Solving Diff. Equation of Epidemic Model: Help Needed

[madiha.sahar]

I am trying to understand this article at Wikipedia on epidemic deterministic models
http://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology

it is said that if
ds/dt = -b*s(t)*i(t) is divided by dr/dt= ki(t) and is integrated by using chain rule, the answer is S(t) = S(0)exp (-Ro(Rinf - R(0))

but if i solve it, answer i get is r = 1/Ro * lns + c

i have no clue how can i get this answer.

Can anyone help me understand this please.

 

[EnumaElish]

Your solution may well be the inverse of the wiki solution. Ignoring the constant, if s = S(0)exp(-Ro(R - R(0)) then
ln s = ln S0 - Ro r, where r = R - R0.
ln s - ln S0 = -Ro r.
r = -ln(s/S0)/Ro plus a constant. If you normalize to S0 = 1 then r = -ln(s)/Ro + constant. I haven't solved the D.E. but I realized there is a similarity between wiki's and your solution.

 

[madiha.sahar]

I got it :) thanks a bunch!