Calculate d r / d τ by the chain rule, and then check your result by expressing r in terms of τ and differentiating. r = i + 3 t 3 / 2 j + t k ; t = 1 / τ
Calculate d r / d τ by the chain rule, and then check your result by expressing r in terms of τ and differentiating. r = i + 3 t 3 / 2 j + t k ; t = 1 / τ
Calculate
d
r
/
d
τ
by the chain rule, and then check your result by expressing r in terms of
τ
and differentiating.
r
=
i
+
3
t
3
/
2
j
+
t
k
;
t
=
1
/
τ
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
Imagine that we can quarantine infected members of the population, so that they are unable to transmit the disease to others. Let q represent the fraction of the infected population which is quarantined, and let 1-q represent the fraction of the infected population that is not quarantined and can transmit the disease to the susceptible individuals. (Please use google sheets)
a. Rewrite the difference equation for S[t+1] and I[t+1] (from question 1), to incorporate the effects of quarantine. (Hint: quarantine should affect the term representing the proportion of susceptible individuals who are interacting with infected each time step)
b. In the model you developed for question 1 implement the fraction of quarantined people by adding (1-q) to the equations for S and I. Show what happens for a quarantine percentage of 50%, meaning that 50% of infectious people are in quarantine and cannot interact with the susceptible. What can you tell about the impact of quarantine.
University Calculus: Early Transcendentals (4th Edition)
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