(* Generated by JWS Online *)

(* This is an experimental feature of JWS Online. Please report any mistakes.*)

(* Note that the following notable SBML entities or features are not supported in notebook outputyet: *)
    (* Events *)
    (* Constraints *)
    (* Units and UnitDefinitions *)
    (* AlgebraicRules *)
    (* conversionFactors *)

variables = {
Cdiff[t], Commensal\[LetterSpace]Beneficial[t], Commensal\[LetterSpace]Dead[t], Commensal\[LetterSpace]Harmful[t], E[t], E\[LetterSpace]d[t], E\[LetterSpace]i[t], M\[LetterSpace]LP[t], N\[LetterSpace]Lum[t], Th17\[LetterSpace]LP[t], Th17\[LetterSpace]MLN[t], Th1\[LetterSpace]LP[t], Th1\[LetterSpace]MLN[t], eDC\[LetterSpace]LP[t], eDC\[LetterSpace]MLN[t], iTreg\[LetterSpace]LP[t], iTreg\[LetterSpace]MLN[t], tDC\[LetterSpace]LP[t], tDC\[LetterSpace]MLN[t]
};

initialValues = {
Cdiff[0] == 484.0, Commensal\[LetterSpace]Beneficial[0] == 1.0, Commensal\[LetterSpace]Dead[0] == 50000000000.0, Commensal\[LetterSpace]Harmful[0] == 15000000000.0, E[0] == 1052500.0, E\[LetterSpace]d[0] == 0.0, E\[LetterSpace]i[0] == 0.0, M\[LetterSpace]LP[0] == 3250.0, N\[LetterSpace]Lum[0] == 0.0, Th17\[LetterSpace]LP[0] == 0.0, Th17\[LetterSpace]MLN[0] == 0.0, Th1\[LetterSpace]LP[0] == 0.0, Th1\[LetterSpace]MLN[0] == 0.0, eDC\[LetterSpace]LP[0] == 0.0, eDC\[LetterSpace]MLN[0] == 0.0, iTreg\[LetterSpace]LP[0] == 0.0, iTreg\[LetterSpace]MLN[0] == 0.0, tDC\[LetterSpace]LP[0] == 0.0, tDC\[LetterSpace]MLN[0] == 0.0
};

rates = {
Cdiff\[LetterSpace]Death, Cdiff\[LetterSpace]Growth, Commensal\[LetterSpace]Death, Commensal\[LetterSpace]Harmful\[LetterSpace]Death, Commensal\[LetterSpace]Regrowth, E\[LetterSpace]Damage, E\[LetterSpace]Heal, E\[LetterSpace]Inflame, E\[LetterSpace]i\[LetterSpace]Damage, E\[LetterSpace]i\[LetterSpace]Natural\[LetterSpace]Death, M\[LetterSpace]Activation, M\[LetterSpace]Death, N\[LetterSpace]Activation\[LetterSpace]Migration, N\[LetterSpace]Degradation, Th17\[LetterSpace]Degradation, Th17\[LetterSpace]Differentiation, Th17\[LetterSpace]Migration, Th17\[LetterSpace]Plasticity, Th1\[LetterSpace]Degradation, Th1\[LetterSpace]Differentiation, Th1\[LetterSpace]Migration, Treg\[LetterSpace]Degradation, Treg\[LetterSpace]Differentiation, Treg\[LetterSpace]Migration, eDC\[LetterSpace]Degradation, eDC\[LetterSpace]Migration, eDC\[LetterSpace]Production, tDC\[LetterSpace]Degradation, tDC\[LetterSpace]Migration, tDC\[LetterSpace]Production
};

