Simulating the global spread of SARS-CoV-2

Write an ODE metapopulation-type model to describe the global spread of a pathogen like SARS-CoV-2 between countries. You should proceed to the basic mathematical analysis of the model, in order to understand well how model parameters are likely to affect model behaviour.

You will need to decide on the type of model to use: SIR, SLIR (a.k.a. SEIR), SLIAR or something else. You will also need to decide on whether to use an epidemic or an endemic model. Justify your choices.

Then simulate the model with, depending on your computational resources, either a continent or the entire world. Work at the country level. Learn how to pull data regarding country population (see, e.g., this paper and its associated github repo), in order to construct movement using gravity-type weights. (You will also need to find country centroids to incorporate distances between countries.)

Compare the rate of country invasions you obtain (i.e., the number of countries reporting case counts larger than some detection threshold that you will choose) with that observed in real life (see, e.g., Figure 1 here).

Then modify your model to incorporate travel restrictions, both global (acting on all movement rates at the same time) or local (acting on some movement rates).

It could be interesting to consider also the continuous time Markov chain analogue of your model. You could also consider a network model.