkpd-modelling/"},{"id":"reaction-diffusion-glioma-model","kind":"technology","name":"Proliferation-invasion (reaction-diffusion) models of glioma","route":"/technologies/reaction-diffusion-glioma-model/"},{"id":"quantitative-systems-pharmacology","kind":"technology","name":"Quantitative systems pharmacology (QSP)","route":"/technologies/quantitative-systems-pharmacology/"},{"id":"mrd-kinetics-models","kind":"technology","name":"Residual disease kinetics (BCR-ABL halving and ctDNA slopes)","route":"/technologies/mrd-kinetics-models/"},{"id":"tumour-mechanics-models","kind":"technology","name":"Solid stress and tumour mechanobiology models","route":"/technologies/tumour-mechanics-models/"},{"id":"fractionation-repopulation-models","kind":"technology","name":"The four Rs and accelerated repopulation","route":"/technologies/fractionation-repopulation-models/"},{"id":"tumour-control-probability-models","kind":"technology","name":"Tumour control and normal tissue complication probability (TCP and NTCP)","route":"/technologies/tumour-control-probability-models/"},{"id":"tumour-doubling-time","kind":"technology","name":"Tumour volume doubling time","route":"/technologies/tumour-doubling-time/"},{"id":"immune-tumour-dynamics-models","kind":"technology","name":"Tumour-immune dynamics models","route":"/technologies/immune-tumour-dynamics-models/"}],"section":[{"id":"ai-computation","kind":"section","name":"AI & Computation","route":"/fronts/ai-computation/"},{"id":"drug-discovery","kind":"section","name":"Drug Discovery Platforms","route":"/fronts/drug-discovery/"}],"pathway":[{"id":"theories-of-cancer","kind":"pathway","name":"Theories of cancer: how the ideas connect","route":"/pathways/theories-of-cancer/"}],"term":[{"id":"atavistic-theory-of-cancer","kind":"term","name":"Atavistic theory: cancer as a reversion to an ancient programme","route":"/terms/atavistic-theory-of-cancer/"},{"id":"clonal-evolution-theory","kind":"term","name":"Clonal evolution and the ecological view of cancer","route":"/terms/clonal-evolution-theory/"},{"id":"mechanical-theory-of-cancer","kind":"term","name":"Mechanical theory: stiffness, pressure and force as causes","route":"/terms/mechanical-theory-of-cancer/"}]}}