Assignment II (Part II)

Question 1.

Consider the following schematic representation of a system consisting of a two populations, humans

(Host) and mosquitos (Vector), where part of each population is infected and the rest is uninfected

(susceptible).

1. Write down a systems of differential equations to model the dynamics.

Use the following variables:

𝐻𝑠: π‘ˆπ‘›π‘–π‘›π‘“π‘’π‘π‘‘π‘’π‘‘ π»π‘’π‘šπ‘Žπ‘›π‘  (π‘Žπ‘™π‘ π‘œ π‘π‘Žπ‘™π‘™π‘’π‘‘ 𝑠𝑒𝑠𝑐𝑒𝑝𝑑𝑖𝑏𝑙𝑒 β„Žπ‘’π‘šπ‘Žπ‘›π‘ )

𝐻𝐼 : 𝐼𝑛𝑓𝑒𝑐𝑑𝑒𝑑 π»π‘’π‘šπ‘Žπ‘›π‘  (π‘Žπ‘™π‘ π‘œ π‘π‘Žπ‘™π‘™π‘’π‘‘ Host)

𝑀𝑠: π‘ˆπ‘›π‘–π‘›π‘“π‘’π‘π‘‘π‘’π‘‘ π‘€π‘œπ‘ π‘žπ‘’π‘–π‘‘π‘œπ‘  (π‘Žπ‘™π‘ π‘œ π‘π‘Žπ‘™π‘™π‘’π‘‘ 𝑠𝑒𝑠𝑐𝑒𝑝𝑑𝑖𝑏𝑙𝑒 π‘šπ‘œπ‘ π‘žπ‘’π‘–π‘‘π‘œπ‘ )

𝑀𝐼 : 𝐼𝑛𝑓𝑒𝑐𝑑𝑒𝑑 π‘€π‘œπ‘ π‘žπ‘’π‘–π‘‘π‘œπ‘  (π‘Žπ‘™π‘ π‘œ π‘π‘Žπ‘™π‘™π‘’π‘‘ Vector)

π‘Ÿπ‘€π» = π‘‘π‘Ÿπ‘Žπ‘›π‘ π‘šπ‘–π‘ π‘ π‘–π‘œπ‘› π‘Ÿπ‘Žπ‘‘π‘’ 1 = π‘‘π‘Ÿπ‘Žπ‘›π‘ π‘šπ‘–π‘ π‘ π‘–π‘œπ‘› π‘Ÿπ‘Žπ‘‘π‘’ π‘“π‘Ÿπ‘œπ‘š π‘€π‘œπ‘ π‘žπ‘’π‘–π‘‘π‘œ π‘‘π‘œ π»π‘’π‘šπ‘Žπ‘›

π‘Ÿπ»π‘€ = π‘‘π‘Ÿπ‘Žπ‘›π‘ π‘šπ‘–π‘ π‘ π‘–π‘œπ‘› π‘Ÿπ‘Žπ‘‘π‘’ 2 = π‘‘π‘Ÿπ‘Žπ‘›π‘ π‘šπ‘–π‘ π‘ π‘–π‘œπ‘› π‘Ÿπ‘Žπ‘‘π‘’ π‘“π‘Ÿπ‘œπ‘š π»π‘’π‘šπ‘Žπ‘› π‘‘π‘œ π‘€π‘œπ‘ π‘žπ‘’π‘–π‘‘π‘œ

𝛽 = π‘π‘–π‘Ÿπ‘‘β„Ž π‘Ÿπ‘Žπ‘‘π‘’ = π‘€π‘œπ‘ π‘žπ‘’π‘–π‘‘π‘œ π‘π‘–π‘Ÿπ‘‘β„Ž π‘Ÿπ‘Žπ‘‘π‘’

𝛾 = π‘‘π‘’π‘Žπ‘‘β„Ž π‘Ÿπ‘Žπ‘‘π‘’ = π‘€π‘œπ‘ π‘žπ‘’π‘–π‘‘π‘œ π‘‘π‘’π‘Žπ‘‘β„Ž π‘Ÿπ‘Žπ‘‘π‘’

Question 2.

Consider the following schematic representation of the SIR model.

1. Write down a system of differential equations to model the dynamics of the system.

2. Prove the conservation of total population.

3. Give a numerical scheme to estimate the dynamics.

4. Given the initial population, I=4, S=96 and R=0, compute the values at t=1.

Use:

step size Δ𝑑 = 0.2.

Transmission rate=0.001

Recovery rate=0.05

Question 3.

Investigate the Model in http://gabgoh.github.io/COVID/index.html

1. What are the human populations of the model.

2. Draw a diagram (as in the above questions) to depict interactions and the dynamics of the

populations.

3. What is the meaning of 𝑅0 value?

4. Build your own simulation of the model using NetLogo.

For more interesting simulation of Covid-19 see https://towardsdatascience.com/covid19-top-7-online-

interactive-simulations-curated-fa4282889875

Johnson Family Episode 2

Johnson Family Episode 2 Program Transcript

[PHONE BUZZING]

SANDY HARRIS: Hello?

VICKI FRANCIS: Is this Sandy Harris?

SANDY HARRIS: Yes. Yes, it is.

VICKI FRANCIS: I'm Vicki Francis. I'm a nurse at City General. You're with the sexual assault response team, right?

SANDY HARRIS: Yes, I am.

VICKI FRANCIS: Sorry to wake you.

SANDY HARRIS: No, it's fine. What is it?

VICKI FRANCIS: We have a young woman here who says she was raped earlier tonight. Anyway, she's looking for someone to talk to before she goes through a rape kit.

SANDY HARRIS: Yes, yes. Of course.

VICKI FRANCIS: She also says she was pretty intoxicated the time it supposedly happened.

SANDY HARRIS: Supposedly?

VICKI FRANCIS: Well, she had a pretty high BAC when she came in.

SANDY HARRIS: So it's possible she was given a lot of alcohol to drink or GBH, maybe?

VICKI FRANCIS: Given, drank herself, who knows? You know how those frat parties can get, the good ones anyway.

SANDY HARRIS: The good ones, huh? Where can I meet her?

VICKI FRANCIS: She's in a room at the ER. Just check in at the desk. I'll tell them you're coming

SANDY HARRIS: Great. Thank you. Goodbye. Wow. Someone needs a talking to.

Β©2013 Laureate Education, Inc. 1

Johnson Family Episode 2

Johnson Family Episode 2 Additional Content Attribution

MUSIC: Music by Clean Cuts

Original Art and Photography Provided By: Brian Kline and Nico Danks

Β©2013 Laureate Education, Inc. 2

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