(a) On a remote island in the pacific, a new viral infection is spreading among a non-indigenous population of hamsters. The number of newly infected individuals I grows according to dI dt = kol, where ko is a constant and t is measured in days. Since it is suspected that the virus can also infect a native endangered species living on the island, the centre for disease control decides after to days to introduce measures to slow the spread of the virus. After introduction of these measures, I grows according to dI dt where k₁ is a constant and again, t is measured in days. (i) Solve both differential equations assuming I(0) = 1, and I(to) = Io. (ii) Assume that, initially, the number of newly infected hamsters is doubling every 5 days.. introducing the measures, it is halving every 20 days. Determine ko and k₁ in the models above. = 1000 hamsters are infected per day. Comput (iii) The measures are introduced at a point where Io to and round to the nearest day. Also compute how long it takes after introducing the measures un the number of newly infected hamsters drops below 10 per day. Round to the nearest day. = k₁I, If you were not able to determine ko and k₁ in the previous step, you can give your answer depending on ko and k₁.
(a) On a remote island in the pacific, a new viral infection is spreading among a non-indigenous population of hamsters. The number of newly infected individuals I grows according to dI dt = kol, where ko is a constant and t is measured in days. Since it is suspected that the virus can also infect a native endangered species living on the island, the centre for disease control decides after to days to introduce measures to slow the spread of the virus. After introduction of these measures, I grows according to dI dt where k₁ is a constant and again, t is measured in days. (i) Solve both differential equations assuming I(0) = 1, and I(to) = Io. (ii) Assume that, initially, the number of newly infected hamsters is doubling every 5 days.. introducing the measures, it is halving every 20 days. Determine ko and k₁ in the models above. = 1000 hamsters are infected per day. Comput (iii) The measures are introduced at a point where Io to and round to the nearest day. Also compute how long it takes after introducing the measures un the number of newly infected hamsters drops below 10 per day. Round to the nearest day. = k₁I, If you were not able to determine ko and k₁ in the previous step, you can give your answer depending on ko and k₁.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Hi, I have a differential equations question.
Transcribed Image Text:(a) On a remote island in the pacific, a new viral infection is spreading among a non-indigenous population
of hamsters. The number of newly infected individuals I grows according to
dI
dt
= ko I,
where ko is a constant and t is measured in days. Since it is suspected that the virus can also infect a
native endangered species living on the island, the centre for disease control decides after to days to
introduce measures to slow the spread of the virus. After introduction of these measures, I grows
according to
dI
dt
where ki is a constant and again, t is measured in days.
(i) Solve both differential equations assuming I(0) = 1, and I(to) = Io.
(ii) Assume that, initially, the number of newly infected hamsters is doubling every 5 days. After
introducing the measures, it is halving every 20 days. Determine ko and k₁ in the models above.
1000 hamsters are infected per day. Compute
(iii) The measures are introduced at a point where Io
to and round to the nearest day. Also compute how long it takes after introducing the measures until
the number of newly infected hamsters drops below 10 per day. Round to the nearest day.
= k₁I,
=
If you were not able to determine ko and k₁ in the previous step, you can give your answer
depending on ko and k₁.
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