Question

Problem 4.2: An outbreak of African swine fever, a highly contagious disease that's been called "pig Ebola," is ravaging Asia's pig industry with no signs of letting up. The reality is that a pig, if contracting the "Ebola virus", will die. Please do my hypothetical problem: A pig is diagnosed to have contracted Po pig Ebola virus at time t = 0 and these viruses "multiply" subsequently according P' = -aP(M – P) where P(t) is #viruses at time t while a > 0 and M>0 are constants. The pig will die when P(t) → 0. If P > M, the Pig's prognosis, i.e., the time Tpit has left to live, is short. Derive a formula for Tp and for given Po = 1000, M = 100, a = 0.001. Compute the value of Tp.

Answer 1

Salution: Given that p': - PM-P) Plt) - viguses at time t where aro and mxo are constant pig will will die when Plt) a of 5 - Aplm-P) = a (P²_pm) = aplp-m) de adt PCP- m =adt => de p²pm+m2 m² ata I cp-m} m2. Jadt tan a net prm = - dp = m se rodo

s m² sec? odo at (tana)? (m 2 » r m setodo = 2 sdo at (99)? segon 7+70 = out a 7+ you =0(= we have - P- m 2 = m/ tano - tano = 2 (P-M » o = tant ( 22 ) so solution is tan' (21-1)= mat + c = 2p -1 = tan (matt) -> 26 = 1+zan (matt) mdt - l = tan 2 4C

- P(-12= 7 [cittan (mat+c] PCO) = (1+tano ) - Po →ittance Pro > tarc = 220- > c= tanil 20-1) Pig dies when Plt) 00 and this happens only when tan (mg t40):20 - mat + c = 1/2 >> met nec > toma -o) This the time left foor death of pig de Tp » Toba (-o

while Pc = 1000, M: 100, a01001, Value of -103 TP 2 31-0) = 20 (c) Joo 10 catan' ( 2 P 12- tan(2x loge is 100 = tant! (20-12 - zanillo So, Tp = 2001 - tan' (197) = 20 ( 3.14 -1,518) = 20 x0'05258 = 20 x 5,258 x62 = 105'16x16 2 = 1:05 16 TP : o s 18 . Thank you