A Fatal Infectious Disease Is Introduced into a Growing Population $\frac{d S}{d t}=0.2 S-0.05 \mathrm{SI}, \frac{d I}{d t}=0.2 \mathrm{SI}-0.05 \mathrm{I}$

question 92

Multiple Choice

A fatal infectious disease is introduced into a growing population.Let S denote the number of susceptible people at time t and let I denote the number of infected people at time t.Suppose that, in the absence of the disease, the susceptible population grows at a rate proportional to itself, with constant of proportionality 0.2.People in the infected group die at a rate proportional to the infected population with constant of proportionality 0.05.The rate at which people get infected is proportional to the product of the number of susceptibles and the number of infecteds, with constant of proportionality 0.001.Which of the following systems of differential equations are satisfied by S and I?

• A) \(\frac{d S}{d t}=0.2 S-0.05 \mathrm{SI}, \frac{d I}{d t}=0.2 \mathrm{SI}-0.05 \mathrm{I}\)
• B) \(\frac{d S}{d t}=0.001 S-0.2 S I, \frac{d I}{d t}=0.05 S I-0.0017\)
• C) \(\frac{d S}{d t}=0.2 S-0.001 S I, \frac{d I}{d t}=0.001 \mathrm{SI}-0.05 I\)
• D) \(\frac{d S}{d t}=0.05 S-0.001 S I, \frac{d I}{d t}=0.001 S I-0.2 I\)

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