(* 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 = {
N1[t], N2[t], S[t]
};

initialValues = {
N1[0] == 100.0, N2[0] == 0.0, S[0] == 0.111111111111111
};

rates = {
r1, r2, r3, r4, r5
};

rateEquations = {
r1 -> v, r2 -> (N1[t]*S[t])/(1 + S[t]), r3 -> (20*N2[t]*S[t])/(1 + S[t]), r4 -> d*N1[t], r5 -> d*N2[t]
};

parameters = {
d -> 1.0, v -> 10.0, compartment -> 1.0
};

assignments = {

};

events = {

};

speciesAnnotations = {

};

reactionAnnotations = {

};

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

(* Time evolution *)
odes = {
N1'[t] == 10.0*r2 -1.0*r4, N2'[t] == 1.0*r3 -1.0*r5, S'[t] == 1.0*r1 -1.0*r2 -1.0*r3
};
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]}]