(* 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 = {
L[t], P[t], U[t]
};

initialValues = {
L[0] == 7237784.79589, P[0] == 1174269000.0, U[0] == 72377847958.9
};

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

rateEquations = {
v1 -> lambda, v2 -> deltaU*U[t], v3 -> beta*P[t]*U[t], v4 -> deltaP*P[t], v5 -> alphaR*P[t], v6 -> alphaQ*L[t], v7 -> deltaL*L[t], v8 -> alphaQ*L[t]
};

parameters = {
alphaQ -> 0.0005, alphaR -> 5*^-06, beta -> 5.2000106*^-12, deltaL -> 0.0001, deltaP -> 0.5, deltaU -> 0.02, lambda -> 2000000000.0, default -> 1.0
};

assignments = {

};

events = {

};

speciesAnnotations = {

};

reactionAnnotations = {

};

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

(* Time evolution *)
odes = {
L'[t] == 1.0*v5 -1.0*v7 -1.0*v8, P'[t] == 1.0*v6 +1.0*v3 -1.0*v5 -1.0*v4, U'[t] == 1.0*v1 -1.0*v2 -1.0*v3
};
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]}]