rateEquations = {
Cdiff\[LetterSpace]Death -> Lumen*Rate\[LetterSpace]Law\[LetterSpace]for\[LetterSpace]CD\[LetterSpace]Lumen\[LetterSpace]death[Cdiff\[LetterSpace]Death\[LetterSpace]K, Cdiff[t], M\[LetterSpace]LP[t], Cdiff\[LetterSpace]Death\[LetterSpace]m2, N\[LetterSpace]Lum[t], Cdiff\[LetterSpace]Death\[LetterSpace]m3, Commensal\[LetterSpace]Harmful[t]], Cdiff\[LetterSpace]Growth -> Lumen*KSA[Cdiff\[LetterSpace]Growth\[LetterSpace]K, Cdiff[t], Commensal\[LetterSpace]Harmful[t]], Commensal\[LetterSpace]Death -> Commensal\[LetterSpace]Death\[LetterSpace]k1*Lumen*Commensal\[LetterSpace]Dead[t], Commensal\[LetterSpace]Harmful\[LetterSpace]Death -> Lumen*Rate\[LetterSpace]Law\[LetterSpace]for\[LetterSpace]Commensal\[LetterSpace]Harmful\[LetterSpace]Death\[LetterSpace]1[Commensal\[LetterSpace]Harmful\[LetterSpace]Death\[LetterSpace]K, Commensal\[LetterSpace]Harmful[t], N\[LetterSpace]LP, Commensal\[LetterSpace]Harmful\[LetterSpace]Death\[LetterSpace]A1, E\[LetterSpace]i[t], Commensal\[LetterSpace]Harmful\[LetterSpace]Death\[LetterSpace]A2], Commensal\[LetterSpace]Regrowth -> Lumen*Rate\[LetterSpace]Law\[LetterSpace]for\[LetterSpace]Commensal\[LetterSpace]Regrowth[Commensal\[LetterSpace]Regrowth\[LetterSpace]k1, Commensal\[LetterSpace]Beneficial[t], N\[LetterSpace]Lum[t], E\[LetterSpace]i[t], Commensal\[LetterSpace]Regrowth\[LetterSpace]k2, Commensal\[LetterSpace]Dead[t]], E\[LetterSpace]Damage -> Epithelium*Rate\[LetterSpace]Law\[LetterSpace]for\[LetterSpace]E\[LetterSpace]damage[E\[LetterSpace]Damage\[LetterSpace]v, E[t], E\[LetterSpace]Damage\[LetterSpace]k1, N\[LetterSpace]Lum[t], E\[LetterSpace]Damage\[LetterSpace]k2, Th17\[LetterSpace]LP[t], E\[LetterSpace]Damage\[LetterSpace]k3, M\[LetterSpace]LP[t]], E\[LetterSpace]Heal -> Epithelium*E\[LetterSpace]Heal\[LetterSpace]k1*E\[LetterSpace]d[t], E\[LetterSpace]Inflame -> Epithelium*KSA[E\[LetterSpace]Inflame\[LetterSpace]K, E[t], Cdiff[t]], E\[LetterSpace]i\[LetterSpace]Damage -> Epithelium*Rate\[LetterSpace]Law\[LetterSpace]for\[LetterSpace]E\[LetterSpace]damage[E\[LetterSpace]i\[LetterSpace]Damage\[LetterSpace]v, E\[LetterSpace]i[t], E\[LetterSpace]i\[LetterSpace]Damage\[LetterSpace]k1, N\[LetterSpace]Lum[t], E\[LetterSpace]i\[LetterSpace]Damage\[LetterSpace]k2, Th17\[LetterSpace]LP[t], E\[LetterSpace]i\[LetterSpace]Damage\[LetterSpace]k3, M\[LetterSpace]LP[t]], E\[LetterSpace]i\[LetterSpace]Natural\[LetterSpace]Death -> Epithelium*E\[LetterSpace]i\[LetterSpace]Natural\[LetterSpace]Death\[LetterSpace]k1*E\[LetterSpace]i[t], M\[LetterSpace]Activation -> Rate\[LetterSpace]Law\[LetterSpace]for\[LetterSpace]M\[LetterSpace]Activation[M\[LetterSpace]Activation\[LetterSpace]K, M0, M\[LetterSpace]Activation\[LetterSpace]e1, Th17\[LetterSpace]LP[t], Cdiff[t], M\[LetterSpace]Activation\[LetterSpace]e2, iTreg\[LetterSpace]LP[t]], M\[LetterSpace]Death -> Epithelium*M\[LetterSpace]Death\[LetterSpace]k1*M\[LetterSpace]LP[t], N\[LetterSpace]Activation\[LetterSpace]Migration -> Rate\[LetterSpace]Law\[LetterSpace]for\[LetterSpace]N\[LetterSpace]Activation\[LetterSpace]Migration[N\[LetterSpace]Activation\[LetterSpace]Migration\[LetterSpace]v, N\[LetterSpace]LP, Cdiff[t], N\[LetterSpace]Activation\[LetterSpace]Migration\[LetterSpace]k1, E\[LetterSpace]d[t], N\[LetterSpace]Activation\[LetterSpace]Migration\[LetterSpace]k2, Th17\[LetterSpace]LP[t], N\[LetterSpace]Activation\[LetterSpace]Migration\[LetterSpace]k3, iTreg\[LetterSpace]LP[t]], N\[LetterSpace]Degradation -> Lumen*KSA[N\[LetterSpace]Degradation\[LetterSpace]K, N\[LetterSpace]Lum[t], Commensal\[LetterSpace]Beneficial[t]], Th17\[LetterSpace]Degradation -> LP*Th17\[LetterSpace]Degradation\[LetterSpace]k1*Th17\[LetterSpace]LP[t], Th17\[LetterSpace]Differentiation -> MLN*Th17\[LetterSpace]Differentiation\[LetterSpace]k1*eDC\[LetterSpace]MLN[t], Th17\[LetterSpace]Migration -> Th17\[LetterSpace]Migration\[LetterSpace]k1*Th17\[LetterSpace]MLN[t], Th17\[LetterSpace]Plasticity -> LP*Rate\[LetterSpace]Law\[LetterSpace]for\[LetterSpace]Th17plas[Th17\[LetterSpace]Plasticity\[LetterSpace]k1, Th17\[LetterSpace]LP[t], Th17\[LetterSpace]Plasticity\[LetterSpace]k2, Cdiff[t], iTreg\[LetterSpace]LP[t]], Th1\[LetterSpace]Degradation -> LP*Th1\[LetterSpace]Degradation\[LetterSpace]k1*Th1\[LetterSpace]LP[t], Th1\[LetterSpace]Differentiation -> MLN*Rate\[LetterSpace]Law\[LetterSpace]for\[LetterSpace]eDC[Th1\[LetterSpace]Differentiation\[LetterSpace]K, eDC\[LetterSpace]MLN[t], Commensal\[LetterSpace]Dead[t], Commensal\[LetterSpace]Beneficial[t], Th1\[LetterSpace]Differentiation\[LetterSpace]k2, E[t], Th1\[LetterSpace]Differentiation\[LetterSpace]k1], Th1\[LetterSpace]Migration -> Th1\[LetterSpace]Migration\[LetterSpace]k1*Th1\[LetterSpace]MLN[t], Treg\[LetterSpace]Degradation -> LP*Treg\[LetterSpace]Degradation\[LetterSpace]k1*iTreg\[LetterSpace]LP[t], Treg\[LetterSpace]Differentiation -> Treg\[LetterSpace]Differentiation\[LetterSpace]k1*tDC\[LetterSpace]MLN[t], Treg\[LetterSpace]Migration -> Treg\[LetterSpace]Migration\[LetterSpace]k1*iTreg\[LetterSpace]MLN[t], eDC\[LetterSpace]Degradation -> eDC\[LetterSpace]Degradation\[LetterSpace]k1*MLN*eDC\[LetterSpace]MLN[t], eDC\[LetterSpace]Migration -> eDC\[LetterSpace]Migration\[LetterSpace]k1*eDC\[LetterSpace]LP[t], eDC\[LetterSpace]Production -> Rate\[LetterSpace]Law\[LetterSpace]for\[LetterSpace]Effector\[LetterSpace]DC\[LetterSpace]Production\[LetterSpace]1[eDC\[LetterSpace]Production\[LetterSpace]k, Cdiff[t]], tDC\[LetterSpace]Degradation -> Lumen*Rate\[LetterSpace]Law\[LetterSpace]for\[LetterSpace]Effector\[LetterSpace]DC\[LetterSpace]Production\[LetterSpace]1[tDC\[LetterSpace]Degradation\[LetterSpace]k, tDC\[LetterSpace]MLN[t]], tDC\[LetterSpace]Migration -> Lumen*tDC\[LetterSpace]Migration\[LetterSpace]k1*tDC\[LetterSpace]LP[t], tDC\[LetterSpace]Production -> Rate\[LetterSpace]Law\[LetterSpace]for\[LetterSpace]tDC\[LetterSpace]Production[tDC\[LetterSpace]Production\[LetterSpace]K, Cdiff[t], tDC\[LetterSpace]Production\[LetterSpace]k1, Commensal\[LetterSpace]Beneficial[t], Commensal\[LetterSpace]Dead[t], tDC\[LetterSpace]Production\[LetterSpace]k2, E[t], E\[LetterSpace]i[t]]
};

