R-nought - 2024 ACF Regionals @ Cornell

Question

The inverse of this value is used to calculate the proportion of a population that is susceptible when a disease is at endemic equilibrium in the SIR model. For 10 points each:

[10m] Give this value, which represents the expected number of cases directly generated by one case of an infection in a fully susceptible population.

ANSWER: R-nought [or R0; or R-sub-zero; or basic reproduction number]

[10e] The calculation “one minus one-over-R-nought” is used to find the threshold of this kind of immunity, the proportion of a population that must be immune to prevent spread. A highly vaccinated population grants this kind of indirect immunity.

ANSWER: herd immunity

[10h] The calculation of herd immunity relies on this assumption, which classically does not hold for the common cold or STIs. The SIR model makes this assumption while the SIS model does not.

ANSWER: recovered individuals are immune to catching the disease [or recovered individuals are not susceptible; or no reinfection; or equivalents]

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Summary


2024 ACF Regionals @ Cornell	01/27/2024	Y	3	23.33	100%	100%	33%
2024 ACF Regionals @ JMU	01/27/2024	Y	9	17.78	100%	22%	56%
2024 ACF Regionals @ Minnesota	01/27/2024	Y	2	25.00	100%	100%	50%
2024 ACF Regionals @ Nebraska	01/27/2024	Y	5	14.00	80%	40%	20%
2024 ACF Regionals @ Ohio State	01/27/2024	Y	3	16.67	100%	67%	0%
2024 ACF Regionals @ Rutgers	01/27/2024	Y	5	18.00	100%	40%	40%
2024 ACF Regionals @ Imperial	01/27/2024	Y	8	16.25	100%	25%	38%
2024 ACF Regionals @ Vanderbilt	01/27/2024	Y	5	14.00	100%	20%	20%

Data


Cornell B	RIT A	10	10	10	30
Cornell C	Binghamton	10	10	0	20
Cornell A	RIT B	10	10	0	20