This is an important question.

Basically, this questions leads to a consideration of mathematical epidemiology (a mathematical approach to the the study of the incidence and distribution of diseases and other factors relating to health). For an overview of mathematical epidemiology, see

https://www.researchgate.net/topic/Mathematical-Epidemiology

A consideration of algebraic structures in representing and analyzing epidemiological problems is quite natural, since epidemiology focuses on relational structures underlying the incidence and distribution of diseases.

A good place to start in considering such algebraic structures is the Hilbert Book project here on RG:

https://www.researchgate.net/project/The-Hilbert-Book-Model-Project

See, especially:

https://en.wikiversity.org/wiki/Hilbert_Book_Model_Project/Relational_Structures

More to the point, for an important algebra component in the foundations of mathematical epidemiology, see

Article A new approach to the concept of linearity. Some elements fo...

For a Computer Algebra System in mathematical epidemiology, see

https://arxiv.org/pdf/1401.7390.pdf

In particular, see the use of lattices in mathematical epidemiology:

https://arxiv.org/pdf/nlin/0010012.pdf

@ Asep K Supriatna

Do not trust such theories which call different things as (same) elements of a set!

A reform of the formalism (algebra) you can find on my homepage.

[But it is still in work, to be completed in German more the translation.]

I think some epidemiological problems are investigated in the fields of deferential and deference equations and dynamical systems

Thank you for the answers. I will start to read the suggested links.