Ebola: how culture & politics have combined to allow mathematics to drive the epidemic.  Three parameters, amongst several, influence the dynamics of contagion: 
      (1) incubation period, which determines how far an infected individual can travel symptom-free before succumbing.  (Ebola: 1-3 weeks)  
     (2) shedding period, or how long an infected individual can pass on the infection to others.  (Ebola: from first symptoms to even after death.)  
     (3) fatality rate, or the likelihood of death once the infection has been contracted. (Ebola: greater than 60%, up to 90%.) 

For Ebola, these three parameters mean a plague that is capable of out-running the limited infrastructure that has currently been mobilised against it.

This sobering article reviews the rise of the current outbreak of Ebola, and how geography, culture, and politics combined to set the stage for a potential nightmare scenario.

Update: 2019-08-12: Five years after the last major epidemic of Ebola in 2014, scientists believe they now have drugs that can cure ebola. 


References:

[1] How Ebola Sped out of Control, Washington Post, 4 Oct, 2014
http://www.washingtonpost.com/sf/national/2014/10/04/how-ebola-sped-out-of-control/

[2] The Ominous Math of the Ebola Epidemic, Washington Post, 9 Oct, 2014
http://www.washingtonpost.com/national/health-science/the-ominous-math-of-the-ebola-epidemic/2014/10/09/3cad9e76-4fb2-11e4-8c24-487e92bc997b_story.html

[3] Ebola now Curable, 12 Aug, 2019, The Guardian
https://www.theguardian.com/world/2019/aug/12/ebola-now-curable-after-trials-of-drugs-in-drc-say-scientists