Editing Basic reproduction number (section)

==Effective reproduction number==
[[File:R number – the rate of infection; a government video.webm|thumb|An explanation of the <math>R</math> number in simple terms from the [[Welsh Government]].]]
In reality, varying proportions of the population are immune to any given disease at any given time. To account for this, the '''effective reproduction number''' <math>R_e</math> or <math>R</math> is used. <math>R_t</math> is the average number of new infections caused by a single infected individual at time ''t'' in the partially susceptible population. It can be found by multiplying <math>R_0</math> by the fraction ''S'' of the population that is susceptible. When the fraction of the population that is immune increases (i. e. the susceptible population ''S'' decreases) so much that <math>R_e</math> drops below 1, [[herd immunity]] has been achieved and the number of cases occurring in the population will gradually decrease to zero.<ref name="pmid15627236">{{cite journal | vauthors = Garnett GP | title = Role of herd immunity in determining the effect of vaccines against sexually transmitted disease | journal = The Journal of Infectious Diseases | volume = 191 | issue = Suppl 1 | pages = S97-106 | date = February 2005 | pmid = 15627236 | doi = 10.1086/425271 | doi-access = free }}</ref><ref name="pmid24175217">{{cite journal | vauthors = Rodpothong P, Auewarakul P | title = Viral evolution and transmission effectiveness | journal = World Journal of Virology | volume = 1 | issue = 5 | pages = 131–4 | date = October 2012 | pmid = 24175217 | pmc = 3782273 | doi = 10.5501/wjv.v1.i5.131 | doi-access = free }}</ref><ref name="dabmago">{{cite book| vauthors = Dabbaghian V, Mago VK |date=2013|title=Theories and Simulations of Complex Social Systems|url=https://books.google.com/books?id=AdLBBAAAQBAJ&pg=PA134|publisher=Springer|pages=134–35|isbn=978-3642391491|access-date=29 March 2015}}</ref>