Epidemics Pedro Ribeiro de Andrade Gilberto Câmara

Epidemic “In epidemiology, an epidemic occurs when new cases of a certain disease, in a given human population, and during a given period, substantially exceed what is expected based on recent experience.”

Source: Viboud and Chowell (NIH)

Epidemic dynamics (SIR model)

S(t) is used to represent the number of individuals not yet infected with the disease at time t I(t) denotes the number of individuals who have been infected with the disease and are capable of spreading the disease to those in the susceptible category. R(t) is the compartment used for those individuals who have been infected and then recovered from the disease. Those in this category are not able to be infected again or to transmit the infection to others.

Source: Viboud and Chowell (NIH)

SIR model

SIR model in discrete time

Parameter calculation

Source: Viboud and Chowell (NIH)

Epidemic dynamics (SIR model)  Stocks: susceptible, infected, and recovered  Initial stocks: susceptible = 999, infected = 1  Infectious period = 4 days  Run time = 100 days  Each infected contacts 1 other people each day  40% of the contacts cause infection