18-mo hackathon scenario 5 model

[sabinala]

The stock-and-flow-type model for scenario 5 of the 18-month hackathon (found here: https://github.com/gyorilab/mira/blob/main/notebooks/hackathon_2024.02/scenario5/scenario_5_stockflow.json) has two features which cannot be simulated with TA3 tools. These are (1) delay3i and (2) piecewise (see examples below). These should be implemented using interventions instead. Note that Min and Max are fine.

(1) Rate expression with delay3i:

"rate_expression": "net_fr_fatality*delay3i(into_inf_sym_icu_overflow, delay_for_death, 0)",

(2) Rate expression with piecewise:
"rate_expression": "piecewise((0.0, time >= 0.0), (2.0, time >= 1.0), (1.0, time >= 2.0), (0.0, time >= 3.0), (2.0, time >= 4.0), (1.0, time >= 5.0), (2.0, time >= 6.0), (3.0, time >= 7.0), (6.0, time >= 8.0), (2.0, time >= 9.0), (7.0, time >= 10.0), (10.0, time >= 11.0), (4.0, time >= 12.0), (10.0, time >= 13.0), (5.0, time >= 14.0), (11.0, time >= 15.0), (14.0, time >= 16.0), (14.0, time >= 17.0), (26.0, time >= 18.0), (34.0, time >= 19.0), (35.0, time >= 20.0), (45.0, time >= 21.0), (55.0, time >= 22.0), (38.0, time >= 23.0), (34.0, time >= 24.0), (24.0, time >= 25.0), (40.0, time >= 26.0), (16.0, time >= 27.0), (20.0, time >= 28.0), (12.0, time >= 29.0), (23.0, time >= 30.0), (14.0, time >= 31.0), (8.0, time >= 32.0), (14.0, time >= 33.0), (12.0, time >= 34.0), (5.0, time >= 35.0), (9.0, time >= 36.0), (6.0, time >= 37.0), (0.0, time >= 38.0), (0.0, time >= 39.0), (0.0, time >= 40.0), (0.0, time >= 1000.0))",