(* 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 = {
An[t], As[t], Ins[t], Is[t], It[t], Sn[t], Ss[t]
};

initialValues = {
An[0] == 20000.0, As[0] == 0.0, Ins[0] == 145000.0, Is[0] == 0.0, It[0] == 0.0, Sn[0] == 18373000.0, Ss[0] == 0.0
};

rates = {
v\[LetterSpace]1, v\[LetterSpace]10, v\[LetterSpace]11, v\[LetterSpace]12, v\[LetterSpace]13, v\[LetterSpace]14, v\[LetterSpace]15, v\[LetterSpace]16, v\[LetterSpace]17, v\[LetterSpace]18, v\[LetterSpace]19, v\[LetterSpace]2, v\[LetterSpace]20, 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 -> Pi\[LetterSpace]n, v\[LetterSpace]10 -> Rho\[LetterSpace]1*Ins[t], v\[LetterSpace]11 -> Lambda*p*(1 - Psi)*Ss[t], v\[LetterSpace]12 -> Mu*Is[t], v\[LetterSpace]13 -> Sigma*Is[t], v\[LetterSpace]14 -> Rho\[LetterSpace]2*Is[t], v\[LetterSpace]15 -> Mu*It[t], v\[LetterSpace]16 -> Rho\[LetterSpace]3*It[t], v\[LetterSpace]17 -> Mu*An[t], v\[LetterSpace]18 -> Delta\[LetterSpace]1*An[t], v\[LetterSpace]19 -> Mu*As[t], v\[LetterSpace]2 -> Lambda*Sn[t], v\[LetterSpace]20 -> Delta\[LetterSpace]2*As[t], v\[LetterSpace]3 -> Mu*Sn[t], v\[LetterSpace]4 -> k*Sn[t], v\[LetterSpace]5 -> Pi\[LetterSpace]s, v\[LetterSpace]6 -> Lambda*(1 - Psi)*q*Ss[t], v\[LetterSpace]7 -> Mu*Ss[t], v\[LetterSpace]8 -> Mu*Ins[t], v\[LetterSpace]9 -> k*Ins[t]
};

parameters = {
Beta -> 0.4584, Delta\[LetterSpace]1 -> 0.293, Delta\[LetterSpace]2 -> 0.3379, Eta\[LetterSpace]1 -> 0.7203, Eta\[LetterSpace]2 -> 1.3785, Mu -> 0.032, Phi\[LetterSpace]1 -> 0.1, Phi\[LetterSpace]2 -> 7.3471*^-05, Pi\[LetterSpace]n -> 920540.0, Pi\[LetterSpace]s -> 750000.0, Psi -> 0.2915, Rho\[LetterSpace]1 -> 0.2372, Rho\[LetterSpace]2 -> 0.1828, Rho\[LetterSpace]3 -> 0.13, Sigma -> 0.0655, Theta -> 0.1605, c -> 1.5892, k -> 0.0388, m -> 45.1202, p -> 0.1, q -> 0.9, EXT -> 1.0, default -> 1.0
};

assignments = {
Lambda -> (Beta*c*(1 - Theta)*(Eta\[LetterSpace]2*(An[t] + Phi\[LetterSpace]2*As[t]) + Ins[t] + Eta\[LetterSpace]1*(Is[t] + Phi\[LetterSpace]1*It[t])))/(E^((m*(Delta\[LetterSpace]1*An[t] + Delta\[LetterSpace]2*As[t]))/(An[t] + As[t] + Ins[t] + Is[t] + It[t] + Sn[t] + Ss[t]))*(An[t] + As[t] + Ins[t] + Is[t] + It[t] + Sn[t] + Ss[t])), people\[LetterSpace]with\[LetterSpace]HIV -> Ins[t] + Is[t] + It[t]
};

events = {

};

speciesAnnotations = {

};

reactionAnnotations = {

};

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

(* Time evolution *)
odes = {
An'[t] == 1.0*v\[LetterSpace]10 -1.0*v\[LetterSpace]17 -1.0*v\[LetterSpace]18, As'[t] == 1.0*v\[LetterSpace]14 +1.0*v\[LetterSpace]16 -1.0*v\[LetterSpace]19 -1.0*v\[LetterSpace]20, Ins'[t] == 1.0*v\[LetterSpace]2 +1.0*v\[LetterSpace]6 -1.0*v\[LetterSpace]10 -1.0*v\[LetterSpace]8 -1.0*v\[LetterSpace]9, Is'[t] == 1.0*v\[LetterSpace]11 +1.0*v\[LetterSpace]9 -1.0*v\[LetterSpace]12 -1.0*v\[LetterSpace]13 -1.0*v\[LetterSpace]14, It'[t] == 1.0*v\[LetterSpace]13 -1.0*v\[LetterSpace]15 -1.0*v\[LetterSpace]16, Sn'[t] == 1.0*v\[LetterSpace]1 -1.0*v\[LetterSpace]2 -1.0*v\[LetterSpace]3 -1.0*v\[LetterSpace]4, Ss'[t] == 1.0*v\[LetterSpace]4 +1.0*v\[LetterSpace]5 -1.0*v\[LetterSpace]11 -1.0*v\[LetterSpace]6 -1.0*v\[LetterSpace]7
};
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]}]