{Model of antibiotic decay, PD/PK and Physiological Tolerance}
{Hill function for antibiotic concentration dependent growth}
{SOS Induction Model}
{Saturation of the environment, Kmax - logistic model}
METHOD EULER
STARTTIME = 0
STOPTIME=240
DT = 0.02
DTOUT =.1
fmaxs=1  {Maximum growth rate sensitive}
fmins= -10 {Minimum growth rate sensitive}
fmaxr=.1  {Maximum growth rate tolerant}
fminr=-0.2
mic = 1 {MIC}
k=1 {Hill Coefficient}
kmax =1e20 {Saturation level for the population - logistic}
isr=0.0 {Maximum Induction rate sensitive to.tolerant}
ksr=1 {Antibiotic concentration where induction is half maximum}
irs=0 {Maximum repression rate tolerant to sensitive}
init A =10 {Initial Antibiotic concentration}
amax =10 {Antibiotic added at each dose interval}
init S= 5e7 {Initial density of sensitive bacteria}
init T=0  {Initial density of tolerant bacteria}
d =0.5 {Antibiotic decay rate}
d/dt (A) = -d*A + ADD  {change in the concentration of the antibiotic}
psis = ((fmaxs-fmins)*(A/mic)^k)/((A/mic)^k - fmins/fmaxs)
psir= ((fmaxr-fminr)*(A/mic)^k)/((A/mic)^k - fminr/fmaxr)
d/dt (S) =(S*fmaxs - isr*(A/(A+ksr))*S - psis*S +irs*T*(1-(A/(A+Ksr))))*(1-N/Kmax)  {Change in the density of sensitive bacteria}
d/dt (T)= (isr*(A/(A+ksr))*S + fmaxr*T - irs*T*(1-(A/(A+Ksr))) -psir*T)*(1-N/Kmax)
N=S+T
RAT=T/S
dose =12 {Dosing interval Lambda}
init TT=0
d/dt (TT) = 1-GT*2
ADD = IF TT > dose THEN PULSE(amax*2, TIME, 21) ELSE 0
GT= IF TT >dose THEN PULSE(dose, TIME, 21) ELSE 0