# Incorporating forcing functions in the ODE model

**URL:** <https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133>\
**Category:** Probabilistic Programming\
**Tags:** turing, bayesian-inference\
**Created:** [October 21, 2021, 7:47am UTC](https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133 "2021-10-21T07:47:39Z")\
**Posts on this page:** 20\
**Page:** 1

<div class="post-metadata">

**Author:** ![vembha](https://avatars.discourse-cdn.com/v4/letter/v/5fc32e/32.png) [@vembha](https://discourse.julialang.org/u/vembha)\
**Post date:** [October 21, 2021, 7:47am UTC](https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133/1 "2021-10-21T07:47:39Z")

</div>

Hello,

I am new to Turing and Julia, and need some help!

I have been trying to estimate the parameters of a model with a discrete forcing function `q(t)`, where the values of `q(t)` are discrete and are read from a file. Consider the ODE to be following:

```julia
function my_model(du, u, p, t)
    α, β = p
    du = α*q(t)*u - β
end

```

Here, alpha and beta are my parameters, which I tried to estimate by building a model as follows, where I am passing the forcing function data explicitly as a vector:

```julia
@model function fitting_model(observ_data, forcing_data)
    # Some priors...
    α ~ truncated(Normal(0.25, 0.1), 0.1, 0.5)
    β ~ truncated(Normal(0.65, 0.1), 0, 2)
    
    # Parameter vector
    p = [β, α, forcing_data];

    # Defining other required variables like u0, tspan, etc...

    # Then, the (usual) subsequent steps to estimate parameters
    problem = ODEProblem(my_model, u0, tspan, p);
    predicted = solve(problem, Tsit5(), saveat=1.0);

    # Finally matching the predicted data with observ_data
end

```

But running this code resulted in `TypeError: in typeassert, expected Float64, got a value of type ForwardDiff.Dual{Nothing, Float64, 7}`. I am at a dead end, and don’t know how to resolve this issue.

Please, please help me out! 😢

---

<div class="post-metadata">

**Author:** ![tomaklutfu](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tomaklutfu/32/2411_2.png) [@tomaklutfu](https://discourse.julialang.org/u/tomaklutfu)\
**Post date:** [October 21, 2021, 7:55am UTC](https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133/2 "2021-10-21T07:55:25Z")

</div>

Can you add whole code you try to run? If not, check the code for hard coded types. The error suggest you hard coded the type `Float64` somewhere and you got a dual number along the way.

---

<div class="post-metadata">

**Author:** ![vembha](https://avatars.discourse-cdn.com/v4/letter/v/5fc32e/32.png) [@vembha](https://discourse.julialang.org/u/vembha)\
**Post date:** [October 21, 2021, 8:46am UTC](https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133/3 "2021-10-21T08:46:18Z")

</div>

Thank you for the quick reply @tomaklutfu! Please check the complete code below:

```julia
#=
Section 1: Import required packages
=#

using Turing, Distributions, DifferentialEquations, Interpolations
using MCMCChains, Plots, StatsPlots
using CSV, XLSX, DataFrames
using Random
Random.seed!(18431)

#=
Section 2: Read the data file containing observation data and get the NPI data into arrays
=#

my_data = DataFrame(XLSX.readtable("observation_data.xlsx","Sheet1")...);

total_weeks = 36; # Total number of time points
N = 67081000; # Population

y_time = 1:1:total_weeks; # Timepoints (weeks)

y_S = Float64.(my_data.Susceptible); # Susceptible
y_S = y_S[1:total_weeks];

y_D = Float64.(my_data.Deceased); # Deceased
y_D = y_D[1:total_weeks];

y_HC = Float64.(my_data.Hosp_critical); # Critical hospitalizations
y_HC = y_HC[1:total_weeks];

y_T = Float64.(my_data.Hosp_total); # Total hospitalizations
y_T = y_T[1:total_weeks];
y_HNC = y_T - y_HC; # Non-critical hospitalizations

observation_data = [y_S y_D y_HC y_HNC];

wet_data = DataFrame(XLSX.readtable("Wetdata.xlsx","Wetdata")...);
# IPTCC is a forcing function
IPTCC = wet_data.Normalized_IPTCC;
IPTCC = IPTCC[1:total_weeks];

mobil_data = DataFrame(XLSX.readtable("Mobdata.xlsx","Mobdata")...);
# mobil is another forcing function
mobil = mobil_data.Mean;
mobil = mobil[1:total_weeks];

wet_forcing = interpolate(IPTCC, BSpline(Linear()));
mobil_forcing = interpolate(mobil, BSpline(Linear()));

forcing_params = (wet_forcing, mobil_forcing);

#=
Section 3: Define the model and the respective parameters
=#

function epidemic_wildtype(dy, y, p, t)
    S, E, I, Hᵪ, Hₙ, R, D = y;
    β, λ, α, γ, θᵪ, θₙ, γᵪ, γₙ, δᵪ, w, m = p;
    N = 67081000;

    dy[1] = -β*w(t)*m(t)*I*S/N + λ*R; # S
    dy[2] = β*w(t)*m(t)*I*S/N - α*E; # E
    dy[3] = α*E - (γ + θᵪ + θₙ)*I; # I
    dy[4] = θₙ*I - γₙ*Hᵪ; # HNC
    dy[5] = θᵪ*I - (γᵪ + δᵪ)*Hₙ; # HC
    dy[6] = γ*I + γₙ*Hₙ + γᵪ*Hᵪ - λ*R; # R
    dy[7] = δᵪ*Hᵪ; # D
end

#=
Section 4: Define the priors and the Bayesian model
=#

Turing.setadbackend(:forwarddiff)
@model function fitting_epidemic_wildtype(observ_data, w_forcing, m_forcing)
    # Priors of model parameters
    β ~ truncated(Normal(0.65, 0.1), 0, 2)
    λ ~ truncated(Normal(0.5, 0.1), 0, 5)
    α ~ truncated(Normal(0.25, 0.1), 0.1, 0.5)
    γ ~ truncated(Normal(0.05, 0.1), 0, 5)
    γₙ ~ Uniform(0.05, 0.1)
    γᵪ ~ Uniform(0.05, 0.1)
    θₙ ~ Uniform(0.09, 0.75)
    θᵪ ~ Uniform(0.09, 0.75)
    δᵪ ~ Uniform(0.1, 0.8)

    p = [β, λ, α, γ, θᵪ, θₙ, γᵪ, γₙ, δᵪ, w_forcing, m_forcing];

    # Priors of standard deviations
    σ₁ ~ InverseGamma(1, 1) # Susceptible
    σ₂ ~ InverseGamma(1, 1) # Deceased
    σ₃ ~ InverseGamma(2, 3) # Critically hospitalized
    σ₄ ~ InverseGamma(1, 1) # Non-critically hospitalized

    # Initial conditions
    N = 67081000;
    S0 = N;
    I0 = 100;
    y0 = [S0, 0, I0, 0, 0, 0, 0];
    y0 = eltype(p).(y0);

    # Solve the model and compare with observed data
    problem = ODEProblem(epidemic_wildtype, y0, (1, 36), p)
    predicted = solve(problem, Tsit5(), saveat=1.0)

    for i = 1:length(predicted)
        observ_data[i,1] ~ Normal(predicted[1,i], σ₁)
        observ_data[i,2] ~ Normal(predicted[7,i], σ₂)
        observ_data[i,3] ~ Normal(predicted[5,i], σ₃)
        observ_data[i,4] ~ Normal(predicted[4,i], σ₄)
    end
end

#=
Section 5: Run the model-inference system and save the chains
=#

model = fitting_epidemic_wildtype(observation_data, wet_forcing, mobil_forcing);
number_of_chains = 1;
chain = sample(model, NUTS(0.65), MCMCThreads(), 10000, number_of_chains);