parameters = {
M0 -> 1714285.71428571, N\[LetterSpace]LP -> 714285.714285714, iDC\[LetterSpace]E -> 500000.0, nT -> 12000000.0, Treg\[LetterSpace]Degradation\[LetterSpace]k1 -> 0.5069887, eDC\[LetterSpace]Degradation\[LetterSpace]k1 -> 1.72495199303666*^-05, Th17\[LetterSpace]Degradation\[LetterSpace]k1 -> 2.39665140586358, Th1\[LetterSpace]Degradation\[LetterSpace]k1 -> 0.99505694359, N\[LetterSpace]Degradation\[LetterSpace]K -> 2.35932924820229*^-07, E\[LetterSpace]Damage\[LetterSpace]v -> 1.59920673150176*^-06, E\[LetterSpace]Damage\[LetterSpace]k1 -> 1.1*^-05, E\[LetterSpace]Damage\[LetterSpace]k2 -> 2.3381277077344*^-06, E\[LetterSpace]Damage\[LetterSpace]k3 -> 62.5911647602982, eDC\[LetterSpace]Migration\[LetterSpace]k1 -> 10.5, eDC\[LetterSpace]Production\[LetterSpace]k -> 0.55, Cdiff\[LetterSpace]Death\[LetterSpace]K -> 6.27092296294148*^-10, Cdiff\[LetterSpace]Death\[LetterSpace]m2 -> 594.896546415159, Cdiff\[LetterSpace]Death\[LetterSpace]m3 -> 0.102702503781515, N\[LetterSpace]Activation\[LetterSpace]Migration\[LetterSpace]v -> 5.29827880572231*^-05, N\[LetterSpace]Activation\[LetterSpace]Migration\[LetterSpace]k1 -> 0.120935308788409, N\[LetterSpace]Activation\[LetterSpace]Migration\[LetterSpace]k2 -> 0.171190728888258, N\[LetterSpace]Activation\[LetterSpace]Migration\[LetterSpace]k3 -> 0.129717307334483, Cdiff\[LetterSpace]Growth\[LetterSpace]K -> 5*^-11, Treg\[LetterSpace]Migration\[LetterSpace]k1 -> 5.5, Th1\[LetterSpace]Migration\[LetterSpace]k1 -> 1.459, Th17\[LetterSpace]Plasticity\[LetterSpace]k1 -> 1.27393226093773, Th17\[LetterSpace]Plasticity\[LetterSpace]k2 -> 0.0020401460213434, Th17\[LetterSpace]Migration\[LetterSpace]k1 -> 2.50454427171444, E\[LetterSpace]Inflame\[LetterSpace]K -> 0.000171079818745428, E\[LetterSpace]i\[LetterSpace]Damage\[LetterSpace]v -> 0.065, E\[LetterSpace]i\[LetterSpace]Damage\[LetterSpace]k1 -> 0.006, E\[LetterSpace]i\[LetterSpace]Damage\[LetterSpace]k2 -> 0.0106698310809694, E\[LetterSpace]i\[LetterSpace]Damage\[LetterSpace]k3 -> 1.16013457036959*^-06, M\[LetterSpace]Activation\[LetterSpace]K -> 4.5*^-05, M\[LetterSpace]Activation\[LetterSpace]e1 -> 2.0, M\[LetterSpace]Activation\[LetterSpace]e2 -> 0.092308585205372, M\[LetterSpace]Death\[LetterSpace]k1 -> 20.0, Commensal\[LetterSpace]Regrowth\[LetterSpace]k1 -> 4.5*^-10, Commensal\[LetterSpace]Regrowth\[LetterSpace]k2 -> 0.156287382551622, E\[LetterSpace]Heal\[LetterSpace]k1 -> 4000.0, tDC\[LetterSpace]Production\[LetterSpace]K -> 0.0002, tDC\[LetterSpace]Production\[LetterSpace]k1 -> 559.297141527983, tDC\[LetterSpace]Production\[LetterSpace]k2 -> 26.8747332769592, tDC\[LetterSpace]Migration\[LetterSpace]k1 -> 3.65, tDC\[LetterSpace]Degradation\[LetterSpace]k -> 0.00095, Th17\[LetterSpace]Differentiation\[LetterSpace]k1 -> 2255.80469507059, Th1\[LetterSpace]Differentiation\[LetterSpace]K -> 0.0430096, Th1\[LetterSpace]Differentiation\[LetterSpace]k2 -> 9.65568121975566*^-05, Th1\[LetterSpace]Differentiation\[LetterSpace]k1 -> 0.0648415756801505, Treg\[LetterSpace]Differentiation\[LetterSpace]k1 -> 53.9130568911728, Commensal\[LetterSpace]Harmful\[LetterSpace]Death\[LetterSpace]K -> 2.33225*^-05, Commensal\[LetterSpace]Harmful\[LetterSpace]Death\[LetterSpace]A1 -> 0.00478, Commensal\[LetterSpace]Harmful\[LetterSpace]Death\[LetterSpace]A2 -> 0.18, Commensal\[LetterSpace]Death\[LetterSpace]k1 -> 0.0933277452272273, E\[LetterSpace]i\[LetterSpace]Natural\[LetterSpace]Death\[LetterSpace]k1 -> 2.5, Epithelium -> 4.0, LP -> 0.07, Lumen -> 1.0, MLN -> 1.0
};

