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

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
$p 2 T g 3 + S$ $p 2 . T o t a l T G F g 3 + T o t a l T G F$