(* 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 = {
I1[t], I2[t], S[t]
};

initialValues = {
I1[0] == 50.0, I2[0] == 0.0, S[0] == 4950.0
};

rates = {
v\[LetterSpace]1, v\[LetterSpace]2, v\[LetterSpace]3, v\[LetterSpace]4, v\[LetterSpace]5, v\[LetterSpace]6, v\[LetterSpace]7, v\[LetterSpace]8
};

rateEquations = {
v\[LetterSpace]1 -> b*(I1[t] + I2[t] + S[t]), v\[LetterSpace]2 -> (Beta*c*(I1[t] + a*I2[t])*S[t])/(I1[t] + I2[t] + S[t]), v\[LetterSpace]3 -> d*S[t], v\[LetterSpace]4 -> d*I1[t], v\[LetterSpace]5 -> k1*I1[t], v\[LetterSpace]6 -> Alpha*I2[t], v\[LetterSpace]7 -> d*I2[t], v\[LetterSpace]8 -> k2*I2[t]
};

parameters = {
Alpha -> 0.2, Beta -> 0.5, a -> 0.6, b -> 0.001, c -> 0.3, d -> 0.0006, k1 -> 0.019, k2 -> 0.0159, EXT -> 1.0, default -> 1.0
};

assignments = {
N -> I1[t] + I2[t] + S[t]
};

events = {

};

speciesAnnotations = {

};

reactionAnnotations = {

};

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

(* Time evolution *)
odes = {
I1'[t] == 1.0*v\[LetterSpace]6 +1.0*v\[LetterSpace]2 -1.0*v\[LetterSpace]5 -1.0*v\[LetterSpace]4, I2'[t] == 1.0*v\[LetterSpace]5 -1.0*v\[LetterSpace]6 -1.0*v\[LetterSpace]7 -1.0*v\[LetterSpace]8, S'[t] == 1.0*v\[LetterSpace]1 -1.0*v\[LetterSpace]3 -1.0*v\[LetterSpace]2
};
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]}]