(* 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 = {
E[t], H[t], I[t], M[t]
};

initialValues = {
E[0] == 0.0001, H[0] == 5000000.0, I[0] == 0.0, M[0] == 10000.0
};

rates = {
v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9
};

rateEquations = {
v1 -> lambda, v10 -> (k1*E[t]*I[t])/(1 + beta*I[t]), v11 -> (k2*E[t]*M[t])/(1 + gamma*M[t]), v2 -> d1*H[t], v3 -> alfa*H[t]*M[t], v4 -> delta*I[t], v5 -> (p1*E[t]*I[t])/(1 + beta*I[t]), v6 -> r*I[t], v7 -> mu*M[t], v8 -> (p2*E[t]*M[t])/(1 + gamma*M[t]), v9 -> d2*E[t]
};

parameters = {
alfa -> 9*^-07, beta -> 0.0005, d1 -> 0.0083, d2 -> 0.04, delta -> 1.0, gamma -> 0.000667, k1 -> 2.5*^-05, k2 -> 1.03*^-05, lambda -> 41500.0, mu -> 48.0, p1 -> 1*^-08, p2 -> 1*^-08, r -> 12.0, default -> 1.0
};

assignments = {

};

events = {

};

speciesAnnotations = {

};

reactionAnnotations = {

};

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

(* Time evolution *)
odes = {
E'[t] == 1.0*v10 +1.0*v11 -1.0*v9, H'[t] == 1.0*v1 -1.0*v2 -1.0*v3, I'[t] == 1.0*v3 -1.0*v4 -1.0*v5, M'[t] == 1.0*v6 -1.0*v8 -1.0*v7
};
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]}]