(* 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 = {
x[t], y[t], z[t]
};

initialValues = {
x[0] == 50.0, y[0] == 50.0, z[0] == 2.0
};

rates = {
v1, v2, v2a, v3, v4, v5, v6, v7, v8
};

rateEquations = {
v1 -> lambda, v2 -> p*x[t], v2a -> (p*x[t]^2)/Tm, v3 -> d*x[t], v4 -> beta*x[t]*y[t], v5 -> a*y[t], v6 -> k*y[t]*z[t], v7 -> s*y[t], v8 -> b*z[t]
};

parameters = {
Tm -> 1500.0, a -> 0.24, b -> 0.02, beta -> 0.002, d -> 0.01, k -> 0.001, lambda -> 10.0, p -> 0.03, s -> 0.2, default -> 1.0
};

assignments = {

};

events = {

};

speciesAnnotations = {

};

reactionAnnotations = {

};

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

(* Time evolution *)
odes = {
x'[t] == 1.0*v2 +1.0*v1 -1.0*v2a -1.0*v4 -1.0*v3, y'[t] == 1.0*v4 -1.0*v5 -1.0*v6, z'[t] == 1.0*v7 -1.0*v8
};
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]}]