  Oncolytic virotherapy, utilizing genetically modified viruses to combat
cancer and trigger anti-cancer immune responses, has garnered significant
attention in recent years. In our previous work arXiv:2305.12386, 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. We formally derive the continuum
limit of the model and carry out a systematic quantitative comparison between
this system of PDEs and the individual-based model in two spatial dimensions.
Furthermore, we describe the traveling 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. Some parameter ranges give rise to
oscillations of cell number in both models, in line with the behaviour of the
corresponding nonspatial model, which presents Hopf bifurcations. Nevertheless,
in some situations the behaviours of the two models may differ significantly,
suggesting that stochasticity plays a key role in the dynamics. Our results
highlight that a too rapid immune response, before the infection is
well-established, appears to decrease the efficacy of the therapy and thus some
care is needed when oncolytic virotherapy is combined with immunotherapy. 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.
