This is the same stochastic branching-process model as the 3D spheroid, flattened onto a 2D tumor-cell lattice. An oncolytic virus selectively replicates inside tumor cells while sparing healthy tissue; when an infected cell's lytic timer expires it bursts, rolling one infection attempt against each living neighbor:
at burst: P(infect neighbor) = β (one roll per neighbor, per burst)
Cell bursts at t = t_infect + T_lytic, releasing antigen and dying
Antigen pool A(t): dA/dt = −decay·A, +1 per burst event
T-cell recruitment: spawn chance ∝ k_prime · A(t) · dt (up to a pool cap)
Lysis is immunogenic: dying tumor cells release damage-associated molecular patterns alongside tumor-associated antigens. This "in situ vaccination" primes T cells that then kill not only infected cells but also nearby uninfected tumor cells — a bystander/epitope-spreading effect distinct from direct viral lysis.
Whether the virus dies out or sweeps the colony is an epidemic-threshold effect: each burst infects roughly β × (neighbor count) new cells on average, so spread only sustains itself once that product exceeds 1 — low infectivity on a sparse lattice fizzles out exactly like a sub-critical branching process, which this build verifies numerically against the same rule used in the 3D source.
- Infectivity β — probability, rolled once per neighbor at the moment a cell bursts, that an adjacent healthy tumor cell becomes infected.
- Lytic period — time from infection to cell burst; shorter periods spread the virus faster but give the immune system less time to catch up.
- Immune priming rate — how strongly released antigen recruits new T cells into the colony.
- T-cell kill rate — probability per second a T cell adjacent to a tumor cell (infected or bystander) clears it.
- Inject Virus — infects the central cell of the colony, starting a fresh wave of spread.
Real-world relevance: this is the mechanism behind approved oncolytic viruses like T-VEC (talimogene laherparepvec, an engineered HSV-1) — direct tumor lysis combined with converting a "cold" (immune-excluded) tumor into a "hot" one that recruits systemic anti-tumor T-cell immunity. Drag to pan and scroll to zoom the flat colony map.