a Given these assumptions about the fifictitia epidemic, write down the two laws of motion for St and It in terms of St, It, C, p, α, β, γ , and the λs.b What conditions must be true if the populations of infected and uninfected people are in steady state (that is, they do not change over time)?c Assume γ = 0. Interpret this assumption.d Now assume γ >β. Interpret this assumption.e Assuming γ >β, solve for I∗ as a function of C, p, α, β, γ , and the λs. [Hint:As a fifirst step, you should add your two equations from part (b) to derive a relationship between I∗ and S∗.]f How does a change in the price of p affffect the steady-state level of I∗? 14 The SIR-style diagram in Figure 21.8 demonstrates the dynamics of a new diseasecalled fictitia that is sweeping the nation. Fictitia is different from the disease wediagrammed in Section 21.2 in a number of ways:• There is no vaccine for fictitia and no way to recover from it, so there is no recoveredpopulation.● Fictitia renders patients sterile, so the birth rate is proportional to the size of thesusceptible population, not the whole population.• Fortunately, there are some costly self-protective activities h that people can take toavoid contracting fictitia. Their rate of use depends on both the cost of the activitiesp and the prevalence of the disease I,. Specifically, the rate of use h(p,1)=C-ap+yl, for constant C.BirthSusceptibleX StAbSt[31,-h(p.)] StInfectedXa, ItDeathFigure 21.8. The SIR model space for fictitia.S₂4Abst[3,-h(p.)]S,size of the susceptible groupsize of the infected groupnumber of birthsРh(p. l)XdsX,number of infectionsprice of costly self-protective activitiesrate of costly self-protective activitiesdeath rate of susceptible groupdeath rate of infected group

The question asks to write down the laws of motion for the susceptible and infected populations,…

Answered: a Given these assumptions about the…

Human Anatomy & Physiology (11th Edition)

11th Edition

ISBN:9780134580999

Author:Elaine N. Marieb, Katja N. Hoehn

Publisher:Elaine N. Marieb, Katja N. Hoehn

Chapter1: The Human Body: An Orientation

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Problem 1RQ: The correct sequence of levels forming the structural hierarchy is A. (a) organ, organ system,...

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a Given these assumptions about the fifictitia epidemic, write down the two laws of motion for St and It in terms of St, It, C, p, α, β, γ , and the λs.

b What conditions must be true if the populations of infected and uninfected people are in steady state (that is, they do not change over time)?

c Assume γ = 0. Interpret this assumption.

d Now assume γ >β. Interpret this assumption.

e Assuming γ >β, solve for I∗ as a function of C, p, α, β, γ , and the λs. [Hint:As a fifirst step, you should add your two equations from part (b) to derive a relationship between I∗ and S∗.]

f How does a change in the price of p affffect the steady-state level of I∗?

14 The SIR-style diagram in Figure 21.8 demonstrates the dynamics of a new disease
called fictitia that is sweeping the nation. Fictitia is different from the disease we
diagrammed in Section 21.2 in a number of ways:
• There is no vaccine for fictitia and no way to recover from it, so there is no recovered
population.
● Fictitia renders patients sterile, so the birth rate is proportional to the size of the
susceptible population, not the whole population.
• Fortunately, there are some costly self-protective activities h that people can take to
avoid contracting fictitia. Their rate of use depends on both the cost of the activities
p and the prevalence of the disease I,. Specifically, the rate of use h(p,1)=C-ap+
yl, for constant C.
Birth
Susceptible
X St
AbSt
[31,-h(p.)] St
Infected
Xa, It
Death
Figure 21.8. The SIR model space for fictitia.
S₂
4
Abst
[3,-h(p.)]S,
size of the susceptible group
size of the infected group
number of births
Р
h(p. l)
Xds
X,
number of infections
price of costly self-protective activities
rate of costly self-protective activities
death rate of susceptible group
death rate of infected group

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