(* 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 = {
alpha[t], gamma[t], p[t]
};

initialValues = {
alpha[0] == 100.0, gamma[0] == 20.0, p[0] == 0.0
};

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

rateEquations = {
v1 -> k1, v2 -> (k2*(c*el*ep*ve*alpha[t]*(1 + c*ep*alpha[t]) + es*alpha[t]*(1 + es*alpha[t])*(1 + gamma[t])^2))/(el*(1 + c*ep*alpha[t])^2 + (1 + es*alpha[t])^2*(1 + gamma[t])^2), v3 -> k3*(gamma[t] - p[t]), v4 -> k4*p[t]
};

parameters = {
EXTERNAL -> 0.0, c -> 1*^-05, el -> 500000.0, ep -> 0.9090909, es -> 0.9090909, k1 -> 0.7, k2 -> 3.98, k3 -> 0.07, k4 -> 10.0, ve -> 1.0, s -> 0.0, default\[LetterSpace]compartment -> 1.0
};

assignments = {

};

events = {

};

speciesAnnotations = {

};

reactionAnnotations = {

};

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

(* Time evolution *)
odes = {
alpha'[t] == 1.0*v1 -1.0*v2, gamma'[t] == 1.0*v2 -1.0*v3, p'[t] == 1.0*v3 -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]}]