Question

in 2015, there was a zika virus outbreak in barrancas, colombia. the average contact rate from the infected mosquitoes were 3 people per day. the transmission probability was 50%, and the duration of infectiousness was 10 days. the population density was 16. using the formula, find the $r_0$ $r_0=\frac{\betacdot kappacdot d}{sqrt{sigma}}$ - $\beta$ = contact rate (number of contacts per day) - $kappa$ = transmission probability per contact - $d$ = duration of infectiousness - $sigma$ = a modifier for population density or other factors. a 37.50 b 0.9375 c 3.75 d 93.75

Explanation:

Step1: Identify the values

Given $\beta = 3$ (contacts per day), $\kappa=0.5$ (transmission probability per contact), $D = 10$ (duration of infectiousness), $\sigma = 16$ (population - density modifier).

Step2: Substitute values into formula

$R_{0}=\frac{\beta\cdot\kappa\cdot D}{\sqrt{\sigma}}=\frac{3\times0.5\times10}{\sqrt{16}}$.

Step3: Calculate numerator and denominator

The numerator is $3\times0.5\times10 = 15$. The denominator is $\sqrt{16}=4$.

Step4: Compute $R_{0}$

$R_{0}=\frac{15}{4}=3.75$.

Answer:

C. 3.75