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May 22nd, 2019, 10:54 AM  #1 
Newbie Joined: May 2019 From: Romania Posts: 3 Thanks: 0  Elements of game theory
The federal government desires to inoculate its citizens against a certain flu virus. The virus has two strains, and the proportions in which the two strains occur in the virus population are not known. Two vaccines have been developed. Vaccine 1 is 85% effective against strain 1 and 70% effective against strain 2. Vaccine 2 is 60% effective against strain 1 and 90% effective against strain 2. What inoculation policy should the government adopt? 
May 22nd, 2019, 01:42 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,770 Thanks: 700 
Use both?

May 22nd, 2019, 01:58 PM  #3  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,205 Thanks: 901 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Either way we have the equations: $\displaystyle V_1 = (1  0.85) s_1 + (1  0.70) s_2$ $\displaystyle V_2 = (1  0.60) s_1 + (1  0.90) s_2$ Where we wish to minimize $\displaystyle s_1 + s_2$. I need someone to check my logic here. Is this the correct setup? Dan  
May 22nd, 2019, 02:15 PM  #4 
Member Joined: Oct 2018 From: USA Posts: 78 Thanks: 54 Math Focus: Algebraic Geometry 
I know nothing of Game Theory either but just as an intuition V1 : $(10.85)+(10.7) = 0.45$ V2: $(10.6)+(10.9) = 0.5$ Since $0.45 < 0.5$ vaccine 1 is more effective.....? Could be wrong but it seems reasonable. 

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