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Q49 - Transmission and Recovery Parameters in the SIR Model

Theoretical 2 Real exam question - full text reproduced under IBO's CC BY-NC-SA 4.0 license
Ecology

SIR model was developed by Kermack and McKendrick (1927) to explain dynamics of an infectious diseases. In this model, there are only three subgroups in the population including susceptible, infected, and recovered (S, I, and R respectively). The model assumes that everyone is born susceptible and there is no passive immunity for the infants, everyone who recovers from the disease is immune, the probability of getting the infection is the same for every susceptible person, and people in each group die with their own per capita death rate (mS, mI, and mR). In this model, if a susceptible person contacts with an infected one, infection will be transmitted by probability of A and the rate of recovery is B.

Using the information and data, determine which of the statements are true or which are false.

A. For the disease to remain in the population without adding any new source of infection, A should be at least equal to B.
B. The smaller the minimal infectious dose (the amount of pathogen required to cause an infection), the higher the A is.
C. If the disease is very lethal, it is more likely for it to be self-limited (the epidemic will finish all by itself).
D. If the infection period is longer, a higher proportion of population is infected.
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Question reproduced from IBO 2018, Theoretical Paper 2, licensed under CC BY-NC-SA 4.0 - attributed to the International Biology Olympiad. Open the full exam PDF · Community solutions (unofficial)