```

Hope it helps to debug! Thanks in advance.

---

<div class="post-metadata">

**Author:** ![baggepinnen](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/baggepinnen/32/693_2.png) [@baggepinnen](https://discourse.julialang.org/u/baggepinnen)\
**Post date:** [October 21, 2021, 10:45am UTC](https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133/4 "2021-10-21T10:45:24Z")

</div>

> [@vembha](#):
>
> `dy[1]`

This array might be expecting a `Float64` eltype. The eltype of this array is likely defined to be the same as that of `y0`. I would try to update y0 to

```julia
y0 = eltype(p).(y0)

```

this makes `y0` an array of the same element type as the parameter vector `p`, which is probably of type `Dual`.

---

<div class="post-metadata">

**Author:** ![vembha](https://avatars.discourse-cdn.com/v4/letter/v/5fc32e/32.png) [@vembha](https://discourse.julialang.org/u/vembha)\
**Post date:** [October 21, 2021, 11:23am UTC](https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133/5 "2021-10-21T11:23:15Z")

</div>

Thank you @baggepinnen for the quick response. Unfortunately, it looks like the eltype still doesn’t solve it. The error now is `MethodError: no constructors have been defined for Any`. As far as I can see, all the data is of `Float64` type, so don’t really know how/where the `Any` type is coming from!

Any help is really appreciated! 😓

---

<div class="post-metadata">

**Author:** ![nilshg](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/nilshg/32/2283_2.png) [@nilshg](https://discourse.julialang.org/u/nilshg)\
**Post date:** [October 21, 2021, 12:10pm UTC](https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133/6 "2021-10-21T12:10:32Z")

</div>

```julia
DataFrame(XLSX.readtable("observation_data.xlsx","Sheet1")...)

```

Will mean that all your data will be of type `Any` - try the `infer_eltypes = true` kwarg.

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [October 21, 2021, 12:44pm UTC](https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133/7 "2021-10-21T12:44:07Z")

</div>

> [@vembha](#):
>
> The error now is `MethodError: no constructors have been defined for Any` .

Post the whole error. That stacktrace that you are ignoring is the most important part.

