(* 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 = {
w[t], x[t], y1[t], y2[t], y3[t], z1[t], z2[t], z3[t]
};

initialValues = {
w[0] == 0.0, x[0] == 2.0, y1[0] == 0.0, y2[0] == 0.45, y3[0] == 0.45, z1[0] == 0.0, z2[0] == 0.072103, z3[0] == 0.0180258
};

rates = {
v1, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v2, v20, v21, v22, v23, v24, v3, v4, v5, v6, v7, v8, v9
};

rateEquations = {
v1 -> lambda, v10 -> p*y2[t]*z2[t], v11 -> q*w[t]*y2[t], v12 -> a*y3[t], v13 -> p*y3[t]*z3[t], v14 -> q*w[t]*y3[t], v15 -> c1*y1[t]*z1[t], v16 -> b*z1[t], v17 -> c2*y2[t]*z2[t], v18 -> b*z2[t], v19 -> c3*y3[t]*z3[t], v2 -> d*x[t], v20 -> b*z3[t], v21 -> k1*w[t]*y1[t], v22 -> k2*w[t]*y2[t], v23 -> k3*w[t]*y3[t], v24 -> b*w[t], v3 -> beta1*x[t]*y1[t], v4 -> beta2*x[t]*y2[t], v5 -> beta3*x[t]*y3[t], v6 -> a*y1[t], v7 -> p*y1[t]*z1[t], v8 -> q*w[t]*y1[t], v9 -> a*y2[t]
};

parameters = {
a -> 0.1, b -> 0.4, beta1 -> 0.08, beta2 -> 0.075, beta3 -> 0.06, c1 -> 0.9, c2 -> 0.9, c3 -> 0.9, d -> 0.5, k1 -> 0.4, k2 -> 0.4, k3 -> 0.4, lambda -> 1.0, p -> 0.3, q -> 0.2, default -> 1.0
};

assignments = {

};

events = {

};

speciesAnnotations = {

};

reactionAnnotations = {

};

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

(* Time evolution *)
odes = {
w'[t] == 1.0*v22 +1.0*v23 +1.0*v21 -1.0*v24, x'[t] == 1.0*v1 -1.0*v5 -1.0*v4 -1.0*v3 -1.0*v2, y1'[t] == 1.0*v3 -1.0*v8 -1.0*v6 -1.0*v7, y2'[t] == 1.0*v4 -1.0*v11 -1.0*v10 -1.0*v9, y3'[t] == 1.0*v5 -1.0*v14 -1.0*v12 -1.0*v13, z1'[t] == 1.0*v15 -1.0*v16, z2'[t] == 1.0*v17 -1.0*v18, z3'[t] == 1.0*v19 -1.0*v20
};
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]}]