Modeling the pandemic is a critical problem. A good model should help us better understand how it is growing and also how it may end. This is a "system dynamics" problem.
I'm sure those doing the models have some sophisticated tools. They are probably using some form of system dynamics. However, to my understanding, there is no formal standard for the modeling language and tools.
System dynamics has been around for many years. You can learn more about it in a book described at http://web.mit.edu/jsterman/www/BusDyn2.html You will find examples of similar but more limited social systems.
The basic concept is that things flow from sources through stocks and more flows with feedback loops. The flow rates, feedback loops and stock levels are determined by statistical formulas and the dynamic evolution of the system is analyzed over a period of time.
I have included a rather simple model of the public mental health system in Michigan, below, that likely is similar for other states.
This is over-simplified, but demonstrates the general concept.
There is a need for a modeling language standard so that more people can develop and share expertise, and models can be shared, but, more importantly, so that parts of models, the data and the formulas can be more readily shared, and so that the basic modeling techniques can be refined and extended, potentially to support networks of distributed, contributing components.
Many who read this may be familiar with the Object Management Group (OMG), and the development of specifications for computer-based modeling languages. I am co-chair of the Business Modeling and Integration task force, and have considered the possibility of a system dynamics modeling initiative, but I have not sparked much interest among those who would build or buy modeling tools that would implement such a standard. Maybe the time is now.
The scope of a pandemic model could be very large since there are many stocks and flows, or simpler systems (more like the example, above) can generalize stocks, such as patients in all hospitals, or in a region, as consolidated stocks.
At the same time, the statistical formulas should support statistical probability ranges, so that we can analyze the best, worse and most likely changes under different circumstances, and understand the key points at which the growth might be most effectively mitigated and the recovery might be more graceful.
Similar models must be applied to the economy as it is affected by the pandemic, ways to mitigate the adverse consequences as the pandemic grows and wanes, and the measures to gracefully compensate both as the pandemic grows and as we recover.
While I am sure there are models, they tend to be focused on narrower interests, particularly business and financial interests. Development of pandemic models would also surface additional economic, social and healthcare factors that may help mitigate the impact on many people who may otherwise be overlooked. In addition, in the long run, it may enable us to better improve our economic and healthcare systems to avoid and mitigate the consequences of future pandemics.