---

<div class="post-metadata">

**Author:** ![vembha](https://avatars.discourse-cdn.com/v4/letter/v/5fc32e/32.png) [@vembha](https://discourse.julialang.org/u/vembha)\
**Post date:** [October 21, 2021, 1:39pm UTC](https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133/8 "2021-10-21T13:39:12Z")

</div>

My bad! Just realized that the whole stacktrace is important. Here it is:

```julia
┌ Warning: Only a single thread available: MCMC chains are not sampled in parallel      
└ @ AbstractMCMC C:\Users\Bharadwaj\.julia\packages\AbstractMCMC\BPJCW\src\sample.jl:291
ERROR: LoadError: TaskFailedException

    nested task error: TaskFailedException       
    Stacktrace:
     [1] wait
       @ .\task.jl:322 [inlined]
     [2] threading_run(func::Function)
       @ Base.Threads .\threadingconstructs.jl:34
     [3] macro expansion
       @ .\threadingconstructs.jl:93 [inlined]   
     [4] macro expansion
       @ C:\Users\Bharadwaj\.julia\packages\AbstractMCMC\BPJCW\src\sample.jl:342 [inlined]
     [5] (::AbstractMCMC.var"#31#41"{Bool, Base.Iterators.Pairs{Symbol, UnionAll, Tuple{Symbol}, NamedTuple{(:chain_type,), Tuple{UnionAll}}}, Int64, Int64, Vector{Any}, Vector{UInt64}, Vector{DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}}, Vector{DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}}, Vector{Random._GLOBAL_RNG}})()
       @ AbstractMCMC .\task.jl:411

        nested task error: MethodError: no constructors have been defined for Any
        Stacktrace:
          [1] _broadcast_getindex_evalf
            @ .\broadcast.jl:648 [inlined]
          [2] _broadcast_getindex
            @ .\broadcast.jl:621 [inlined]
          [3] getindex
            @ .\broadcast.jl:575 [inlined]
          [4] copy
            @ .\broadcast.jl:922 [inlined]
          [5] materialize
            @ .\broadcast.jl:883 [inlined]
          [6] fitting_epidemic_wildtype( __model__ ::DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}, __varinfo__ ::DynamicPPL.UntypedVarInfo{DynamicPPL.Metadata{Dict{AbstractPPL.VarName, Int64}, Vector{Distribution}, Vector{AbstractPPL.VarName}, Vector{Real}, Vector{Set{DynamicPPL.Selector}}}, Float64}, __context__ ::DynamicPPL.SamplingContext{DynamicPPL.SampleFromUniform, DynamicPPL.DefaultContext, Random._GLOBAL_RNG}, observ_data::Matrix{Float64}, w_forcing::Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, m_forcing::Interpolations.BSplineInterpolation{Float64, 1, 
Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}})
            @ Main c:\Users\Bharadwaj\Indian Institute of Science\COVID-19 variant study - General\codes_wildtype_fitting\discourse_NPI_code.jl:100
          [7] macro expansion
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\model.jl:465 [inlined]
          [8] _evaluate
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\model.jl:448 [inlined]
          [9] evaluate_threadunsafe
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\model.jl:421 [inlined]
         [10] Model
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\model.jl:389 [inlined]
         [11] Model
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\model.jl:383 [inlined]
         [12] VarInfo
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\varinfo.jl:127 [inlined]
         [13] VarInfo
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\varinfo.jl:126 [inlined]
         [14] step(rng::Random._GLOBAL_RNG, model::DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}, spl::DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}; resume_from::Nothing, kwargs::Base.Iterators.Pairs{Symbol, Int64, Tuple{Symbol}, NamedTuple{(:nadapts,), Tuple{Int64}}})
            @ DynamicPPL C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\sampler.jl:69
         [15] macro expansion
            @ C:\Users\Bharadwaj\.julia\packages\AbstractMCMC\BPJCW\src\sample.jl:123 [inlined]
         [16] macro expansion
            @ C:\Users\Bharadwaj\.julia\packages\AbstractMCMC\BPJCW\src\logging.jl:15 [inlined]
         [17] mcmcsample(rng::Random._GLOBAL_RNG, model::DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}, sampler::DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, N::Int64; progress::Bool, progressname::String, callback::Nothing, discard_initial::Int64, thinning::Int64, chain_type::Type, kwargs::Base.Iterators.Pairs{Symbol, Int64, Tuple{Symbol}, NamedTuple{(:nadapts,), Tuple{Int64}}})
            @ AbstractMCMC C:\Users\Bharadwaj\.julia\packages\AbstractMCMC\BPJCW\src\sample.jl:114
         [18] #sample#40
            @ C:\Users\Bharadwaj\.julia\packages\Turing\uMQmD\src\inference\hmc.jl:133 [inlined]
         [19] macro expansion
            @ C:\Users\Bharadwaj\.julia\packages\AbstractMCMC\BPJCW\src\sample.jl:351 [inlined]
         [20] (::AbstractMCMC.var"#927#threadsfor_fun#42"{UnitRange{Int64}, Bool, Base.Iterators.Pairs{Symbol, UnionAll, Tuple{Symbol}, NamedTuple{(:chain_type,), Tuple{UnionAll}}}, Int64, Vector{Any}, Vector{UInt64}, Vector{DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}}, Vector{DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}}, Vector{Random._GLOBAL_RNG}})(onethread::Bool)
            @ AbstractMCMC .\threadingconstructs.jl:81
         [21] (::AbstractMCMC.var"#927#threadsfor_fun#42"{UnitRange{Int64}, Bool, Base.Iterators.Pairs{Symbol, UnionAll, Tuple{Symbol}, NamedTuple{(:chain_type,), Tuple{UnionAll}}}, Int64, Vector{Any}, Vector{UInt64}, Vector{DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}}, Vector{DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}}, Vector{Random._GLOBAL_RNG}})()
            @ AbstractMCMC .\threadingconstructs.jl:48
Stacktrace:
  [1] sync_end(c::Channel{Any})
    @ Base .\task.jl:369
  [2] macro expansion
    @ .\task.jl:388 [inlined]
  [3] macro expansion
    @ C:\Users\Bharadwaj\.julia\packages\AbstractMCMC\BPJCW\src\sample.jl:320 [inlined]
  [4] macro expansion
    @ C:\Users\Bharadwaj\.julia\packages\ProgressLogging\6KXlp\src\ProgressLogging.jl:328 [inlined]
  [5] macro expansion
    @ C:\Users\Bharadwaj\.julia\packages\AbstractMCMC\BPJCW\src\logging.jl:8 [inlined]
  [6] mcmcsample(rng::Random._GLOBAL_RNG, model::DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}, sampler::DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, ::MCMCThreads, N::Int64, nchains::Int64; progress::Bool, progressname::String, kwargs::Base.Iterators.Pairs{Symbol, UnionAll, Tuple{Symbol}, NamedTuple{(:chain_type,), Tuple{UnionAll}}})
    @ AbstractMCMC C:\Users\Bharadwaj\.julia\packages\AbstractMCMC\BPJCW\src\sample.jl:314
  [7] sample(rng::Random._GLOBAL_RNG, model::DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}, sampler::DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, ensemble::MCMCThreads, N::Int64, n_chains::Int64; chain_type::Type, progress::Bool, kwargs::Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
    @ Turing.Inference C:\Users\Bharadwaj\.julia\packages\Turing\uMQmD\src\inference\Inference.jl:217
  [8] sample
    @ C:\Users\Bharadwaj\.julia\packages\Turing\uMQmD\src\inference\Inference.jl:217 [inlined]
  [9] #sample#6
    @ C:\Users\Bharadwaj\.julia\packages\Turing\uMQmD\src\inference\Inference.jl:202 [inlined]
 [10] sample
    @ C:\Users\Bharadwaj\.julia\packages\Turing\uMQmD\src\inference\Inference.jl:202 [inlined]
 [11] #sample#5
    @ C:\Users\Bharadwaj\.julia\packages\Turing\uMQmD\src\inference\Inference.jl:189 [inlined]
 [12] sample(model::DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}, alg::NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}, ensemble::MCMCThreads, N::Int64, n_chains::Int64)
    @ Turing.Inference C:\Users\Bharadwaj\.julia\packages\Turing\uMQmD\src\inference\Inference.jl:189
 [13] top-level scope
    @ c:\Users\Bharadwaj\Indian Institute of Science\COVID-19 variant study - General\codes_wildtype_fitting\discourse_NPI_code.jl:120
in expression starting at c:\Users\Bharadwaj\Indian Institute of Science\COVID-19 variant study - General\codes_wildtype_fitting\discourse_NPI_code.jl:120

