ODE Model

$\displaystyle {\frac {dP}{dt}}$	$\textstyle =$	$\displaystyle k_{RA} R A -k_PP,$	(1)
$\displaystyle {\frac {dR}{dt}}$	$\textstyle =$	$\displaystyle -k_{RA} RA +k_PP- k_RR + k_1r,$	(2)
$\displaystyle {\frac {dA}{dt}}$	$\textstyle =$	$\displaystyle -k_{RA}R A +k_PP +k_2L- k_AA,$	(3)
$\displaystyle {\frac {dL}{dt}}$	$\textstyle =$	$\displaystyle k_{3}l - k_LL.$	(4)
$\displaystyle {\frac {dS}{dt}}$	$\textstyle =$	$\displaystyle k_4s-k_SS.,$	(5)
$\displaystyle {\frac {ds}{dt}}$	$\textstyle =$	$\displaystyle V_s\frac{P}{K_s+P}-k_ss,$	(6)
$\displaystyle {\frac {dr}{dt}}$	$\textstyle =$	$\displaystyle V_r\frac{P}{K_r+P}-k_rr + r_0,$	(7)
$\displaystyle {\frac {dl}{dt}}$	$\textstyle =$	$\displaystyle V_l\frac{P}{K_l+P}\frac{1}{K_S+S}-k_ll + l_0$	(8)