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Table 1 Model events, adapted from [11], where N i is a host’s total worm burden, of which n i are female worms, Ber() is a Bernoulli-distributed random variable and δ() is the Dirac delta function

From: The importance of patient compliance in repeated rounds of mass drug administration (MDA) for the elimination of intestinal helminth transmission

Event Definition Rate
Worm acquisition by host i, aged a \( {\mathrm{N}}_{\mathrm{i}}\to {\mathrm{N}}_{\mathrm{i}}+1 \)
\( {\mathrm{n}}_{\mathrm{i}}\to {\mathrm{n}}_{\mathrm{i}}+\mathrm{B}\mathrm{e}\mathrm{r}(0.5) \)
\( \upbeta \left({\mathrm{a}}_i\right){\uplambda}_{\mathrm{i}}\mathrm{L} \) per host per unit of time
Worm death in host i \( {\mathrm{N}}_{\mathrm{i}}\to {\mathrm{N}}_{\mathrm{i}}-1 \)
\( {\mathrm{n}}_{\mathrm{i}}\to {\mathrm{n}}_{\mathrm{i}}-\mathrm{B}\mathrm{e}\mathrm{r}(0.5) \)
\( \upsigma \) per worm per unit of time
Host birth/death for host aged a At death, host is replaced with a newborn; \( {\mathrm{N}}_{\mathrm{i}}={\mathrm{n}}_{\mathrm{i}}=0 \) and all host variables reset. \( \upmu \left({\mathrm{a}}_{\mathrm{i}}\right) \) per unit of time
Treatment of host i, aged a \( {\mathrm{N}}_{\mathrm{i}}={\mathrm{N}}_{\mathrm{i}}*\left(1-\left[\mathrm{drug}\;\mathrm{eff}.\right]\right) \) \( \updelta \left(\mathrm{t}-{\mathrm{t}}_{\mathrm{j}}\right)\mathrm{g}\left({\mathrm{a}}_{\mathrm{i}}\right) \)