Question

formula 3 points
there are about 781 susceptible people living in an isolated community. individual who catches an novel disease stay sick for about 1.6 days, and you estimate the chance an infected individual will pass the disease to a susceptible they meet is 0.0002. what is ( r_0 ) for this disease? use 2 decimal places only, without units. wrong entries wont be corrected.
remember that: ( r_0 = s\beta l ) or ( r_0 = s\beta / v )
also: ( l = 1/v ), and ( v = 1/l )
answer

Explanation:

Step1: Identify variables

We know:

• \( S = 781 \) (number of susceptible individuals)
• \( \beta = 0.0002 \) (transmission probability per contact)
• Duration of illness \( D = 1.6 \) days, so \( L = 1.6 \) (length of infectious period), and \( v=\frac{1}{L}=\frac{1}{1.6}=0.625 \) (recovery rate, reciprocal of infectious period)

Step2: Use formula \( R_0 = \frac{S\beta}{v} \)

Substitute the values:
\( S = 781 \), \( \beta = 0.0002 \), \( v = 0.625 \)
\( R_0=\frac{781\times0.0002}{0.625} \)

Step3: Calculate numerator

\( 781\times0.0002 = 0.1562 \)

Step4: Divide by denominator

\( R_0=\frac{0.1562}{0.625}=0.24992\approx0.25 \)

Answer:

\( 0.25 \)