The ForceOfInfection option in DynamicTransmissionModel is using \[RightArrow] instead of \[Rule] or ->. This code works:
In[14]:=
treatmentModelData =
DynamicTransmissionModel[treatmentModel, t,
ForceOfInfection -> {{\[Lambda], {\[ScriptCapitalA], \
\[ScriptCapitalI]}, {"Standard", Automatic}}}];
In[15]:= Keys@treatmentModelData
Out[15]= {"Variables", "ComponentTransitions", \
"StoichiometricMatrix", "Rates", "Equations", "TimeSymbol", \
"ForceOfInfection"}
The message from NextGenerationMatrix means that the disease-free equilibrium that was supplied does not give 0 on the rhs of the equations when the DFE is substituted in.
Looking at the model, I see that there are two places where a space for implicit multiplication is missing:
Transition[\[ScriptCapitalS], \[Beta] \[Lambda][
t] + \[Beta] \[Omega]\[Lambda][t], \[ScriptCapitalE]]
should have a space between omega and lambda:
Transition[\[ScriptCapitalS], \[Beta] \[Lambda][
t] + \[Beta] \[Omega] \[Lambda][t], \[ScriptCapitalE]]
and
Transition[\[ScriptCapitalE], \[Gamma]\[Rho], \[ScriptCapitalI]]
should have a space between gamma and rho:
Transition[\[ScriptCapitalE], \[Gamma] \[Rho], \[ScriptCapitalI]]
A space for implicit multiplication is also missing in the numerator for V of the DFE:
V -> (\[Kappa]\[CapitalLambda])/(\[Mu] (\[Kappa] + \[Mu]))
should have a space between kappa and Lambda:
V -> (\[Kappa] \[CapitalLambda])/(\[Mu] (\[Kappa] + \[Mu]))
Now, looking more closely at the model, it's not clear why the transition from S to E has two forces of infection. Moreover, the transition from V to E is missing a force of infection. After you make the corrections above, please think about your model and modify the infection transitions accordingly.