```

This is the error I am getting after incorporating the suggestions of @baggepinnen and @nilshg. Please check this and help me out!

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [October 21, 2021, 2:21pm UTC](https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133/9 "2021-10-21T14:21:30Z")

</div>

> [@vembha](#):
>
> `c:\Users\Bharadwaj\Indian Institute of Science\COVID-19 variant study - General\codes_wildtype_fitting\discourse_NPI_code.jl:100`

which line is line 100 in your code?

---

<div class="post-metadata">

**Author:** ![vembha](https://avatars.discourse-cdn.com/v4/letter/v/5fc32e/32.png) [@vembha](https://discourse.julialang.org/u/vembha)\
**Post date:** [October 21, 2021, 2:35pm UTC](https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133/10 "2021-10-21T14:35:49Z")

</div>

> [@vembha](#):
>
> `y0 = eltype(p).(y0);`

@ChrisRackauckas Hello! This was the line 100.

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [October 21, 2021, 2:45pm UTC](https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133/11 "2021-10-21T14:45:29Z")

</div>

Put an `@show typeof(y0)` and `@show eltype(p)` right before that line and share what they print out.

---

<div class="post-metadata">

**Author:** ![vembha](https://avatars.discourse-cdn.com/v4/letter/v/5fc32e/32.png) [@vembha](https://discourse.julialang.org/u/vembha)\
**Post date:** [October 21, 2021, 3:11pm UTC](https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133/12 "2021-10-21T15:11:55Z")

</div>

This is the output from the two lines:

```julia
┌ Warning: Only a single thread available: MCMC chains are not sampled in parallel      
└ @ AbstractMCMC C:\Users\Bharadwaj\.julia\packages\AbstractMCMC\BPJCW\src\sample.jl:291
typeof(y0) = Vector{Int64}
eltype(p) = Any
ERROR: LoadError: TaskFailedException

```

… and the previously mentioned error continues.

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [October 21, 2021, 3:29pm UTC](https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133/13 "2021-10-21T15:29:16Z")

</div>

`eltype(p) is `Any` because you put functions in there.

```julia
p = [β, λ, α, γ, θᵪ, θₙ, γᵪ, γₙ, δᵪ, w_forcing, m_forcing];

```

So instead you want to upconvert to just the scalar dual types. In fact, it would be better to do:

```julia
p = (β, λ, α, γ, θᵪ, θₙ, γᵪ, γₙ, δᵪ, w_forcing, m_forcing);

```

so that is type-stable, and then do:

```julia
y0 = typeof(β).(y0)

```

so it converts `y0` to a dual.

