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Table 12 Transition rates calculations from the mathematical equations for case 3

From: Investigating mathematical models of immuno-interactions with early-stage cancer under an agent-based modelling perspective

Agent Transition Mathematical equation Transition rate
Effector Cell Reproduce p 1 I E g 1 + I × p 1 - q 1 S q 2 + S p 1 × T o t a l I L _ 2 g 1 + T o t a l I L _ 2 × p 1 - q 1 × T o t a l T G F B e t a q 2 + T o t a l T G F B e t a
  Die μ 1 E mu 1
  ProduceIL2 p 3 T E ( g 4 + T ) ( 1 + a l p h a S ) p 3 . T o t a l T u m o u r ( g 4 + T o t a l T u m o u r ) ( 1 + a l p h a . T o t a l T G F )
  KillTumour a a . T E g 2 + T a a × T o t a l T u m o u r × T o t a l E f f e c t o r g 2 + T o t a l T u m o u r
Tumour Cell Reproduce ( a T ( 1 - T 1000000000 ) ) ( T o t a l T u m o u r . a ( 1 - T o t a l T u m o u r 1000000000 ) )
  Die ( a T ( 1 - T 1000000000 ) ) ( T o t a l T u m o u r . a ( 1 - T o t a l T u m o u r 1000000000 ) )
  DieKilledByEffector a a . T E g 2 + T message from effector
  ProduceTGF p 4 T 2 t e t a 2 + T 2 p 4 T u m o u r C e l l s t e t a 2 + T u m o u r C e l l s 2
  EffectorRecruitment c T 1 + γ S c 1 + g a m m a . T o t a l t G F
IL-2 Loss μ 2 I mu 2
TGF-β Loss μ 3 S mu 3
  Stimulates
TumourGrowth
p 2 T g 3 + S p 2 . T o t a l T G F g 3 + T o t a l T G F