$\frac{d[BLA]_{T}}{dt}= \frac{\beta _{BLA}}{1+ \lbrack \frac{[LacI]_{T}}{K_{LacI}\lbrack 1+\lbrack \frac{[IPTG]}{K_{IPTG}}\rbrack ^{\eta _{IPTG}}\rbrack }\rbrack ^{\eta _{LacI}}}- \gamma _{BLA}[BLA]_{T}$

$\frac{d\lbrack TorA\rbrack _{T}}{dt}= \frac{\beta _{TorA}}{1+ \lbrack \frac{\lbrack LacI\rbrack _{T}}{K_{LacI}\lbrack 1+\lbrack \frac{\lbrack IPTG\rbrack }{K_{IPTG}}\rbrack ^{\eta _{IPTG}}\rbrack }\rbrack ^{\eta _{LacI}}}- \gamma _{TorA}\lbrack TorA\rbrack _{T}$

$\lbrack BLA\rbrack _{T}=\lbrack BLA\rbrack +\lbrack BLA,TorA\rbrack +\lbrack BLA,BLA\rbrack +\frac{\lbrack BLA,TorA\rbrack _{per}}{10}$

$\lbrack TorA\rbrack _{T}=\lbrack TorA\rbrack +\lbrack BLA,TorA\rbrack +\lbrack TorA,TorA\rbrack +\frac{\lbrack BLA,TorA\rbrack _{per}}{10}+\frac{\lbrack TorA,TorA\rbrack _{per}}{10}$

$[BLA,TorA] = \frac{\lbrack BLA][TorA\rbrack }{K_{d,BLATorA}}$

$[BLA,BLA] = \frac{\lbrack BLA][BLA\rbrack }{K_{d,BLABLA}}$

$[TorA,TorA] = \frac{\lbrack TorA][TorA\rbrack }{K_{d,TorATorA}}$

$\frac{d\lbrack BLA,TorA\rbrack {per}}{dt}= \frac{k{TAT,BLATorA}\lbrack TAT\rbrack {T}K{m,t,TorATorA}[BLA,TorA]}{K_{m,t,TorATorA}\lbrack BLA,TorA\rbrack

$\frac{d\lbrack TorA,TorA\rbrack _{per}}{dt}= \frac{k_{TAT,TorATorA}\lbrack TAT\rbrack _{T}K_{m,t,BLATorA}\lbrack TorA,TorA\rbrack }{K_{m,t,TorATorA}\lbrack BLA,TorA\rbrack + K_{m,t,TorATorA}K_{m,t,BLATorA}+ K_{m,t,BLATorA}\lbrack TorA,TorA\rbrack }- \gamma _{TorATorAperi}\lbrack TorA,TorA\rbrack _{per}$

$\frac{d[TAT]_{T}}{dt}=\beta _{TAT}-\gamma _{TAT}[TAT]_{T}$

$\frac{d[LacI]_{T}}{dt}= \beta _{LacI} - \gamma _{LacI}[LacI]_{T}$

$\lbrack IPTG\rbrack =[IPTG]_{ext}$

$\frac{d[Amp]}{dt}= k_{t,Amp}(\lbrack Amp\rbrack _{ext}-\lbrack Amp\rbrack ) - \gamma _{Amp}\lbrack Amp\rbrack - k_{Amp}\lbrack Amp\rbrack - \frac{k_{cat,BLATorAperi}\lbrack BLA,TorA\rbrack _{per}[Amp]}{K_{m,BLATorAperi}+[Amp] }$

$\frac{d[aMPp]}{dt}= k_{Amp}\lbrack Amp\rbrack - \gamma _{aMPp}\lbrack aMPp\rbrack $

