Table 1 Fitted relationships between infection age and quantities of interest

Patent Fraction, D(\(\alpha\))

\({\left\{ \begin{array}{ll} 1 &{} \text {if}\ \alpha \le 6 \\ 1.12 - .02 \ \alpha &{} \text {if}\ 6 < \alpha \le 18 \\ \left( 1+e^{-1.52+0.0151 \alpha }\right) ^{-1} &{} \text {if}\ \alpha >18 \end{array}\right. }\)

\(\log _{10}\) Asexual parasitaemia, P(\(\alpha\))

\({\left\{ \begin{array}{ll} 0, &{} \text {if}\ \alpha \le 0 \\ 3.10 + .278 \ \alpha , &{} \text {if}\ 0< \alpha \le 6 \\ 5.12 - .0743 \ \alpha , &{} \text {if}\ 6 < \alpha \le 18 \\ 3.85 - .00843 \ \alpha , &{} \text {if}\ \alpha >18 \end{array}\right. }\)

Fever Probability, F(P(\(\alpha\)))

\(\frac{.859 e^{3.45 P(\alpha )}}{58200 + e^{3.45 P(\alpha )}}\)

\(\log _{10}\) gametocytaemia, G(\(L_9 P(\alpha )\))

\(-0.684+.892L_9 P(\alpha ), L_9 P(\alpha ) = P(\alpha -9)\)

Transmission Efficiency, c(G(\(\alpha\)))

\(\frac{.683 e^{2.14 G(\alpha )}}{131 + e^{2.14 G(\alpha )}}\)