(* 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 = {
A[t], E[t], G[t], R[t]
};

initialValues = {
A[0] == 1.0, E[0] == 0.0, G[0] == 100000000.0, R[0] == 0.0
};

rates = {
r10, r11, r1a, r1b, r2, r3, r4, r5, r6, r7, r8, r9
};

rateEquations = {
r10 -> b1*A[t], r11 -> sigma1*A[t]*R[t], r1a -> (v\[LetterSpace]max*G[t])/(k + G[t]), r1b -> (f*v\[LetterSpace]max*G[t])/(k + G[t]), r2 -> gamma*E[t], r3 -> beta*A[t], r4 -> pi1*A[t]*E[t], r5 -> lambdaE*A[t], r6 -> muA*A[t], r7 -> muR*R[t], r8 -> muE*E[t], r9 -> muG*G[t]
};

parameters = {
b1 -> 0.25, beta -> 200.0, f -> 0.0001, gamma -> 2000.0, k -> 50000000.0, lambdaE -> 1000.0, muA -> 0.25, muE -> 0.25, muG -> 5.0, muR -> 0.25, pi1 -> 0.016, sigma1 -> 3*^-06, v\[LetterSpace]max -> 125000.0, A\[LetterSpace]im -> 0.0, body -> 1.0
};

assignments = {
R0 -> (f*gamma*lambdaE*v\[LetterSpace]max)/(k*mA*mG*muE), mG -> muG + v\[LetterSpace]max/k, mA -> b1 + muA
};

events = {

};

speciesAnnotations = {

};

reactionAnnotations = {

};

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

(* Time evolution *)
odes = {
A'[t] == 1.0*r1b -1.0*r6 -1.0*r10 -1.0*r11, E'[t] == 1.0*r5 -1.0*r8, G'[t] == 1.0*r2 -1.0*r1a -1.0*r9, R'[t] == 1.0*r3 +1.0*r4 -1.0*r7
};
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]}]