A hybrid discrete-continuum modelling approach for the interactions of the immune system with oncolytic viral infections

Oncolytic virotherapy, which employs genetically engineered viruses to target cancer cells and stimulate anti-tumour immune response, has emerged as a promising therapeutic strategy. In our previous work, we developed a stochastic agent-based model elucidating the spatial dynamics of infected and uninfected cells within solid tumours. Building upon this foundation, we present a novel stochastic agent-based model to describe the intricate interplay between the virus and the immune system; the agents' dynamics are coupled with a balance equation for the concentration of the chemoattractant that guides the movement of immune cells. To better understand the macroscopic behavior, we derive a formal continuum limit of the model and compare it quantitatively to the individual-based simulations in two spatial dimensions. Furthermore, we describe the travelling waves of the three populations, with the uninfected proliferative cells trying to escape from the infected cells while immune cells infiltrate the tumour. Simulations show a good agreement between agent-based approaches and numerical results for the continuum model. In certain parameter regimes, both the agent-based and continuum models exhibit oscillatory behavior, echoing Hopf bifurcations seen in non-spatial analogues. However, divergences between the models in specific cases highlight the critical role of stochasticity. Notably, we find that a premature immune response may undermine therapeutic efficacy, emphasising the importance of timing and modulation in combined immunovirotherapy approaches. This further suggests the importance of clinically improving the modulation of the immune response according to the tumour's characteristics and to the immune capabilities of the patients.