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

initialValues = {
A[0] == 200.0, I1[0] == 5000.0, I2[0] == 1000.0, S[0] == 3800.0
};

rates = {
v\[LetterSpace]1, v\[LetterSpace]10, v\[LetterSpace]11, v\[LetterSpace]12, v\[LetterSpace]13, v\[LetterSpace]2, v\[LetterSpace]3, v\[LetterSpace]4, v\[LetterSpace]5, v\[LetterSpace]6, v\[LetterSpace]7, v\[LetterSpace]8, v\[LetterSpace]9
};

rateEquations = {
v\[LetterSpace]1 -> Q\[LetterSpace]0, v\[LetterSpace]10 -> Delta\[LetterSpace]2*I2[t], v\[LetterSpace]11 -> Mu*I2[t], v\[LetterSpace]12 -> Alpha*A[t], v\[LetterSpace]13 -> Mu*A[t], v\[LetterSpace]2 -> (Beta\[LetterSpace]1*I1[t]*S[t])/(A[t] + I1[t] + I2[t] + S[t]), v\[LetterSpace]3 -> (Beta\[LetterSpace]2*Epsilon*I2[t]*S[t])/(A[t] + I1[t] + I2[t] + S[t]), v\[LetterSpace]4 -> Mu*S[t], v\[LetterSpace]5 -> (Beta\[LetterSpace]2*(1 - Epsilon)*I2[t]*S[t])/(A[t] + I1[t] + I2[t] + S[t]), v\[LetterSpace]6 -> Theta*I1[t], v\[LetterSpace]7 -> Delta\[LetterSpace]1*I1[t], v\[LetterSpace]8 -> Mu*I1[t], v\[LetterSpace]9 -> k*I1[t]*I2[t]
};

parameters = {
Alpha -> 1.0, Beta\[LetterSpace]1 -> 1.5, Beta\[LetterSpace]2 -> 0.5, Delta\[LetterSpace]1 -> 0.2, Delta\[LetterSpace]2 -> 0.1, Epsilon -> 0.01, Mu -> 0.02, Q\[LetterSpace]0 -> 2000.0, Theta -> 0.015, k -> 1*^-05, EXT -> 1.0, default -> 1.0
};

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

events = {

};

speciesAnnotations = {

};

reactionAnnotations = {

};

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

(* Time evolution *)
odes = {
A'[t] == 1.0*v\[LetterSpace]7 +1.0*v\[LetterSpace]10 -1.0*v\[LetterSpace]12 -1.0*v\[LetterSpace]13, I1'[t] == 1.0*v\[LetterSpace]5 +1.0*v\[LetterSpace]2 -1.0*v\[LetterSpace]7 -1.0*v\[LetterSpace]9 -1.0*v\[LetterSpace]8 -1.0*v\[LetterSpace]6, I2'[t] == 1.0*v\[LetterSpace]9 +1.0*v\[LetterSpace]3 +1.0*v\[LetterSpace]6 -1.0*v\[LetterSpace]11 -1.0*v\[LetterSpace]10, S'[t] == 1.0*v\[LetterSpace]1 -1.0*v\[LetterSpace]3 -1.0*v\[LetterSpace]4 -1.0*v\[LetterSpace]5 -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]}]