Table 1.

Notations.

A	A set of epidemic areas, A = {a1, a2, … , aJ}
B	A set of EMRCs, B = {b1, b2, … , bI}
M	A set of medical reliefs, M = Mp + Mt. Mp and Mt are sets of prophylactic and treatment reliefs, respectively. Mp = {m1, m2, … , ml}, Mt = {$m_{l+1}$, ml+2, … , ml+k}
$Q_{\mathit{it}}^p$	Available amount of relief p in EMRC i in time period t
$W_{\mathit{it}}$	Available transportation capacity in EMRC i in time period t
Ct	Maximum budget in time period t
$c_{\mathit{ijt}}^p$	Unit distribution cost of relief p from EMRC i to area j in time period t
${\theta }^p$	Demand of medical relief p needed per unit time per demander
${\alpha }^p$	Mortality increase caused by unit dissatisfaction of medical relief $p\text{,}p\in \mathit{Mt}$
${\beta }^p$	Infection rate increase caused by unit dissatisfaction of medical relief $p\text{,}p\in \mathit{Mp}$
${\alpha }_M$	The highest mortality rate that can be withstood
${\beta }_M$	The highest infection rate that can be withstood
$S_j^c(t)\text{,}{S}_j^v\left(t\right)$	Numbers of common and vulnerable susceptible people in area j at moment t
$E_j^c\left(t\right)\text{,}{E}_j^v\left(t\right)$	Numbers of common and vulnerable exposed people in area j at moment t
$I_j^c\left(t\right)\text{,}{I}_j^v\left(t\right)$	Numbers of common and vulnerable infectious people in area j at moment t
$R_j^c\left(t\right)\text{,}{R}_j^v\left(t\right)$	Numbers of common and vulnerable recovered people in area j at moment t
$S_{\mathit{jt}}^c\text{,}{S}_{\mathit{jt}}^v$	The approximate average numbers of common and vulnerable susceptible people in area j in time period t
$E_{\mathit{jt}}^c\text{,}{E}_{\mathit{jt}}^v$	The approximate average numbers of common and vulnerable exposed people in area j in time period t
$I_{\mathit{jt}}^c\text{,}{I}_{\mathit{jt}}^v$	The approximate average numbers of common and vulnerable infectious people in area j in time period t
$A_j^c\text{,}{A}_j^v$	Constant net input of common and vulnerable people to area j
${\beta }_j^c\text{,}{\beta }_j^v$	Common and vulnerable infection rate in area j
${\delta }_j$	Contact coefficient in area j
ε	Exposure rate (the rate at which exposed individuals become infectious)
${\gamma }_j^c\text{,}{\gamma }_j^v$	Common and vulnerable recovery rate in area j
${\mu }_j$	Diagnosis rate in area j
$d_j^c\text{,}{d}_j^v$	Natural mortality rate of common and vulnerable people in area j
${\alpha }_j^c\text{,}{\alpha }_j^v$	Disease mortality rate of common and vulnerable people in area j
$D_{\mathit{jt}}^p$	Demand for medical relief p in area j in time period t
${\mathit{Inv}}_{\mathit{jt}}^p$	The inventory of relief p in area j at the beginning of time period t
$x_{\mathit{ijt}}^p$	The amount of medical relief p sent from EMRC i to area j in time period t