I did seemingly find exactly what you want just not in Julia, rather in R language:
Note, you can use it as-is with RCall.jl, if you just need something to practically work (even without translating the code).
It’s not a whole lot of code if you want to translate (all or maybe you only need) part of it to Julia. Note, the GPL license, so it’s free to use or translate, keeping the same copyleft license. Your whole program will fall under GPL 3.0, not a problem for using, possibly for distributing. GPL 3.0 is not compatible with all licences, but that’s only a problem for distributing code, you can always legally use privately, and that also means legally within your company.
I did look up code in other languages, C, C++, MATLAB, Rust and Python. The good thing about Python code would be you can also call it, still needs its runtime, but PythonCall.jl takes care of installation of dependencies (and Python itself). I’ve seen a wrapper made for R code (Alpaca.jl), which used RCall.jl, but as with PyCall.jl you need to take care of installation of dependencies, and R.
I did also find two packages in Python, both missing a license file [EDIT: at least one of, the package chosen, is BSD-licenced] (both have all code in one file):
Maybe useful to you: Titration | kinsaurralde
The titration calculator website […] The titration calculator is written in c++ and runs on aws lambda. The code for the calculator is located at:
GitHub - kinsaurralde/titration
Again a license file is missing.
I did not see such code for Julia, you could look at this (likely incomplete) list:
There’s no R-to-Julia translator available, that I know of (nor even to C++, but info on how is still helpful):
https://adv-r.hadley.nz/rcpp.html
There’s a (partial) MATLAB-to-Julia translator available. I’ve used it, and those languages are most closely related, so might be best to find MATLAB code for this. There’s also a Python-to-Julia (py2many) but I haven’t tried it.
https://adv-r.hadley.nz/translation.html
See also: https://cran.r-project.org/web/packages/titrationCurves/vignettes/titrationCurves.pdf