# Mathematics On January 10 December 2021, 100 students attend a legal rave in Mumbai. While having fun, but unbeknownst to them, 10 of the participants had

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On January 10 December 2021, 100 students attend a legal rave in Mumbai. While having fun, but unbeknownst to them, 10 of the participants had just been exposed (and cannot transmit yet) to COVID-19, while other 10 are already infectious (and can transmit further). The infection starts to spread in the City according to the following model

We here assume equal birth and death rates, and the parameter values N = 250, 000, a = 1/14, β = 8 and γ = TR/TC and m = TD/TC (in the notations from the below Table).

 Total Cases (TC) Total Deaths (TD) Total Recovered (TR) Active Cases (AC) Serious Critical (SC) 3,316,019 87,295 1,503,654 1,725,070 3,672

Table : Coronavirus information

· Solve the problem numerically (you may use a built-in routine) and discuss the dynamics of the population compartments (S, E, I, R) if the conditions stay the same.

· Estimate in how many days will the 30 beds available in the (ICU) at the Hospital be filled. Discuss the emergency budget required to order extra beds at £200k/unit, to accommodate all ICU patients at the peak.

· Discuss some actions for “flattening the curve” and model their impact.

Hint. Relate to the model parameters and discuss the role played by R0.

· Formulate and discuss (briefly) two extensions of the model, which consider other realistic features (vaccination, mutations of the virus (delta, omicron), reinfection, etc). Hint. The evaluation checks the model description, equations, simulations, analysis.

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