How to decipher SciMLBase OptimizationBase OptimizationForwardDiffExt warnings?

Specific Domains Optimization (Mathematical)
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1

When fitting a DE params to data, I get warnings like this one:

┌ Warning: dt(2.842170943040401e-14) <= eps(t)(218.2272500679591) , and step error estimate = 2.359923922574841. 
Aborting. 
There is either an error in your model specification or the true solution is unstable 
(or the true solution can not be represented in the precision of ForwardDiff.Dual{ForwardDiff.Tag{OptimizationForwardDiffExt.var"#37#55"{SciMLBase.OptimizationFunction{true, ADTypes.AutoForwardDiff{nothing, Nothing}, typeof(Main.pureopt.sir_subject), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}, OptimizationBase.ReInitCache{Vector{Float64}, Vector{Int64}}}, Float64}, Float64, 7}).
└ @ SciMLBase ~/.julia/packages/SciMLBase/JUp1I/src/integrator_interface.jl:632

┌ Warning: Failed to achieve finite new evaluation point, using alpha=0
└ @ LineSearches ~/.julia/packages/LineSearches/G1LRk/src/hagerzhang.jl:148
  1. What is the function dt(x)? Where does its argument 2.842170943040401e-14 come from?
  2. What is the function eps(t)(y)? Where does its argument 218.2272500679591 come from?
  3. What’s the problem with dt(x) <= eps(t)(y)? How is it related to the step error estimate 2.35?
  4. What is the precision of ForwardDiff.Dual?
  5. Is it fine that ForwardDiff.Dual consists mainly of Nothing?
  6. How can I get an insight into the values that cause this warning?
2

I struggled for a bit on trying to make this error message clear so I would love some help on this. what this is saying is at time t=218.2272500679591, the simulation’s dt (difference between the current time and previous time) has been forced down to 2.842170943040401e-14, and even with that small a dt, the error estimate was greater than 1, which means that the step had too large an error for us to accept the time step even at this miniscule dt.
This causes a problem since this value of dt is less than or equal to eps(218.2272500679591), so if we tried to take steps, those steps would not advance time do to floating point error e.g. `t+dt/2 == t.

Generally this warning happens when the problem you are trying to solve is mathematically unsolvable (e.g. your u or du/dt go to infinity in finite time), or you have a bug in your implimentation.