Chapter 17.1, Problem 44E

Dengue Fever In tropical regions, dengue fever is a significant health problem that affects nearly 100 million people each year. Using data collected from the 2002 dengue epidemic in Colima. Mexico, researchers have estimated that the incidence I (number of new cases in a given year) of dengue can be predicted by the following function.

     $I\left(p,a,m,n,e\right)={\left(25.54+0.04p-7.92a+2.62m+4.46n+0.15e\right)}^2,$

 where p is the precipitation (mm), a is the mean temperature (°C), m is the maximum temperature (°C),m is the minimum temperature (°C), and e is the evaporation (mm). Source: Journal of Environmental Health.

(a)    Estimate the incidence of a dengue fever outbreak for a region with 80 mm of rainfall, average temperature of 23°C, maximum temperature of 34°C, minimum temperature of 16°C, and evaporation of 50 mm.

(b)    Which variable has a negative influence on the incidence of dengue? Describe this influence and what can be inferred mathematically about the biology of the fever.