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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)
Source: Viboud and Chowell (NIH)
Source: Viboud and Chowell (NIH)
Source: Viboud and Chowell (NIH)
Source: Viboud and Chowell (NIH)
Source: Viboud and Chowell (NIH)
Source: Viboud and Chowell (NIH)
Source: Viboud and Chowell (NIH)
Epidemic dynamics (SIR model)
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)
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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