---

<div class="post-metadata">

**Author:** ![vembha](https://avatars.discourse-cdn.com/v4/letter/v/5fc32e/32.png) [@vembha](https://discourse.julialang.org/u/vembha)\
**Post date:** [October 21, 2021, 6:39pm UTC](https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133/14 "2021-10-21T18:39:02Z")

</div>

Tried the modifications you suggested, and this time got different error.

```julia
nested task error: BoundsError: attempt to access 36-element interpolate(::Vector{Float64}, BSpline(Linear())) with element type Float64 at index [NaN]
        Stacktrace:
          [1] throw_boundserror(A::Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, I::Tuple{Float64})
            @ Base .\abstractarray.jl:651
          [2] BSplineInterpolation
            @ C:\Users\vembh\.julia\packages\Interpolations\3gTQB\src\b-splines\indexing.jl:6 [inlined]
          [3] getindex(itp::Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, i::Float64)
            @ Interpolations .\deprecated.jl:72
          [4] epidemic_wildtype...

```

at line 61, where line 61 is `dy[1] = -β*w(t)*m(t)*I*S/N + λ*R;` and line 106 is `predicted = solve(problem, Tsit5(), saveat=1.0)`.

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [October 21, 2021, 7:38pm UTC](https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133/15 "2021-10-21T19:38:05Z")

</div>

Are you solving past the time point where you interpolate? Before that line add `@show t` and figure out what the last point being interpolated is. That should make easy to then do `w(t)` or `m(t)` and reproduce the error without Turing.

---

<div class="post-metadata">

**Author:** ![vembha](https://avatars.discourse-cdn.com/v4/letter/v/5fc32e/32.png) [@vembha](https://discourse.julialang.org/u/vembha)\
**Post date:** [October 22, 2021, 6:07am UTC](https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133/16 "2021-10-22T06:07:02Z")

</div>

1. I do not think I am solving beyond the last point of interpolation. The image below proves that! I am solving for time interval `(1, 36)` and the interpolated forcing functions have the values at the same time points.

 ![image](https://global.discourse-cdn.com/julialang/original/3X/7/9/79d05a3459a5e63e3f6d93f3144d7f3b0ba91307.png)

1. I am posting the code here again for convenience and the error (which is completely new this time and does not show `BoundsError`) getting generated. Incorporating only your suggestions @ChrisRackauckas:

```julia
#=
Section 1: Import required packages
=#

using Turing, Distributions, DifferentialEquations, Interpolations
using MCMCChains, Plots, StatsPlots
using CSV, XLSX, DataFrames
using Random
Random.seed!(18431)

#=
Section 2: Read the data file containing observation data and get the NPI data into arrays
=#

my_data = DataFrame(XLSX.readtable("observation_data.xlsx","Sheet1"; infer_eltypes = true)...);

total_weeks = 36; # Total number of time points
N = 67081000; # Population

y_time = 1:1:total_weeks; # Timepoints (weeks)

y_S = Float64.(my_data.Susceptible); # Susceptible
y_S = y_S[1:total_weeks];

y_D = Float64.(my_data.Deceased); # Deceased
y_D = y_D[1:total_weeks];

y_HC = Float64.(my_data.Hosp_critical); # Critical hospitalizations
y_HC = y_HC[1:total_weeks];

y_T = Float64.(my_data.Hosp_total); # Total hospitalizations
y_T = y_T[1:total_weeks];
y_HNC = y_T - y_HC; # Non-critical hospitalizations

observation_data = [y_S y_D y_HC y_HNC];

wet_data = DataFrame(XLSX.readtable("Wetdata.xlsx","Wetdata"; infer_eltypes = true)...);
# IPTCC is a forcing function
IPTCC = wet_data.Normalized_IPTCC;
IPTCC = IPTCC[1:total_weeks];

mobil_data = DataFrame(XLSX.readtable("Mobdata.xlsx","Mobdata"; infer_eltypes = true)...);
# mobil is another forcing function
mobil = mobil_data.Mean;
mobil = mobil[1:total_weeks];

wet_forcing = interpolate(IPTCC, BSpline(Linear()));
mobil_forcing = interpolate(mobil, BSpline(Linear()));

forcing_params = (wet_forcing, mobil_forcing);

#=
Section 3: Define the model and the respective parameters
=#

function epidemic_wildtype(dy, y, p, t)
    S, E, I, Hᵪ, Hₙ, R, D = y;
    β, λ, α, γ, θᵪ, θₙ, γᵪ, γₙ, δᵪ, w, m = p;
    N = 67081000;

    dy[1] = -β*w(t)*m(t)*I*S/N + λ*R; # S
    dy[2] = β*w(t)*m(t)*I*S/N - α*E; # E
    dy[3] = α*E - (γ + θᵪ + θₙ)*I; # I
    dy[4] = θₙ*I - γₙ*Hᵪ; # HNC
    dy[5] = θᵪ*I - (γᵪ + δᵪ)*Hₙ; # HC
    dy[6] = γ*I + γₙ*Hₙ + γᵪ*Hᵪ - λ*R; # R
    dy[7] = δᵪ*Hᵪ; # D
end

#=
Section 4: Define the priors and the Bayesian model
=#

Turing.setadbackend(:forwarddiff)
@model function fitting_epidemic_wildtype(observ_data, w_forcing, m_forcing)
    # Priors of model parameters
    β ~ truncated(Normal(0.65, 0.1), 0, 2)
    λ ~ truncated(Normal(0.5, 0.1), 0, 5)
    α ~ truncated(Normal(0.25, 0.1), 0.1, 0.5)
    γ ~ truncated(Normal(0.05, 0.1), 0, 5)
    γₙ ~ Uniform(0.05, 0.1)
    γᵪ ~ Uniform(0.05, 0.1)
    θₙ ~ Uniform(0.09, 0.75)
    θᵪ ~ Uniform(0.09, 0.75)
    δᵪ ~ Uniform(0.1, 0.8)

    p = (β, λ, α, γ, θᵪ, θₙ, γᵪ, γₙ, δᵪ, w_forcing, m_forcing);

    # Priors of standard deviations
    σ₁ ~ InverseGamma(1, 1) # Susceptible
    σ₂ ~ InverseGamma(1, 1) # Deceased
    σ₃ ~ InverseGamma(2, 3) # Critically hospitalized
    σ₄ ~ InverseGamma(1, 1) # Non-critically hospitalized

    # Initial conditions
    N = 67081000;
    S0 = N;
    I0 = 100;
    y0 = [S0, 0, I0, 0, 0, 0, 0];
    @show typeof(y0)
    @show eltype(p)
    y0 = typeof(β).(y0);

    # Solve the model and compare with observed data
    problem = ODEProblem(epidemic_wildtype, y0, (1, 36), p)
    predicted = solve(problem, Tsit5(), saveat=1)

    for i = 1:length(predicted)
        observ_data[i,1] ~ Normal(predicted[1,i], σ₁)
        observ_data[i,2] ~ Normal(predicted[7,i], σ₂)
        observ_data[i,3] ~ Normal(predicted[5,i], σ₃)
        observ_data[i,4] ~ Normal(predicted[4,i], σ₄)
    end
end

#=
Section 5: Run the model-inference system and save the chains
=#

model = fitting_epidemic_wildtype(observation_data, wet_forcing, mobil_forcing);
number_of_chains = 1;
chain = sample(model, NUTS(0.65), MCMCThreads(), 10000, number_of_chains);

