Multi-scale mathematical models have emerged as potent tools in understanding the complex dynamics of malaria transmission. Such models can be constructed in two ways, primarily. First, a single integrated model can be developed that encompasses one or more scales directly, from the molecular interactions of the parasite with its human and mosquito hosts, up to the population dynamics of disease spread. This approach offers the advantage of a unified framework that can capture direct interactions between different scales. However, it often faces challenges related to computational complexity and the integration of disparate data types. Alternatively, one can build
a collection of models, each dedicated to a specific scale, and then link these models to address overarching questions that span multiple scales. This modular approach facilitates focused refinement at each scale and can be computationally more manageable. However, ensuring consistent and meaningful communication between the individual scale models can be intricate.

I have been studying both methodologies, with their respective advantages and drawbacks, and how they have provided valuable insights into malaria dynamics, highlighting the versatility and adaptability of multi-scale modeling techniques. In my opinion here is the ABS of multiscale modeling:

• Asimovian: «In the year 12,067 of the Galactic Era (G.E.), Hari Seldon, mathematician and psychologist, developed psychohistory, a new field of science that allows the prediction of future events through accurate modeling based on sociology, psychology, mathematics and statistics.» Premise behind Isaac Asimov’s “Foundation”, 1951 (-18 G.E.) The Asimovian approach is to include sociocultural factors into modeling, in addition to the traditional approaches.
• Boxian: «Since all models are wrong… simple but evocative models are the signature of the great scientist.» Box, George E. P. (1976), “Science and statistics”, Journal of the American Statistical Association, 71 (356): 791–799. The Boxian approach is to make models as simple as possible, yet insightful.
• Coxian: «The idea that complex physical, biological or sociological systems can be exactly described by a few formulae is patently absurd.» Cox, David. R. (1995), “Comment on “Model uncertainty, data mining and statistical inference””, Journal of the Royal Statistical Society, Series A, 158: 455–456. The Coxian approach is to include more complexity into models.

I am personally inclined to follow the Asimovian approach. That is, you must absolutely include sociocultural factors into multiscale modeling. Making this statement is easy, but following through… that is where the rubber meets the road. I have developed a few approaches to do this, but it is the subject of another post.