# Table 3 Summary of Poisson regression models used in this study

Poisson regression modela RMSE
Hwalien County
$Y\left(t\right)=exp\left[{\beta }_{0}+{\beta }_{1}t+{\beta }_{2}{t}^{2}+{\beta }_{3}\sum _{n=1}^{5}sin\left(2n\pi t∕12\right)+{\beta }_{4}\sum _{n=1}^{5}cos\left(2n\pi t∕12\right)+{\beta }_{\mathsf{\text{5}}}{T}_{\mathsf{\text{mean}},t-3}\right]$ 2.66 (T1)
$Y\left(t\right)=exp\left[\begin{array}{c}{\beta }_{0}+{\beta }_{1}t+{\beta }_{2}{t}^{2}+{\beta }_{3}\sum _{n=1}^{5}sin\left(2n\pi t∕12\right)+{\beta }_{4}\sum _{n=1}^{5}cos\left(2n\pi t∕12\right)+{\beta }_{5}{T}_{\mathsf{\text{mean}},t-3}\\ +{\beta }_{6}ag{e}_{t}\end{array}\right]$ 2.48 (T2)
$Y\left(t\right)=exp\left[\begin{array}{c}{\beta }_{0}+{\beta }_{1}t+{\beta }_{2}{t}^{2}+{\beta }_{3}\sum _{n=1}^{5}sin\left(2n\pi t∕12\right)+{\beta }_{4}\sum _{n=1}^{5}cos\left(2n\pi t∕12\right)+{\beta }_{5}{T}_{\mathsf{\text{mean}},t-3}\\ +{\beta }_{\mathsf{\text{6}}}ag{e}_{t}+{\beta }_{7}mal{e}_{t}+{\beta }_{\mathsf{\text{8}}}femal{e}_{t}\end{array}\right]$ 2.34 (T3)
Taitung County
$Y\left(t\right)=exp\left[{\beta }_{0}+{\beta }_{1}t+{\beta }_{2}{t}^{2}+{\beta }_{3}\sum _{n=1}^{5}sin\left(2n\pi t∕12\right)+{\beta }_{4}\sum _{n=1}^{5}cos\left(2n\pi t∕12\right)+{\beta }_{\mathsf{\text{5}}}{T}_{\mathsf{\text{max}},t-2}\right]$ 2.64 (T4)
$Y\left(t\right)=exp\left[\begin{array}{c}{\beta }_{0}+{\beta }_{1}t+{\beta }_{2}{t}^{2}+{\beta }_{3}\sum _{n=1}^{5}sin\left(2n\pi t∕12\right)+{\beta }_{4}\sum _{n=1}^{5}cos\left(2n\pi t∕12\right)+{\beta }_{5}{T}_{\mathsf{\text{max}},t-2}\\ +{\beta }_{6}ag{e}_{t}\end{array}\right]$ 2.63 (T5)
$Y\left(t\right)=exp\left[\begin{array}{c}{\beta }_{0}+{\beta }_{1}t+{\beta }_{2}{t}^{2}+{\beta }_{3}\sum _{n=1}^{5}sin\left(2n\pi t∕12\right)+{\beta }_{4}\sum _{n=1}^{5}cos\left(2n\pi t∕12\right)+{\beta }_{5}{T}_{\mathsf{\text{max}},t-2}\\ +{\beta }_{\mathsf{\text{6}}}ag{e}_{t}+{\beta }_{7}mal{e}_{t}+{\beta }_{\mathsf{\text{8}}}femal{e}_{t}\end{array}\right]$ 2.63 (T6)
1. a Y(t) represents expected incidence rate of tuberculosis, β 0 stands for intercept, β 1 stands for linear time trend, β 2 stands for quadratic time trend, β 3 and β 4 stands for the seasonality, β 5 stands for monthly maximum and mean temperature (°C), t - 3 in the subscript represents the 3-month lag time and t - 2 in the subscript represents the 2-month lag time, β 6 stands for the effect for age, β 7 stands for the effect for male, and β 8 stands for the effect for female.
2. RMSE = Root mean squared error.