Mathematical model for immune checkpoint inhibitors with delayed responses

¹ The University of Sydney, Sydney, Australia
² The Government of NSW, Australia
³ The University of Sydney, Australia

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 19 April 2025
Accepted: 2 February 2026

Abstract

We introduce a set of ordinary differential equations (ODE) that qualitatively reproduces delayed responses observed in immune checkpoint blockade therapy, such as anti-CTLA-4 Ipilimumab. Immune checkpoint inhibitors have revolutionised cancer treatment, offering durable responses in some patients, but their efficacy is often hindered by delayed anti-tumour immune responses. Our ODE system can be considered as two modular submodels: one focusing on dendritic cell (DC) dynamics within the tumour microenvironment and the other on T cell activation within lymph nodes. Together, these submodels provide a mechanistic framework to explore the interplay between immune activation and tumour-driven suppression. By calibrating key parameters, our models naturally reproduce clinically observed phenomena that range from no response to delayed anti-tumour activity. Simulations suggest that insufficient co-stimulatory signals by DCs may play a key role in delayed responses. Furthermore, we offer a framework on how individual immune profiles shape treatment outcomes in anti-CTLA-4 and anti-PD-1 combination therapies. Our model also suggests potential insights into long-term dynamics, including tumour dormancy, oscillatory behaviour and the conditions necessary for durable tumour eradication. We hope this exploratory study will inspire further research into the intricate and nuanced dynamics of tumour-immune interactions.