Travel restrictions model

The main engine or the core of the model is know as a Markov chain. It's a way of defining events on a time line based on probabilities. By simulating the chain you can unroll a possible outcome of the chain of events. The epidemic might errupt or die out.

When the computer picks events to perform it's like throwing darts at a checker board where the sizes of the squares are proportional to the prababilites in question. 3 events for each municipality, so the are 289x3 squares to throw at.

The procedure runs as follows. First you pick an "event". An event is the transition of one individual to the next state with the probability as we mentioned. There are 289 municipalies and 3 events possible events for each. In other words about 900 possible events to decide upon. The Markov chains way of picking one of these is analagous to thowing darts at a checker board where the size of each square was proportional to the probability.

The time distribution curves look like slopes which are steep at first, the gentle. It's what's called an exponential distribution. It signifies that you are likely pick shorter times than longer. The more event queuing up, the steeper the curve.

Once picked, we want to know when it's supposed to occur, at what time. In a Markov chain, times are described by an exponential distribution. You can see it in the figure on the previous page. The graph means that short time intervals are more probable than longer. Throwing a dice will tell you where on the curve the time interval is picked. The slope of the curve is controled by the sum of probabilities, the size of the checker board if you will. So the more events you have stacking up, the steeper the curve and the shorter the time interval. This makes sense since the if you have alot of things waiting to occur, then the time between them is bound to be short, whereas if dormant events are spread out in time. So the Markov chain describes events occuring rather slow at first, then picking up speed as time progresses. Exactly like an epidemic. Once more and more become infectious, events describing transitions from susceptible to latent start queuing up, in the community where the infectous are as well as those connected to it by the travel network. Things will start to pick up.