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:
π»π : ππππππππ‘ππ π»π’ππππ (πππ π ππππππ π π’π ππππ‘ππππ βπ’ππππ )
π»πΌ : πΌπππππ‘ππ π»π’ππππ (πππ π ππππππ Host)
ππ : ππππππππ‘ππ πππ ππ’ππ‘ππ (πππ π ππππππ π π’π ππππ‘ππππ πππ ππ’ππ‘ππ )
ππΌ : πΌπππππ‘ππ πππ ππ’ππ‘ππ (πππ π ππππππ Vector)
πππ» = π‘ππππ πππ π πππ πππ‘π 1 = π‘ππππ πππ π πππ πππ‘π ππππ πππ ππ’ππ‘π π‘π π»π’πππ
ππ»π = π‘ππππ πππ π πππ πππ‘π 2 = π‘ππππ πππ π πππ πππ‘π ππππ π»π’πππ π‘π πππ ππ’ππ‘π
π½ = ππππ‘β πππ‘π = πππ ππ’ππ‘π ππππ‘β πππ‘π
πΎ = ππππ‘β πππ‘π = πππ ππ’ππ‘π ππππ‘β πππ‘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 Ξπ‘ = 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 π 0 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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