```

Error without the Turing error part:

```julia
nested task error: InexactError: Int64(161//1000)
        Stacktrace:
          [1] Integer
            @ .\rational.jl:110 [inlined]
          [2] convert(#unused#::Type{Int64}, x::Rational{Int64})
            @ Base .\number.jl:7
          [3] OrdinaryDiffEq.Tsit5ConstantCache(T::Type, T2::Type)
            @ OrdinaryDiffEq C:\Users\Bharadwaj\.julia\packages\OrdinaryDiffEq\Zi9Zh\src\tableaus\low_order_rk_tableaus.jl:604
          [4] alg_cache(alg::Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}, u::Vector{Float64}, rate_prototype::Vector{Float64}, #unused#::Type{Float64}, #unused#::Type{Float64}, #unused#::Type{Int64}, uprev::Vector{Float64}, uprev2::Vector{Float64}, f::ODEFunction{true, typeof(epidemic_wildtype), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, 
Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, t::Int64, dt::Int64, reltol::Float64, p::Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, calck::Bool, #unused#::Val{true})
            @ OrdinaryDiffEq C:\Users\Bharadwaj\.julia\packages\OrdinaryDiffEq\Zi9Zh\src\caches\low_order_rk_caches.jl:350
          [5] __init(prob::ODEProblem{Vector{Float64}, Tuple{Int64, Int64}, true, Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, ODEFunction{true, typeof(epidemic_wildtype), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, alg::Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}, timeseries_init::Tuple{}, ts_init::Tuple{}, ks_init::Tuple{}, recompile::Type{Val{true}}; saveat::Int64, tstops::Tuple{}, d_discontinuities::Tuple{}, save_idxs::Nothing, save_everystep::Bool, save_on::Bool, save_start::Bool, save_end::Nothing, callback::Nothing, dense::Bool, calck::Bool, dt::Int64, dtmin::Nothing, dtmax::Int64, force_dtmin::Bool, adaptive::Bool, gamma::Rational{Int64}, abstol::Nothing, reltol::Nothing, qmin::Rational{Int64}, qmax::Int64, qsteady_min::Int64, qsteady_max::Int64, beta1::Nothing, beta2::Nothing, qoldinit::Rational{Int64}, controller::Nothing, fullnormalize::Bool, failfactor::Int64, maxiters::Int64, internalnorm::typeof(DiffEqBase.ODE_DEFAULT_NORM), internalopnorm::typeof(LinearAlgebra.opnorm), isoutofdomain::typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), unstable_check::typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), verbose::Bool, timeseries_errors::Bool, dense_errors::Bool, advance_to_tstop::Bool, stop_at_next_tstop::Bool, initialize_save::Bool, progress::Bool, progress_steps::Int64, progress_name::String, progress_message::typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), userdata::Nothing, allow_extrapolation::Bool, initialize_integrator::Bool, alias_u0::Bool, alias_du0::Bool, initializealg::OrdinaryDiffEq.DefaultInit, kwargs::Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
            @ OrdinaryDiffEq C:\Users\Bharadwaj\.julia\packages\OrdinaryDiffEq\Zi9Zh\src\solve.jl:295
          [6] #__solve#471
            @ C:\Users\Bharadwaj\.julia\packages\OrdinaryDiffEq\Zi9Zh\src\solve.jl:4 [inlined]
          [7] #solve_call#42
            @ C:\Users\Bharadwaj\.julia\packages\DiffEqBase\FtYIB\src\solve.jl:61 [inlined]
          [8] solve_up(prob::ODEProblem{Vector{Float64}, Tuple{Int64, Int64}, true, Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, ODEFunction{true, typeof(epidemic_wildtype), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, sensealg::Nothing, u0::Vector{Float64}, p::Tuple{Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, args::Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!)}; kwargs::Base.Iterators.Pairs{Symbol, Int64, Tuple{Symbol}, NamedTuple{(:saveat,), Tuple{Int64}}})
            @ DiffEqBase C:\Users\Bharadwaj\.julia\packages\DiffEqBase\FtYIB\src\solve.jl:87
          [9] #solve#43
            @ C:\Users\Bharadwaj\.julia\packages\DiffEqBase\FtYIB\src\solve.jl:73 [inlined]
         [10] fitting_epidemic_wildtype( __model__ ::DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}, __varinfo__ ::DynamicPPL.UntypedVarInfo{DynamicPPL.Metadata{Dict{AbstractPPL.VarName, Int64}, Vector{Distribution}, Vector{AbstractPPL.VarName}, Vector{Real}, Vector{Set{DynamicPPL.Selector}}}, Float64}, __context__ ::DynamicPPL.SamplingContext{DynamicPPL.SampleFromUniform, DynamicPPL.DefaultContext, Random._GLOBAL_RNG}, observ_data::Matrix{Float64}, w_forcing::Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, m_forcing::Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}})
            @ Main c:\Users\Bharadwaj\Indian Institute of Science\COVID-19 variant study - General\codes_wildtype_fitting\discourse_NPI_code.jl:106
         [11] macro expansion
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\model.jl:465 [inlined]
         [12] _evaluate
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\model.jl:448 [inlined]
         [13] evaluate_threadunsafe
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\model.jl:421 [inlined]
         [14] Model
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\model.jl:389 [inlined]
         [15] Model
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\model.jl:383 [inlined]
         [16] VarInfo
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\varinfo.jl:127 [inlined]
         [17] VarInfo
            @ C:\Users\Bharadwaj\.julia\packages\DynamicPPL\RcfQU\src\varinfo.jl:126 [inlined]
         [18] step(rng::Random._GLOBAL_RNG, model::DynamicPPL.Model{typeof(fitting_epidemic_wildtype), (:observ_data, :w_forcing, :m_forcing), (), (), Tuple{Matrix{Float64}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}}, Tuple{}, DynamicPPL.DefaultContext}, spl::DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}; resume_from::Nothing, kwargs::Base.Iterators.Pairs{Symbol, Int64, Tuple{Symbol}, NamedTuple{(:nadapts,), Tuple{Int64}}})

