Table 1.

Effect of Annual Mass Drug Administration (MDA) in Terms of Mean Worm Burden (MWB) Percent Reduction Among Local Human Populations

Seasonality	MDA Efficacy ${\epsilon }_H$ ,%	Time of MDA, Fraction of Seasonal Cycle
		0	1/10	1/4	1/2	3/4	9/10
Type I
Strong seasonality amplitude $a=0.9$	50	87.1	86.5	82.7	89.3	89.2	88.1
	55	90.6	90.0	90.6	92.5	92.5	91.5
	70	97.1	96.8	97.1	98.1	98.2	97.7
Moderate seasonality amplitude $a=0.5$	50	82.8	82.3	82.2	83.6	84.1	83.4
	55	86.9	86.3	86.2	87.6	88.2	87.5
	70	95.3	94.9	94.8	95.7	96.2	95.8
Type II
Strong seasonality amplitude $a=0.6$	50	90.3	89.6	90.7	92.7	92.0	91.3
	55	93.2	92.5	93.5	94.7	94.6	94.0
	70	98.1	97.8	98.3	98.7	98.8	98.6
Moderate seasonality amplitude $a=0.3$	50	82.9	82.3	82.2	84.0	84.6	83.7
	55	87.0	86.4	86.3	87.9	88.5	87.8
	70	95.4	94.9	94.7	95.9	96.4	95.9

Data are percent reduction in MWB.

We simulated a 6-year MDA regimen for a Macdonald-type model system having dynamic snail populations with seasonal carrying capacity function $K(t,a)$ of trigonometric types I or peak type II. Impact was measured in terms of relative MWB reduction for local residents (year 6 over endemic year 0) using seasonal average values $\overline{w}(Y_6,\tau )/\overline{w}(Y_0,\tau )$ of MWB. We examined several different values of intraseasonal timing for MDA, $\tau =\{0,\frac{1}{10},\frac{1}{4},\frac{1}{2},\frac{3}{4},\frac{9}{10}\}$, as fractions of the seasonal cycles, 3 possible levels of MDA efficacy (instantaneous reduction of mean worm burden) ${\epsilon }_H=\{50\mathrm{\%},55\mathrm{\%},70\mathrm{\%}\}$ as the combined effect of drug efficacy (fraction of killed worms) and population coverage fraction, and 2 values of seasonal amplitude, $a$. The optimal timing (highlighted in bold) varied in the range ${}^1╱{}_2<\tau <{}^3╱{}_4$. The optimum was close to mid-season $\tau \approx {}^1╱{}_2$ in the presence of strong seasonal amplitude ($a$) and shifted toward $\tau \approx {}^3╱{}_4$ at moderate seasonal amplitude ($a$).