Vaccination and population dynamics of an epidemic
I think it does make sense - with a population density for finland that is so low, the disease with such a low beta cannot communicate to enough people to propagate. 

The number of people who have this disease will be fewer each week.  I think this makes sense because at 16 / km^2, you can expect that practically nobody will ever see each other.  

This is a flawed model though because it assumes that the mean density is uniform.  In a city like Helsinki (2,800 / km^2) you would expect the disease to get caught by nearly everyone in just a week.  

Helsinki: n = 94.5%

In Lapland (which has a population density of less than 2/km^2) , the transmission rate (beta) of 0.0015 translates to 0.003 incidents per week.  This is not a terribly catchy disease, you probably have to kiss someone, wear their clothes, or eat off their plate to get it. With only 2 people per km^2 the chances of this happening appear to be poor, though even here families tend to get the disease and the model breaks down. 

So to sum up, the model is consistent within itself, BUT it is a baby model and makes some broad assumptions that do not help it describe the dynamics of the disease in a national scope or in a highly detailed scope.  It probably describes the chances balls will collide in a box as well as disease spreading.