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Information about epidemics

Published on October 5, 2007

Author: Nathaniel

Source: authorstream.com

News Travels Fast!:  News Travels Fast! The Maths Behind Epidemics Gossip!:  Gossip! Imagine you hear a bit of gossip! You tell it to only a few people, “Don’t tell anyone you say”, but… They do tell some people, but only a few!... …and so on… How many people know by the end of the day? Example:  Example You tell 2 your news at 9:00am Within 30 minutes each of these people have told 2 other people Who then each tell 2 others This continues till the end of school at 3:00pm How many people know at home time? Example:  Example 8:30am – 1 person knows 9:00am – 3 people know (1 + 2) 9:30am – 7 people know (1 + 2 + 4) 10:00am – 15 people know (1 + 2 + 4 + 8) 10:30am – 31 people know (1 + 2 + 4 + 8 +16) … 3:00pm – 1 + 2 + 4 + 8 + 16 + … + 211 + 212 + 213 = 16383!!! The Spread Factor:  The Spread Factor The single most important number in epidemics! How many people each person tells – in this case the spread factor was 2 If instead each person had told 3 other people then by home-time 2,391,484 people would know!!!! The Spread Factor:  The Spread Factor Spread Factor = 3 – 2,391,484 Spread Factor = 2 – 16,383 Spread Factor = 1 – 13 What about a spread factor less than 1? The Spread Factor:  The Spread Factor Spread Factor = ½ Does this mean I only tell ½ a person? No, it means that only ½ of the people that are told go on to tell someone else. With a spread Factor = ½ at home-time we can expect that only 2 people know including you! (1 + (½) + (½)2 + (½)3 + …) Diseases:  Diseases The same is true for Diseases – each disease has it’s own spread factor Epidemics will have spread factors greater then 1 The higher the spread factor, the more contagious the disease! If we can get the spread factor to less than 1 then the disease will die away – how? Same is also true for computer viruses!! Different Diseases:  Different Diseases

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