(* 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]
};

initialValues = {
x[0] == 2.5, y[0] == 1.0
};

rates = {
v1, v2, v3, v4, v5
};

rateEquations = {
v1 -> lambda, v2 -> beta*x[t]*y[t], v3 -> d*x[t], v4 -> a*y[t], v5 -> alpha*x[t]*y[t]
};

parameters = {
a -> 0.4, alpha -> 0.2, beta -> 0.2, d -> 0.02, lambda -> 0.2, default -> 1.0
};

assignments = {

};

events = {

};

speciesAnnotations = {

};

reactionAnnotations = {

};

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

(* Time evolution *)
odes = {
x'[t] == 1.0*v1 -1.0*v5 -1.0*v2 -1.0*v3, y'[t] == 1.0*v2 -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]}]