$\frac{d[AmpR]_{T}}{dt}= \beta _{AmpR} - \gamma _{AmpR}[AmpR]_{T}$

$\frac{d[TetC]}{dt}= \frac{\beta _{TetC}}{1+ \lbrack \frac{[AmpR]_{T}}{K_{AmpR}\lbrace 1+\lbrack \frac{\lbrack aMPp\rbrack }{K_{aMPp}}\rbrack ^{\eta _{aMPp}}\rbrace }\rbrack ^{\eta _{AmpR}}}- \gamma _{TetC}[TetC]$

$\frac{d[Tet]}{dt}= k_{t,Tet}(\lbrack Tet\rbrack _{ext}-\lbrack Tet\rbrack ) - \gamma _{Tet}\lbrack Tet\rbrack - k_{Tet}\lbrack Tet\rbrack - \frac{k_{cat,TetC}\lbrack TetC\rbrack [Tet]}{K_{m,TetC}+[Tet] }$

$Growth= \min (\frac{1}{1+ \lbrack \frac{Tet}{K_{g,Tet}}\rbrack ^{\eta _{Tet}}} , \frac{1}{1+ \lbrack \frac{Amp}{K_{g,Amp}}\rbrack ^{\eta _{Amp}}})$

$\frac{d[BLA]_{T}}{dt}= \frac{\beta _{BLA}}{1+\Big(\frac{[LacI]_{T}/K_{LacI}}{ 1+\big( [IPTG]/K_{IPTG}\big) ^{\eta _{IPTG}} }\Big) ^{\eta _{LacI}}}- \gamma _{BLA}[BLA]_{T}$

$\frac{d[TorA]_{T}}{dt}= \frac{\beta _{TorA}}{1+\Big(\frac{[LacI]_{T}/K_{LacI}}{ 1+\big( [IPTG]/K_{IPTG}\big) ^{\eta _{IPTG}} }\Big) ^{\eta _{LacI}}}- \gamma _{TorA}[TorA]_{T}$

$\frac{d[BLA,TorA]{per}}{dt}= \frac{k{TAT,BLATorA}[TAT]_{T}[BLA]}{[BLA]

$\frac{d[TAT]_{T}}{dt}=\beta _{TAT}-\gamma _{TAT}[TAT]_{T}$

$\frac{d[LacI]_{T}}{dt}= \beta _{LacI} - \gamma _{LacI}[LacI]_{T}$

$\frac{d[Amp]}{dt}= k_{t,Amp}(\lbrack Amp\rbrack _{ext}-\lbrack Amp\rbrack ) - \gamma _{Amp}\lbrack Amp\rbrack - k_{Amp}\lbrack Amp\rbrack - \frac{k_{cat,BLATorAperi}\lbrack BLA,TorA\rbrack _{per}[Amp]}{K_{m,BLATorAperi}+[Amp] }$

$\frac{d[aMPp]}{dt}= k_{Amp}\lbrack Amp\rbrack - \gamma _{aMPp}\lbrack aMPp\rbrack $

$\frac{d[AmpR]_{T}}{dt}= \beta _{AmpR} - \gamma _{AmpR}[AmpR]_{T}$

$\frac{d[TetC]}{dt}= \frac{\beta _{TetC}}{1+ \lbrack \frac{[AmpR]_{T}}{K_{AmpR}\lbrace 1+\lbrack \frac{\lbrack aMPp\rbrack }{K_{aMPp}}\rbrack ^{\eta _{aMPp}}\rbrace }\rbrack ^{\eta _{AmpR}}}- \gamma _{TetC}[TetC]$

$\frac{d[Tet]}{dt}= k_{t,Tet}(\lbrack Tet\rbrack _{ext}-\lbrack Tet\rbrack ) - \gamma _{Tet}\lbrack Tet\rbrack - k_{Tet}\lbrack Tet\rbrack - \frac{k_{cat,TetC}\lbrack TetC\rbrack [Tet]}{K_{m,TetC}+[Tet] }$

$\mu = min\big( \mu_{max}-m_{amp}[Amp],\mu_{max}-m_{Tet}[Tet] \big)$