Thursday, July 23, 2009 the swine flu should roll out, and back again

so the beeb reports 100,000 people have h1n1, mainly in under 14s.

Schools finished last friday, i.e. 6 days ago, and in the younger age group, people are infections for 2 days more (7 days), and shed virus thru skin (i.e. touching) - assume most these kids are in families of 4 on average, one would expect all those in the family to be infected during this period too (but not necessarily displaying symptoms just yet), which means an underestimate by *4 - i.e. 400,000. assume most these people are infected last weekend (when kids came home from school and socialised most) and then went to work as normal monday - they would infect (but with lower probability) a fraction of the people they socialise with (on average a person's social group is 150 - this is in physical world, people in family, friends and colleagues) - say per day they infect 1% - i.e 1 person - by end of the week (tomorrow) you'd expect to see the number grow * 7 - ie. 2.8M. This weekend, the rest of the family (except the, curiously, and luckily, mainly immune grannies and grandpas) get it and nex week, those 2.8M infect around 7* more, i.e. 21M

so I'd predict the epidemic peaks with 1/2 the population infected by mid august, but then as everyone who's had i is now immune (we hope) form re-infection, the faction still infectious is decreasing, and the faction not yet infected is decreasing, so the rate should fall fairly fast til september...

that's my 2 cents.

oh, background - i'm using handwavy approcximation to the SIR model (good for pandemics over large numbers) - see
wikipedia entry for SIR for more details

dI = [ beta * I * S ] - [R * I]

where beta is contact rate (we meet that many people a day)
I is number infected so far
and S is susecptability
and R is recover rate

so in discrete terms, with a 1 day step
taking beta as 4 and S as 1/3
and R 1/4 (recovery time as 7 days)
I grows at nearly doubling per day until we hit about 1/2... as per above
and this then starts to fall....

No comments: