2. Vaccines make is possible to prevent epidemics. If individuals are vaccinated, then the cannot catch...

 

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2. Vaccines make is possible to prevent epidemics. If individuals are vaccinated, then the cannot catch the disease, even if they come in direct contact with an infected individual. However, the time it take to develop a vaccine may make it impossible to vaccinate everyone in a population before a disease arrives. (a) For the SIR model, which initial conditions guarantee that I'(t) < 0? HINT: Your answer should be in terms of the parameters a and 3. (b) For given values of a and 3, what fraction of a population must be vaccinated before a disease arrives in order to prevent an epidemic? 2. Vaccines make is possible to prevent epidemics. If individuals are vaccinated, then the cannot catch the disease, even if they come in direct contact with an infected individual. However, the time it take to develop a vaccine may make it impossible to vaccinate everyone in a population before a disease arrives. (a) For the SIR model, which initial conditions guarantee that I'(t) < 0? HINT: Your answer should be in terms of the parameters a and 3. (b) For given values of a and 3, what fraction of a population must be vaccinated before a disease arrives in order to prevent an epidemic?

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