7.2 Interpreting R₀

Even without calculating the value of R₀ (reproduction number), the structure of Equation 7 gave us some insight into how to prevent a West Nile virus outbreak. We knew that higher R₀ values (above one) mean a greater chance of an outbreak and lower R₀ values (below one) mean a lesser chance of an outbreak.

Simply by looking at the expression for R₀, we saw that the mosquito abundance was in the numerator and the bird abundance in the denominator. This told us that decreasing the mosquito abundance would decrease R₀, and decrease the chance of an outbreak. It also told us that decreasing the bird abundance would have the opposite effect: it would increase R₀, and increase the chance of an outbreak.

At first, this seemed like a surprising result. Why would removing birds from this system increase the chance of a West Nile virus outbreak? The answer, it turned out, followed from our initial assumption of frequency-dependent disease transmission.

Under this assumption, birds are generally plentiful and a mosquito can always find a blood meal. As long as this is the case, reducing the bird abundance would not reduce the mosquito biting rate. Instead, the remaining birds would be bitten more often. This would concentrate the disease transmission on those birds, making it more likely that they would become infected, and transmit the infection back to the mosquitoes. We visualized this relationship by plotting R₀ as a function of the relative numbers of mosquitoes and birds (FIGURE 5).

Results Q8

The expression for R₀ also allowed us to calculate the threshold number of mosquitoes per bird that would lead to a West Nile virus outbreak. We determined this number by setting R₀ to its threshold value of one, and rearranging Equation 7 to solve for the threshold value of the ratio N_M0/N_B0. Above this threshold, a disease outbreak would be predicted to occur. Below the threshold, it would not.

Results Q9