Hi folks,

Been doing a lot of work with the great SciML ecosystem and building more familiarity with its offerings.

I am struggling with an ODE that I am trying to model. Here is the equation:

\frac{dI}{dt} = a \cdot \frac{B}{k + B} \cdot S - r \cdot I

Which I wrote in the function:

```
I(a, k, r, S, B, I) = (a * S) * (B / (k + B)) - r * I
```

As a, k, and r are constants, I replaced them in my formulation as follows:

```
I(S, B, I) = (1 * S) * (B / (10e6 + B)) - 0.2 * I
```

For this ODE, I had the initial values for S, B, and I:

```
initial_values =
[
H - 1, # S(0)
0, # B(0)
1, # I(0)
]
```

Where `H`

is a population count comes from me looping over a set number of population counts. I read up on how to pass multiple parameters to my ODE using DifferentialEquations.jl and came up with a final function formulation that looked like this:

```
I(I, p, t) = ((a_1 * p[1]) * (p[2] / (k_1 + p[2]))) - (r_1 * p[3])
```

My full code is as follows:

```
# Setting up labeling of the figure
fig = Figure(fontsize = 24);
ax = Axis(fig[1, 1],
title = L"Plot of $I$",
xlabel = L"t",
ylabel = L"Population Size"
);
# Time interval from $0$ to $20$ days
tspan = (0, 20)
# Total human populations
populations = [5000, 6000, 7000, 8000, 9000, 10000]
# ODE I am evaluating
I(I, p, t) = ((a_1 * p[1]) * (p[2] / (k_1 + p[2]))) - (r_1 * p[3])
# Looping through different population sizes
for H in populations
initial_values =
[
H - 1, # S(0)
0, # B(0)
1, # I(0)
]
# Set-up ODE
prob = ODEProblem(I, 1, tspan, initial_values)
# Use Tsit5 solver for non-stiff ODEs
sol = solve(prob, Tsit5(), reltol = 1e-8, abstol = 1e-8)
lines!(ax, sol.t, sol.u, label = L"H = $H")
end
# Show plot
fig
```

However, the figure output (below) doesnâ€™t seem to be matching what I expect (next figure).

Even though the values arenâ€™t exactly the same (they shouldnâ€™t be since I am looking at different populations), they are all coming out to the same line and I donâ€™t see any behavior variation that I would expect like in the second figure.

Could anyone point out to me what I may be doing wrong with my `ODEProblem`

set-up? I was thinking I am somehow screwing up my implementation but unsure where.

Thanks!

~ tcp

P.S. For full transparency, this is part of a homework assignment but I am allowed collaboration.