On December 28th 2021, 110 students attend a legal rave in Mumbai. While having fun, but unbeknownst to them, 12 of the participants had just been exposed (and can not transmit yet) to COVID-19, while other 12 are already infectious (and can transmit further). The infection starts to spread in the City according to the following model

where t represents time (1 unit = 1 day), and the parameters are

We here assume equal birth and death rates, and the parameter values N = 350, 000, a = 1/14, β = 10 and γ = TR/TC and m = TD/TC (in the notations from the below table)

1. Solve the problem numerically and discuss the dynamics of the population compartments (S, E, I, R) if the conditions stay the same. 
2. Estimate in how many days will the 30 beds available in the ICU at Hospital be filled. Discuss the emergency budget required to order extra beds at $300k/unit, to accommodate all ICU patients at the peak.
3. Discuss some actions for “flattening the curve” and model their impact.

ds dt dE dt dl dt dR dt =bN - mS BIS N BIS N - (m + a)E = aE - (y + m)I =yl-mR, (Susceptible) (Exposed) (Infected) (Recovered)