Simulation Assignment - PDF Attached

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: 𝑈𝑛𝑖𝑛𝑓𝑒𝑐𝑡𝑒𝑑 𝐻𝑢𝑚𝑎𝑛𝑠 (𝑎𝑙𝑠𝑜 𝑐𝑎𝑙𝑙𝑒𝑑 𝑠𝑢𝑠𝑐𝑒𝑝𝑡𝑖𝑏𝑙𝑒 ℎ𝑢𝑚𝑎𝑛𝑠)

𝐻𝐼 : 𝐼𝑛𝑓𝑒𝑐𝑡𝑒𝑑 𝐻𝑢𝑚𝑎𝑛𝑠 (𝑎𝑙𝑠𝑜 𝑐𝑎𝑙𝑙𝑒𝑑 Host)

𝑀𝑠: 𝑈𝑛𝑖𝑛𝑓𝑒𝑐𝑡𝑒𝑑 𝑀𝑜𝑠𝑞𝑢𝑖𝑡𝑜𝑠 (𝑎𝑙𝑠𝑜 𝑐𝑎𝑙𝑙𝑒𝑑 𝑠𝑢𝑠𝑐𝑒𝑝𝑡𝑖𝑏𝑙𝑒 𝑚𝑜𝑠𝑞𝑢𝑖𝑡𝑜𝑠)

𝑀𝐼 : 𝐼𝑛𝑓𝑒𝑐𝑡𝑒𝑑 𝑀𝑜𝑠𝑞𝑢𝑖𝑡𝑜𝑠 (𝑎𝑙𝑠𝑜 𝑐𝑎𝑙𝑙𝑒𝑑 Vector)

𝑟𝑀𝐻 = 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 1 = 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝑓𝑟𝑜𝑚 𝑀𝑜𝑠𝑞𝑢𝑖𝑡𝑜 𝑡𝑜 𝐻𝑢𝑚𝑎𝑛

𝑟𝐻𝑀 = 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 2 = 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝑓𝑟𝑜𝑚 𝐻𝑢𝑚𝑎𝑛 𝑡𝑜 𝑀𝑜𝑠𝑞𝑢𝑖𝑡𝑜

𝛽 = 𝑏𝑖𝑟𝑡ℎ 𝑟𝑎𝑡𝑒 = 𝑀𝑜𝑠𝑞𝑢𝑖𝑡𝑜 𝑏𝑖𝑟𝑡ℎ 𝑟𝑎𝑡𝑒

𝛾 = 𝑑𝑒𝑎𝑡ℎ 𝑟𝑎𝑡𝑒 = 𝑀𝑜𝑠𝑞𝑢𝑖𝑡𝑜 𝑑𝑒𝑎𝑡ℎ 𝑟𝑎𝑡𝑒

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 Δ𝑡 = 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