Table 2.

Effect of Annual Molluscicide Application in Terms of Mean Worm Burden (MWB) Reduction in the Human Host Population

Seasonality	Molluscicide Efficacy${\epsilon }_S$ ,%	Time Points Within the Seasonal Cycle for Molluscicide Application $\tau$
		0	1/10	1/4	1/2	3/4	9/10
Type I
Strong seasonality amplitude $a=0.9$	50	13.5	13.3	8.0	3.8	8.4	11.9
	70	20.3	19.4	11.9	5.7	13.5	18.3
	90	30.7	28.2	17.1	10.6	23.8	29.4
Moderate seasonality amplitude $a=0.5$	50	8.8	8.7	7.5	4.8	6.4	8.1
	70	13.7	13.6	11.3	7.8	10.3	12.8
	90	22.0	21.1	17.0	12.3	17.8	21.2
Type II
Strong seasonality amplitude $a=0.6$	50	19.2	18.0	9.2	6.5	13.2	17.2
	70	27.0	24.9	12.8	8.5	19.6	24.8
	90	38.0	33.9	17.6	14.2	32.0	37.1
Moderate seasonality amplitude $a=0.3$	50	9.3	9.2	7.7	4.5	6.4	8.4
	70	14.5	14.3	11.5	7.0	10.4	13.4
	90	23.1	22.1	17.2	11.6	18.3	22.2

Data are percent reduction in MWB.

A 6-year control program was simulated using a Macdonald-type model system having a dynamic snail population seasonality with carrying capacity function $K(t,a)$ of trigonometric type I or peak type II structure. As for Table 1, progress was measured by relative seasonal average reduction of MWB $\overline{w}(Y_6,\tau )/\overline{w}(Y_0,\tau )$. We examined several possible intraseasonal timings for molluscicide application,$\tau =\{0,\frac{1}{10},\frac{1}{4},\frac{1}{2},\frac{3}{4},\frac{9}{10}\}$, as fractions of the seasonal cycle, 3 possible levels of molluscicide efficacy (percent of killed snails) ${\epsilon }_S=\{50\mathrm{\%},70\mathrm{\%},90\mathrm{\%}\}$, and 2 choices of the seasonal amplitude parameter (moderate or high). Optimal timing for molluscicide control in all cases was $\tau =0$ (highlighted in bold), ie, at the start/end of the season, when the snail population or its carrying capacity reached its maximum.