```

where line 106 is `predicted = solve(problem, Tsit5(), saveat=1)`. Hope this helps; sorry for the mess! 😪

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [October 22, 2021, 2:13pm UTC](https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133/17 "2021-10-22T14:13:17Z")

</div>

> [@vembha](#):
>
> `(1, 36)`

Make your time a floating point type: `(1.0,36.0)`. That should be caught and fixed automatically, but let’s see if that’s all that’s left now.

---

<div class="post-metadata">

**Author:** ![vembha](https://avatars.discourse-cdn.com/v4/letter/v/5fc32e/32.png) [@vembha](https://discourse.julialang.org/u/vembha)\
**Post date:** [October 23, 2021, 6:38am UTC](https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133/18 "2021-10-23T06:38:29Z")

</div>

This brought back the `BoundsError` error that I posted previously! 😪 Posting the part of the (extremely long) error message stacktrace.

```julia
nested task error: BoundsError: attempt to access 36-element interpolate(::Vector{Float64}, BSpline(Linear())) with element type Float64 at index [NaN]
        Stacktrace:
          [1] throw_boundserror(A::Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, I::Tuple{Float64})
            @ Base .\abstractarray.jl:651
          [2] BSplineInterpolation
            @ C:\Users\Bharadwaj\.julia\packages\Interpolations\3gTQB\src\b-splines\indexing.jl:6 [inlined]
          [3] epidemic_wildtype(dy::Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.Core.var"#f#1"{DynamicPPL.TypedVarInfo{NamedTuple{(:β, :λ, :α, :γ, :γₙ, :γᵪ, :θₙ, :θᵪ, :δᵪ, :σ₁, :σ₂, :σ₃, :σ₄), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:β, Tuple{}}, Int64}, Vector{Truncated{Normal{Float64}, Continuous, Float64}}, Vector{AbstractPPL.VarName{:β, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:λ, Tuple{}}, Int64}, Vector{Truncated{Normal{Float64}, Continuous, Float64}}, Vector{AbstractPPL.VarName{:λ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:α, Tuple{}}, Int64}, Vector{Truncated{Normal{Float64}, Continuous, Float64}}, Vector{AbstractPPL.VarName{:α, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:γ, Tuple{}}, Int64}, Vector{Truncated{Normal{Float64}, Continuous, Float64}}, Vector{AbstractPPL.VarName{:γ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:γₙ, Tuple{}}, Int64}, Vector{Uniform{Float64}}, Vector{AbstractPPL.VarName{:γₙ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:γᵪ, Tuple{}}, Int64}, Vector{Uniform{Float64}}, Vector{AbstractPPL.VarName{:γᵪ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:θₙ, Tuple{}}, Int64}, Vector{Uniform{Float64}}, Vector{AbstractPPL.VarName{:θₙ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:θᵪ, Tuple{}}, Int64}, Vector{Uniform{Float64}}, Vector{AbstractPPL.VarName{:θᵪ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:δᵪ, Tuple{}}, Int64}, Vector{Uniform{Float64}}, Vector{AbstractPPL.VarName{:δᵪ, Tuple{}}}, 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            @ Main C:\Users\Bharadwaj\Indian Institute of Science\COVID-19 variant study - General\codes_wildtype_fitting\discourse_NPI_code.jl:61

```

Here, line 61 is the first differential equation.

