Mathematical models of the effectiveness and persistence of mosquito repellents.

Two models of the effectiveness and persistence of mosquito repellents on the skin were developed from published functions and data. The probit plane model, Y = a + b1X1 + b2X2, relates the response (Y, in probits) of the mosquito test population to the log dose (X1) of repellent applied and the test period, or elapsed time from the time of application (X2). The exponential decay model, Z = X1 + (b2/b1)X2, estimates the repellent residue (log-1 Z) from X1 and X2. The models were validated with original data from tests of deet (N,N-diethyl-3-methylbenzamide) and ethyl hexanediol (2-ethyl-1,3-hexanediol) on the forearm against the yellow fever mosquito, Aedes aegypti. The probit plane model was evaluated as Y = 8.83 + 1.56 X1-0.69X2 for deet and Y = 8.67 + 1.68X1 - 0.92X2 for ethyl hexanediol when X1 is in log mg/cm2 and X2 is in hours. The exponential decay model was evaluated as Z = X1 - 0.45X2 for deet and Z = X1 - 0.55X2 for ethyl hexanediol. The decay constant (lambda) and half-life (t1/2) were estimated as 1.03 hr-1 and 0.67 hr for deet and 1.26 hr-1 and 0.55 hr for ethyl hexanediol from the slope parameter (b2/b1) of the decay model. Applicable correlation coefficients, standard errors and confidence limits are given. The introduction of these models of the pharmacodynamics of mosquito repellents is a step toward establishing a rational basis for the research, development, testing and evaluation of repellents and for their regulation by the government.(ABSTRACT TRUNCATED AT 250 WORDS)