Table 3 Summary of Pandemic and Non-pandemic Model

Data Model

❖ Data as counts

Y _j,t ∼Pois(λ _j,t )

❖ Data as a proportion

$\mathit{\text{Log}}\left(Y_{j,t}\right)\sim N\left({\mu }_{j,t},{\displaystyle {\sigma }_j^2}\right)$

Process Model

❖ Pandemic Model

     ▪ Data as counts

μ _j,t  = θ _j,t  ⋅ X _t  + φ _j,t

     ▪ Data as a proportion

Log(λ _j,t ) = θ _j,t  ⋅ X _t  + φ _j,t

     ▪ “Completeness”

${\theta }_{j,t}={\beta }_{j,t,1}+{\displaystyle \sum _{l=2}^M{\beta }_{j,t,l}\cdot {\displaystyle k_{l-1,\theta ,t}^p}}$

     ▪ “Excess”

${\phi }_{j,t}=a_{j,t,1}+{\displaystyle \sum _{r=2}^N{a}_{j,t,r}\cdot {\displaystyle k_{r-1,\phi ,t}^p}}$

❖ Non-pandemic Model

     ▪ Data as counts and as a proportion

$\mathit{\text{Log}}\left(Y_{j,t}\right)\sim N\left({\mu }_{j,t},{\displaystyle {\sigma }_j^2}\right)$

${\mu }_{j,t}=P_{s,j,t,1}+P_{s,j,t,2}\cdot {\displaystyle k_{1,t}^{\mathit{np}}}+P_{s,j,t,3}\cdot {\displaystyle k_{2,t}^{\mathit{np}}}+P_{s,j,t,4}\cdot {\displaystyle k_{3,t}^{\mathit{np}}}$

Parameter Model: non-informative priors

❖ Pandemic Model

$a_{j,t,r}\sim N\left({\mu }_a,{\sigma }_a^2\right);r=1,....,N$

${\beta }_{j,t,l}\sim N\left({\mu }_{\beta },{\sigma }_{\beta }^2\right);r=1,....,M$

$\tau \equiv 1/{\sigma }_j^2\sim \mathit{Gamma}\left(a,b\right)$

❖ Non-pandemic Model

$P_{s,j,t,n}\sim N\left({\mu }_p,{\sigma }_p^2\right);n=1,2,3$

τ∼Gamma(a, b)