I am someone who has never studied Epidemics (or much applied mathematics), my background is probability theory, specifically McKean-Vlasov SDE. I was wondering if anyone in the area could suggest me the best literature on the subject :
I'm looking of a general introduction, and a more in depth focus on the stochastic modelling approach.
Stay Safe :)
"An Introduction to Mathematical Epidemiology" by Maia Martcheva is a recent book that covers many aspects of mathematical epidemiology including SDE with further references.
"An Introduction to Stochastic Processes with Applications to Biology" by Linda J S Allen is becoming a classic text, but it is introductory/intermediate and does not cover much epidemiology.
"Mathematical models in population biology and epidemiology" by Fred Brauer and Carlos Castillo-Chavezis is another classic text but focuses mostly on the dynamics side.
"Mathematical tools for understanding infectious diseases" by Odo Diekmann, Hans Heesterbeek, and Tom Britton is another one that focuses on building up lots of tools and has a little bit of everything.
You could probably start learning these with a year or two of analysis and differential equations. The probability part usually drives the underlying processes but isn't explicitly stated. For example, $x' = dx$ assumes a certain probability distribution in the process of deriving this equation. But in practice, these types of information are used without mentioning the underlying probability/stochastic processes.
I suggest reading some of it to see what approaches interest you the most. Then read up some research articles/monographs for the in-depth parts.