Table 2.

List of model equations used for West Nile virus forecasting in South Dakota.

Model	Equation
Base	$\text{logit}\left(p_{i,t}\right)=c_{0i}+cyc\left(w\right)$
Mosq	$\text{logit}\left(p_{i,t}\right)=c_{0i}+c_1{m}_{i,t}+cyc\left(w\right)$
Env	$\text{logit}\left(p_{i,t}\right)=c_{0i}+\sum _{k=1}^2\sum _{l=0}^L{s}_k\left(l\right)u_{i,t-l}$
EnvAnom	$\text{logit}\left(p_{i,t}\right)=c_{0i}+cyc\left(w\right)+\sum _{k=1}^2\sum _{l=0}^L{s}_k\left(l\right)a_{i,t-l}$
EnvSv	$\text{logit}\left(p_{i,t}\right)=c_{0i}+\sum _{k=1}^2\sum _{l=0}^L{s}_k\left(l,w\right)u_{i,t-l}$
EnvSvAnom	$\text{logit}\left(p_{i,t}\right)=c_{0i}+cyc\left(w\right)+\sum _{k=1}^2\sum _{l=0}^L{s}_k\left(l,w\right)a_{i,t-l}$
Comb	$\text{logit}\left(p_{i,t}\right)=c_{0i}+c_1{m}_{i,t}+\sum _{k=1}^2\sum _{l=0}^L{s}_k\left(l\right)u_{i,t-l}$
CombAnom	$\text{logit}\left(p_{i,t}\right)=c_{0i}+c_1{m}_{i,t}+cyc\left(w\right)+\sum _{k=1}^2\sum _{l=0}^L{s}_k\left(l\right)a_{i,t-l}$
CombSv	$\text{logit}\left(p_{i,t}\right)=c_{0i}+c_1{m}_{i,t}+\sum _{k=1}^2\sum _{l=0}^L{s}_k\left(l,w\right)u_{i,t-l}$
CombSvAnom	$\text{logit}\left(p_{i,t}\right)=c_{0i}+c_1{m}_{i,t}+cyc\left(w\right)+\sum _{k=1}^2\sum _{l=0}^L{s}_k\left(l,w\right)a_{i,t-l}$

Note: $p_{i,t}$ is the probability of one or more WNV cases in county $i$ at time $t$; $c_{oi}$ is a county-level fixed effect; $m_{i,t}$ is the mosquito infection growth rate (MIGR) in county i at time t; $c_1$ is the parameter for MIGR; cyc(w) is a cyclical seasonal function; k indexes two meteorological variables; l indexes daily lags up to $L=120$ days in the past; $s_k\left(l\right)$ is a thin-plate spline function of lag days; $s_k\left(l,w\right)$ is a thin-plate spline function of lag days and week of the year; $u_{i,t-l}$ is an untransformed meteorological variable for county i at time $t–l$ and $a_{i,t-l}$ is an anomalized meteorological variable for county i at time $t–l$. Base, baseline; Comb, combined; CombAnom, combined with anomalies; CombSv, combined with seasonally varying distributed lags; CombSvAnom, combined with anomalies and seasonally varying distributed lags; Ens2, two model ensemble; Ens3, three model ensemble; Ens4, four model ensemble; Env, environmental; EnvAnom, environmental with anomalies; EnvSv, environmental with seasonally varying distributed lags; EnvSvAnom, environmental with anomalies and seasonally varying distributed lags; Mosq, mosquito.