(* 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 = {
A[t], E[t], I[t]
};

initialValues = {
A[0] == 1.11, E[0] == 2.1, I[0] == 10.0
};

rates = {
U1, U2, U3, U6\[LetterSpace]plus\[LetterSpace]3U7, U6\[LetterSpace]plus\[LetterSpace]U7\[LetterSpace]minus\[LetterSpace]U8
};

rateEquations = {
U1 -> cell*J*P, U2 -> cell*T*W2*I[t], U3 -> cell*M^0.41*T^0.52*W3, U6\[LetterSpace]plus\[LetterSpace]3U7 -> 2*cell*U, U6\[LetterSpace]plus\[LetterSpace]U7\[LetterSpace]minus\[LetterSpace]U8 -> cell*U*(1 - M^k*T^n*W)
};

parameters = {
J -> 100.0, P -> 0.121, U -> 0.02, W -> 0.01, W2 -> 0.2, W3 -> 13.48, k -> -1.0, n -> 1.2, cell -> 1.0
};

assignments = {
T -> (A[t] + 3*E[t] - (A[t]^2 + 6*A[t]*E[t] - 3*E[t]^2)^0.5)/6, M -> (7*A[t] - 3*E[t] - (A[t]^2 + 6*A[t]*E[t] - 3*E[t]^2)^0.5)/6
};

events = {

};

speciesAnnotations = {
I[t]->"http://identifiers.org/obo.chebi/CHEBI:29101", I[t]->"http://identifiers.org/kegg.compound/C01330"
};

reactionAnnotations = {

};

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

(* Time evolution *)
odes = {
A'[t] == 1.0*U6\[LetterSpace]plus\[LetterSpace]U7\[LetterSpace]minus\[LetterSpace]U8 , E'[t] == 1.0*U3 -1.0*U2 -1.0*U6\[LetterSpace]plus\[LetterSpace]3U7, I'[t] == 1.0*U1 -3.0*U2
};
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]}]