{Toxin-Mediated Cycling -l in chemostat culture}
{Autocatalytic production of toxin by B1}
{Allows for the invasion of a second population that does not produce the toxin but is sensitive to it, B2}
{Model similar to that used in Cornejo et al. Oscillations in continuous culture populations of}
{Streptococcus pneumoniae: population dynamics and the evolution of clonal suicide. Proc. Roy. Soc. B. 276: 99-1008, 2009.}
METHOD RK4
STARTTIME = 0
STOPTIME=1000
DT = 0.001
DTOUT =1
init R = 500 {Resource concentration}
init B1 =1e8 {Density of toxin producing strain}
init B2 =10 {Density of non-toxin producing strain}
init T1 =50 {Toxin 1 concentration}
c=500 {Reservoir resource concentration}
w=0.1 {Dilution rate}
x11= 5E-6 {Toxin adsorption-kill rate 1 by toxin 1}
x12 =5e-5 {Toxin adsorption-kill rate 2 by toxin 1}
e=1e-7 {conversion efficiency}
y1=4E-10 {Toxin production parameteR 1}
k=0.25 {Monod constant}
vB1=.5{Max growth B1}
vB2=.6 {Max growth rate B2}
psiB1 = vB1*R/(k+R)
psiB2=vB2*R/(k+R)
dx1 = 0.1 {Toxin decay rate}
ex=1 {Exponent for the toxin equations}
d/dt (R) = w*(c-R) - psiB1*B1*e -psiB2*B2*e
d/dt (B1) = psiB1*B1 - x11*B1*T1 - w*B1
d/dt (B2) = psiB2*B2 - x12*B2*T1 - w*B2
d/dt (T1) = y1*B1*T1^ex - w*T1 - dx1*T1