Suppose a population of size N is exposed to a contagious disease. If t is the t

Question

Suppose a population of size N is exposed to a contagious disease. If t is the time in days and y is the number of individuals infected at time t, then

y=N1+(N1)ekt, where k is the infection rate. The maximum infection rate occurs at time tm=ln(N1)k.

An island has a native population of 3119, and a sailor from a visiting ship introduces a disease which has an infection rate of

k=0.27. Complete parts a through d.

Suppose a population of size N is exposed to a contagious disease. If t is the time in days and y is the number of individuals infected at time t, then In (N 1 where k is the infection rate. The maximum infection rate occurs at time tm 1 (N-1) An island has a native population of 3119, and a sailor from a visiting ship introduces a disease which has an infection rate of k 0.27. Complete parts a through d. a. Write an equation for the number of natives who remain uninfected. Let z represent the number of uninfected natives

Explanation / Answer

Z is the number of uninfected natives where as y is the no of infected people..

now at a particular time t if y number of natives are infected then the number of uninfected natives are

z = N - y where N is the total number of natives

z = N - N/(1+(N-1)e^(-kt))

=> = N(1+(N-1)e^(-kt) -1)/(1+(N-1)e^(-kt))

=> = N(N-1)e^(-kt)/(1+(N-1)e^(-kt)) = z

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