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Epidemic
This problem treats evolution of epidemic in a cohort. To introduce the model equations, it is easiest to
consider a closed population without births, deaths, migration or other variations in total population.
The scenario in mind is a large population into which a low level of infectious agent is introduced and
where the resulting epidemic occurs sufficiently quickly that demographic processes are not influenced.
The population is then divided into classes of Susceptibles, Infected and Recovered (SIR). For each class.
where B and 1/y are constants that determine the infection transmission rate and infectious period
respectively. Epidemiologists typically do not write the equation for R because S+1+Rz 100%, hence
knowing S and I allow calculating R. These equations have the initial conditions S(0)>0, (O)>0 and R(0)-0.
2.1 Plot in the same graph the three populations with βΞ1Ύ:5 and in time interval [0, 1] (you may need
to change the interval to see all interesting points).Assume the initial condition 1(0)-1.
2.2 After what time is the population of infected and recovered the same? You may use the Matlab
function deval to find the answer.
2.3 What is the maximum percentage of infected population?
2.4 Epidemic may or may not spread to wide population depending on the amount of introduced
infectious agent i.e. I(0) and the reproductive ratio defined as Ro-B/y. Investigate what happens
when the fraction of susceptibles is below and above the threshold 1/Ro. Can you tell what fraction
of infected people it is necessary to put in quarantine to prevent spreading a disease?