Unformatted text preview: a population can be modelled by I = ( b ( t ) S ( t )-r ( t )) I where S ( t ) is number of people that is susceptible to the disease but not infected yet. I ( t ) is number of people actually infected. b,r are proportional function. Now suppose S ( t ) = e-3 t , b = t 2 , and r = 4 , ﬁnd all solutions. Solution First notice that I ( t ) ≡ 0 is the steady-state solution. Then, to I = dI dt = ( b ( t ) S ( t )-r ( t )) I, divide its both sides by I , multiplying its both sides by dt and taking antiderivative we have Z dI I = Z b ( t ) S ( t )-r ( t ) dt The left side is easy to ﬁnd, Z dI I = ln | I | + C (3) Plug in the given functions, we get the right hand side Z b ( t ) S ( t )-r ( t ) dt = Z t 2 e-3 t-4 dt...
View Full Document
This note was uploaded on 10/04/2011 for the course MAP 4231 taught by Professor Dr.han during the Spring '11 term at UNF.
- Spring '11