assignments = {
Rate\[LetterSpace]Law\[LetterSpace]for\[LetterSpace]Commensal\[LetterSpace]Harmful\[LetterSpace]Death\[LetterSpace]1[K_,S_,m1_,A1_,m2_,A2_] -> K*(A1*m1 + A2*m2)*S, Rate\[LetterSpace]Law\[LetterSpace]for\[LetterSpace]Commensal\[LetterSpace]Regrowth[k1_,S_,m1_,m2_,k2_,P_] -> -(k2*P) + k1*m1*m2*S, Rate\[LetterSpace]Law\[LetterSpace]for\[LetterSpace]N\[LetterSpace]Activation\[LetterSpace]Migration[v_,S_,m_,k1_,A1_,k2_,A2_,k3_,I1_] -> (-(I1*k3) + (A1*k1 + A2*k2)*m)*S*v, Rate\[LetterSpace]Law\[LetterSpace]for\[LetterSpace]M\[LetterSpace]Activation[K_,S_,e1_,A1_,A2_,e2_,I1_] -> (A2 + A1*e1 - e2*I1)*K*S, Rate\[LetterSpace]Law\[LetterSpace]for\[LetterSpace]tDC\[LetterSpace]Production[K_,S_,k1_,M1_,M2_,k2_,M3_,M4_] -> K*((k1*M1)/M2 + (k2*M3)/(100 + M4))*S, Rate\[LetterSpace]Law\[LetterSpace]for\[LetterSpace]CD\[LetterSpace]Lumen\[LetterSpace]death[K_,S_,A1_,m2_,A2_,m3_,A3_] -> K*(A1 + A2*m2 - A3*m3)*S, Rate\[LetterSpace]Law\[LetterSpace]for\[LetterSpace]eDC[K_,S_,M1_,M2_,k2_,M3_,k1_] -> (K*M1*S)/(k1*M2 + k2*M3), Rate\[LetterSpace]Law\[LetterSpace]for\[LetterSpace]Effector\[LetterSpace]DC\[LetterSpace]Production\[LetterSpace]1[k_,S_] -> k*S, Rate\[LetterSpace]Law\[LetterSpace]for\[LetterSpace]Th17plas[k1_,s_,k2_,m2_,p_] -> -(k2*m2*p) + k1*s, Rate\[LetterSpace]Law\[LetterSpace]for\[LetterSpace]E\[LetterSpace]damage[v_,S_,k1_,a1_,k2_,a2_,k3_,a3_] -> (a1*k1 + a2*k2 + a3*k3)*S*v, KSA[K_,S_,A_] -> A*K*S
};

events = {

};

speciesAnnotations = {
Cdiff[t]->"http://identifiers.org/taxonomy/1496"
};

reactionAnnotations = {

};

units = {
{"time" -> "", "metabolite" -> "", "extent" -> ""}
};

(* Time evolution *)
odes = {
Cdiff'[t] == 2.0*Cdiff\[LetterSpace]Growth -1.0*eDC\[LetterSpace]Production -1.0*Cdiff\[LetterSpace]Death -1.0*Cdiff\[LetterSpace]Growth -1.0*tDC\[LetterSpace]Production, Commensal\[LetterSpace]Beneficial'[t] ==  -1.0*Commensal\[LetterSpace]Regrowth, Commensal\[LetterSpace]Dead'[t] == 1.0*Commensal\[LetterSpace]Regrowth -1.0*Commensal\[LetterSpace]Death, Commensal\[LetterSpace]Harmful'[t] ==  -1.0*Commensal\[LetterSpace]Harmful\[LetterSpace]Death, E'[t] == 1.0*E\[LetterSpace]Heal -1.0*E\[LetterSpace]Damage -1.0*E\[LetterSpace]Inflame, E\[LetterSpace]d'[t] == 1.0*E\[LetterSpace]Damage +1.0*E\[LetterSpace]i\[LetterSpace]Damage +1.0*E\[LetterSpace]i\[LetterSpace]Natural\[LetterSpace]Death -1.0*E\[LetterSpace]Heal, E\[LetterSpace]i'[t] == 1.0*E\[LetterSpace]Inflame -1.0*E\[LetterSpace]i\[LetterSpace]Damage -1.0*E\[LetterSpace]i\[LetterSpace]Natural\[LetterSpace]Death, M\[LetterSpace]LP'[t] == 1.0*M\[LetterSpace]Activation -1.0*M\[LetterSpace]Death, N\[LetterSpace]Lum'[t] == 1.0*N\[LetterSpace]Activation\[LetterSpace]Migration -1.0*N\[LetterSpace]Degradation, Th17\[LetterSpace]LP'[t] == 1.0*Th17\[LetterSpace]Migration -1.0*Th17\[LetterSpace]Degradation -1.0*Th17\[LetterSpace]Plasticity, Th17\[LetterSpace]MLN'[t] == 1.0*Th17\[LetterSpace]Differentiation -1.0*Th17\[LetterSpace]Migration, Th1\[LetterSpace]LP'[t] == 1.0*Th1\[LetterSpace]Migration -1.0*Th1\[LetterSpace]Degradation, Th1\[LetterSpace]MLN'[t] == 1.0*Th1\[LetterSpace]Differentiation -1.0*Th1\[LetterSpace]Migration, eDC\[LetterSpace]LP'[t] == 1.0*eDC\[LetterSpace]Production -1.0*eDC\[LetterSpace]Migration, eDC\[LetterSpace]MLN'[t] == 1.0*eDC\[LetterSpace]Migration -1.0*eDC\[LetterSpace]Degradation -1.0*Th17\[LetterSpace]Differentiation -1.0*Th1\[LetterSpace]Differentiation, iTreg\[LetterSpace]LP'[t] == 1.0*Treg\[LetterSpace]Migration +1.0*Th17\[LetterSpace]Plasticity -1.0*Treg\[LetterSpace]Degradation, iTreg\[LetterSpace]MLN'[t] == 1.0*Treg\[LetterSpace]Differentiation -1.0*Treg\[LetterSpace]Migration, tDC\[LetterSpace]LP'[t] == 1.0*tDC\[LetterSpace]Production -1.0*tDC\[LetterSpace]Migration, tDC\[LetterSpace]MLN'[t] == 1.0*tDC\[LetterSpace]Migration -1.0*tDC\[LetterSpace]Degradation -1.0*Treg\[LetterSpace]Differentiation
};
timeCourse = NDSolve[Join[odes, initialValues]//.rateEquations//.assignments//.parameters, variables, {t, 0, 100}];

(* Steady-state solution initialized with result of time evolution *)
findRootEquations = odes /.D[_[t],t]->0;
findRootVariables = Partition[Flatten[{#, #/.timeCourse/.t->100} &/@variables],2];
steadyStateVariables = FindRoot[findRootEquations//.rateEquations//.assignments//.parameters, findRootVariables, MaxIterations->100]
fluxes = #//.assignments//.parameters/.steadyStateVariables&/@rateEquations

(* Plot the time evolution of the variables *)
plotTable=Table[Plot[variables[[i]]/.parameters/.timeCourse,{t,0,100},PlotLegends->variables[[i]],PlotRange->Full],{i,Length[variables]}]