Answers to Hone Your Problem-Solving Skills Questions

1. The rodents serve as an alternative, or reservoir, host for the disease. Thus, if leishmaniasis infection can be reduced within rodents, fewer sand flies will carry the disease and fewer humans will be infected.

2. A given disease will become established and spread in a given host population only if the density of susceptible hosts exceeds a critical threshold density (S_t). The concept of a threshold density has considerable medical and ecological importance because it indicates that a disease will not spread if the density of susceptible hosts can be held below the threshold density.

3. The following populations will need to be reduced to S_t, which is 5,000 individuals: population 1 (decrease by 4,000 individuals), population 3 (decrease by 500 individuals), population 5 (decrease by 3,000 individuals), and population 8 (decrease by 5,000 individuals).

4. The threshold density can be raised by taking actions that increase the rate at which infected individuals recover and become immune (thereby increasing m and hence increasing S_t = m∕β). This can be accomplished by early detection and clinical treatment of the disease. The threshold density can also be raised if β, the disease transmission rate, is decreased. This can be achieved by controlling the vector (sand flies) and/or changing the behaviors of the host (e.g., using bug spray).