> [@vembha](#):
>
> `dy[1] = -β*w(t)*m(t)*I*S/N + λ*R; # S`

Hope this helps you @ChrisRackauckas in helping me out…

---

<div class="post-metadata">

**Author:** ![vembha](https://avatars.discourse-cdn.com/v4/letter/v/5fc32e/32.png) [@vembha](https://discourse.julialang.org/u/vembha)\
**Post date:** [October 23, 2021, 10:03am UTC](https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133/19 "2021-10-23T10:03:14Z")

</div>

By the way, when I am just solving the ODE with randomly chosen parameter values (and not using Turing) along with the forcing functions, the code runs error-free! Here is the part of the code without the Turing part:

```julia
#= 
Section 1: Import required packages =#

using Turing, Distributions, DifferentialEquations, Interpolations
using MCMCChains, Plots, StatsPlots
using CSV, XLSX, DataFrames
using Random
Random.seed!(18431)

#= 
Section 2: Read the data file containing observation data and get the NPI data into arrays =#

my_data = DataFrame(XLSX.readtable("UK_weekly_15_July.xlsx", "Sheet1"; infer_eltypes=true)...);

total_weeks = 36; # Total number of time points
N = 67081000; # Population

y_time = 1:1:total_weeks; # Timepoints (weeks)

y_S = Float64.(my_data.Susceptible); # Susceptible
y_S = y_S[1:total_weeks];

y_D = Float64.(my_data.Deceased); # Deceased
y_D = y_D[1:total_weeks];

y_HC = Float64.(my_data.Hosp_critical); # Critical hospitalizations
y_HC = y_HC[1:total_weeks];

y_T = Float64.(my_data.Hosp_total); # Total hospitalizations
y_T = y_T[1:total_weeks];
y_HNC = y_T - y_HC; # Non-critical hospitalizations

observation_data = [y_S y_D y_HC y_HNC];

wet_data = DataFrame(XLSX.readtable("Wetdata.xlsx", "Wetdata"; infer_eltypes=true)...);
# IPTCC is a forcing function
IPTCC = wet_data.Normalized_IPTCC;
IPTCC = IPTCC[1:total_weeks];

mobil_data = DataFrame(XLSX.readtable("Mobdata.xlsx", "Mobdata"; infer_eltypes=true)...);
# mobil is another forcing function
mobil = mobil_data.Mean;
mobil = mobil[1:total_weeks];

wet_forcing = interpolate(IPTCC, BSpline(Linear()));
mobil_forcing = interpolate(mobil, BSpline(Linear()));

#= 
Section 3: Define the model and the respective parameters =#

function epidemic_wildtype!(dy, y, p, t)
    S, E, I, Hᵪ, Hₙ, R, D = y;
    β, λ, α, γ, θᵪ, θₙ, γᵪ, γₙ, δᵪ, w, m = p;
    N = 67081000;

    dy[1] = -β * w(t) * m(t) * I * S / N + λ * R; # S
    dy[2] = β * w(t) * m(t) * I * S / N - α * E; # E
    dy[3] = α * E - (γ + θᵪ + θₙ) * I; # I
    dy[4] = θₙ * I - γₙ * Hᵪ; # HNC
    dy[5] = θᵪ * I - (γᵪ + δᵪ) * Hₙ; # HC
    dy[6] = γ * I + γₙ * Hₙ + γᵪ * Hᵪ - λ * R; # R
    dy[7] = δᵪ * Hᵪ; # D
end

#= 
Section 4: Solve it! =#

p = (0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, wet_forcing, mobil_forcing);
tspan = (1.0, 36.0);
N = 67081000;
S0 = N;
I0 = 100;
y0 = [S0, 0, I0, 0, 0, 0, 0];
problem1 = ODEProblem(epidemic_wildtype!, y0, tspan, p);
solution1 = solve(problem1, Tsit5(), saveat=1.0);

```

Also, even when I am defining the forcing functions as global variables rather than passing them as a part of the parameter vector `p`, the ODE system is being solved error-free. But the same `BoundsError` (mentioned in the previous post) is getting triggered. 😐

---

<div class="post-metadata">

**Author:** ![tomaklutfu](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tomaklutfu/32/2411_2.png) [@tomaklutfu](https://discourse.julialang.org/u/tomaklutfu)\
**Post date:** [October 23, 2021, 10:50am UTC](https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133/20 "2021-10-23T10:50:39Z")

</div>

Can you do `@show t` before that line and see what `w(t)` and `m(t)` give for the last `t` shown before the error? Most likely, those two throw somewhere.

[Next page](https://discourse.julialang.org/t/incorporating-forcing-functions-in-the-ode-model/70133.md?page=2)