MadonnaModel0 {Antibiotic treatment in continuous culture with a wall - biofilm populaiton} {density and resource - dependent, PD, four bacterial populations.} METHOD RK4 STARTTIME = 0 STOPTIME= 160 DT = 0.001 DTOUT = .5 {Variables} init A =0 {Initial [ab]} init N =1e9{Density iable planktonic sensitive bacteria} init R =1 {Resource concentration} init D = 0 {Density Dead planktonic bacteria} init P =0 {IDensity of planktonic Persistent bacteria} init B = 0 {Density of the wall (Biofilm) population} {Parameters} {Maximum and mininum growth rates} psimax = 1 {Maximum growth rate - Sensitive} psimin= -2 {Minimum growth rate - Sensitive} psimaxp = 0.001 {Maximum growth rate - Persistant} psiminp= -0.01 {Minimum growth rate - Persistant} psimaxb = 0.001 {Maximum growth rate - Bioflim- wall} psiminb= -0.00001 {Minimum growth rate - - Biofilm-wall} {Density effects} Mmin = 1 {Minimum MIC} Mmax = 40 {Maximum MIC} pd =0 {Density effect on MIC} cr =0.9 {Coefficient for the resource effect on psimin} kappa = 1 {Hill Coefficient} e= 5e-7 {Conversion efficiency?} kr=0.25 {monod constant - resource} kmax = 1e7 {Monod for density-dependent antibiotic function} w =0 {flow rate planktonic population} wb=0.0001{flow rate wall B population} C=500 {Reservoir concentration} f=0 {rate of conversion of dead cells into resources} yp=0.001 {Rate of production of persistent cells from active} yd=0.00001 {Rate of production of active cells from persistent} yb=0.001 {Rate at which the wall is layed down} yw=0.01 {Rate at which wall migrates to planktonic} {Antibiotic decay} {dA is the total anibiotic decay rate} ddx =0.01 {Density independent antibiotic decay rate} dv=1e-9 { Per viable cell decay coefficient} dk= 1e-9 {Per killed cell decay component} da=ddx +NT*dv +dk*D {Density dependent MIC} MD= Mmin + pd*((Mmax*NT)/(NT+kmax)) {Resource and density dependent hill functions} {Susceptible population} pmax= psimax*R/(R+kr) pmin = psimin*(1-cr) +cr*(R/(R+kr))*psimin hill = ((pmax-pmin)*((A/MD)^kappa))/((A/MD)^kappa - pmin/pmax) psi =pmax - hill {Realized growth rate sensitive} {Persistent Population P} pmaxp= psimaxp*R/(R+kr) pminp = psiminp*(1-cr) +cr*(R/(R+kr))*psiminp hillp = ((pmaxp-pminp)*((A/MD)^kappa))/((A/MD)^kappa - pminp/pmaxp) psip=pmaxp-hillp {Wall Population} pmaxb= psimaxb*R/(R+kr) pminb = psiminb*(1-cr) +cr*(R/(R+kr))*psiminb hillb = ((pmaxb-pminb)*((A/MD)^kappa))/((A/MD)^kappa - pminb/pmaxb) psib=pmaxb-hillb {Equations} d/dt (A) = -da*A -w*A +ADD {Antibiotic} d/dt (D) = N*hill +P*hillp+B*hillb -w*D -f*D {Dead cells} d/dt (N) = N*psi -w*N - yp*N + yd*P -N*yb + B*yw {Planktonic susceptible cells} d/dt (R) = w*(C-R) - e*(N*pmax +P*pmaxp+B*pmaxb)+f*D*e/2 {Resource concentration} d/dt (P) = P*psip +N*yp - P*yd - w*P {Persister population} d/dt (B)=B*psib+N*yb-B*yw-wb*B {Wall, biofilm population} NT=N+P+B {Total viable bacteria} NP=N+P {Total viable planktonic bacteri} {Antibiotic dosing} AMAX=100 dose =24 {Dosing interval} init TT=0 d/dt (TT) = 1- GT/DT ADD = IF TT > dose THEN AMAX/DT ELSE 0 GT= IF TT >dose THEN dose ELSE 0 Geneva5 ]0}000 0 00E= mq ) @rk2DTMb@?w333333?dv &,> F?? &t 1U]MbP?MbP?MbP?(QY*??>?TIMEaANR)1DeqyPB da=MUMD9  ]=Yu? _B? _B  9AI4yy   "E$a&}(*%,9.M0<@BDFHNIiq % X A] 91  &,q .0U01!1 Y1 111A11)1191}1!<Q1 1$)<&1<(9<*A<,1.I1I<