Table 2.

Description of variables and parameters in ZERO-G method.

Variable	Description	Source
$r_{\mathit{it}}$	The reported incidence in zone i at time t	Data
$Z_{\mathit{it}}$	Binomial variable representing if there was zero reported incidence	Data
$h_{\mathit{it}}$	Number of non-focal disease consultations	Data
$n_{\mathit{it}}$	Population count of zone	Data
$X_i$	Longitude of zone i	Data
$Y_i$	Latitude of zone i	Data
$d_{\mathit{ij}}$	Distance between zone i and health facility j. Can be calculated using Euclidean distance or based on actual routing	Data
${\mathrm{\nu }}_{\mathit{jst}}$	Value of health service s provided at health facility j at time t	Data
$m_t$	Month of year (e.g. Jan-Dec) at time t	Data
$N_{\mathit{it}}$	The ZERO-G estimated incidence after correcting for under-ascertainment	Equation (1)
$A_{\mathit{it}}$	FCA-based healthcare access	Equation (2, 3)
$S_{\mathit{jt}}$	Services provided by health facility j at time t	Equation (4)
${\mathrm{\beta }}_s$	Coefficient for health service s	Equation (4)
$\mathrm{\lambda }$	Distance decay coefficient	Equation (5)
$C_{\mathit{jt}}$	Competition at health facility j at time t	Equation (6)
${\mathrm{\beta }}_c$	Scaling coefficient for competition at health facilities	Equation (6)
$g\left(t\right)$	Function describing temporal trend in . Specific function can be adjusted based on need	Equation (7)
${\mathrm{\psi }}_{\mathit{it}}$	Probability of zero reported incidence	Equation (8, 9)
${\mathrm{\beta }}_{z1\cdots z3}$	Coefficients used to estimate probability of zero reported incidence	Equation (9)
$r_{\mathit{it}}^{\ast }$	Zero-adjusted reported incidence	Equation (10)
$RF\left(X\right)$	Function describing random forest algorithm used in data imputation	Equation (10)
$S{I}_{\mathit{it}}$	The sampling intensity in zone i at time t	Equation (11)
$x_1,x_2$	Scaling coefficients for SI	Equation (12)

Parameters estimated via the ZERO-G method have the corresponding equations listed as their source.

Note Subscript $i$ refers to zone $i$ and subscript $t$ refers to month $t$.