Math of Planet Earth 2013, in addition to dealing with the Earth itself (climate, earthquakes, etc.) also deals with the biosphere and humanity’s relationship to it. Certainly the progression and propagation of infectious diseases is an important part of this. Two articles, written for a general audience, provide two examples from the applied mathematics literature that show how mathematics is used to model and understand the progression and propagation of certain kinds of infections.

**The first article** analyzes early viral dynamics in HIV infections with the goal of ultimately better understanding treatment and prevention strategies.

**The second article** also applied to HIV infections, dealing with “viral blips” — episodes of high viral production interspersed by periods of relative quiescence. These quiescent or silent stages are hard to study with experimental models. The article explores how certain mathematical models and analysis can help our understanding.

Both articles are based upon recent papers that appeared in the **SIAM Journal on Applied Mathematics**.