(* 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 = {
S[t], T[t], X[t], Y[t]
};

initialValues = {
S[0] == 1.0, T[0] == 0.0001, X[0] == 120.0, Y[0] == 0.0
};

rates = {
v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9
};

rateEquations = {
v1 -> lambda, v10 -> g*T[t]*Y[t], v11 -> k*T[t]*Y[t], v2 -> mu*X[t], v3 -> beta*S[t]*X[t], v4 -> alfa*Y[t], v5 -> alfa*r*Y[t], v6 -> d*S[t], v7 -> h*S[t]*T[t], v8 -> gamma*S[t]*T[t], v9 -> a*T[t]
};

parameters = {
a -> 0.05, alfa -> 0.2, beta -> 0.1, d -> 72.0, g -> 0.05, gamma -> 1.0, h -> 0.1, k -> 0.05, lambda -> 1.0, mu -> 0.00833, r -> 16.0, default -> 1.0
};

assignments = {
Xy -> X[t] + Y[t], Yi -> Y[t]/(X[t] + Y[t])
};

events = {

};

speciesAnnotations = {

};

reactionAnnotations = {

};

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

(* Time evolution *)
odes = {
S'[t] == 1.0*v5 -1.0*v3 -1.0*v6 -1.0*v7, T'[t] == 1.0*v11 +1.0*v8 -1.0*v9, X'[t] == 1.0*v1 -1.0*v2 -1.0*v3, Y'[t] == 1.0*v3 -1.0*v10 -1.0*v4
};
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]}]