Write the equations and sketch the diagram of a SIR model where:

i) natural births and deaths are taken into account, ii) being cured provides immunity,

iii) one can die from this disease,

iv) on average, people are sick (infectious) for ten weeks. Introduce parameters as necessary and explain what each parameter represents.

b) We will now introduce quarantining in this model using the following information: i) a fraction g of the infected people go into this new state of quarantine per unit of time,

ii) people stay in quarantine on average for 3 weeks, iii) people in quarantine die at the same rate as infected people.