(* 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], N[t]
};

initialValues = {
A[0] == 500.0, I1[0] == 2000.0, I2[0] == 3000.0, N[0] == 20000.0
};

rates = {
v\[LetterSpace]1, v\[LetterSpace]10, v\[LetterSpace]11, v\[LetterSpace]12, 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 -> Q0, v\[LetterSpace]10 -> d*I2[t], v\[LetterSpace]11 -> alpha*A[t], v\[LetterSpace]12 -> d*A[t], v\[LetterSpace]2 -> d*N[t], v\[LetterSpace]3 -> alpha*A[t], v\[LetterSpace]4 -> (beta1*I1[t]*(-A[t] - I1[t] - I2[t] + N[t]))/N[t], v\[LetterSpace]5 -> (beta3*I1[t]*I2[t])/N[t], v\[LetterSpace]6 -> lambda*I1[t], v\[LetterSpace]7 -> d*I1[t], v\[LetterSpace]8 -> (beta2*I2[t]*(-A[t] - I1[t] - I2[t] + N[t]))/N[t], v\[LetterSpace]9 -> delta*I2[t]
};

parameters = {
Q0 -> 2000.0, alpha -> 1.0, beta1 -> 0.925, beta2 -> 0.365, beta3 -> 1.15, d -> 0.02, delta -> 0.2, lambda -> 0.3, EXT -> 1.0, default -> 1.0
};

assignments = {

};

events = {

};

speciesAnnotations = {

};

reactionAnnotations = {

};

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

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