How to read the surface plots?

Question

I was reading this paper and I could not understand this figure. How do you read these kind of graphs? How to interpret the twists and folds; it's not like heat maps that are intuitive. Any help would be appreciated.

Answer 1

The first thing to realize is that what you are interpreting as "twists and folds" is really just an artifact of the way the plot was generated. Given greater resolution. The plot frame is cut off vertically at what looks to be about $R_{0} = 17$, and those three sharp corners that you see are right at that line, so nothing above them will show up - hence the appearance of "twists and folds." In reality, I suspect that if the plot was drawn a bit differently so that it extended above $R_{0} = 17$ it would look like a square piece of paper being lifted up along the diagonal.

As for the interpretation, in this paper $\mu$ is the disease-related death rate, $\beta$ is the transmission rate between infected and healthy (resistant) individuals, and $R_{0}$ is the basic reproduction number - i.e. the average number of secondary infections one infected individual will incur on a susceptible population. What the graph is saying is that $\mu > \beta$, i.e. the disease is killing people faster than they are spreading it, then $R_{0}$ is small, but when $\beta > \mu$, i.e. the disease spreads faster than it kills people, then $R_{0}$ is large.