Modelling the spread of a disease in an epidemic through a country divided into geographical regions

The SIR (susceptible-infectious-recovered) model is a well known method for predicting the number of people (or animals) in a population who become infected by and then recover from a disease. The model can be extended to include other categories, such as carriers who are infected with the disease but unaware that they are infected, or those who die from the disease. In addition, the model can be adapted to model the spread of a disease through a country or state that is divided into a number of geographical regions. The results presented here show that considering the population density in each region, rather than just the population of each region, produces a more accurate simulation of how the disease spreads. This paper also investigates how changing certain parameters in the model, such as the number of people who travel between the regions, affects how rapidly the disease spreads to different regions.