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. 2015 May 17;79:178–200. doi: 10.1016/j.tre.2015.04.007

Table 1.

Notations.

A A set of epidemic areas, A = {a1a2, … , aJ}
B A set of EMRCs, B = {b1b2, … , bI}
M A set of medical reliefs, M = Mp + Mt. Mp and Mt are sets of prophylactic and treatment reliefs, respectively. Mp = {m1m2, … , ml}, Mt = {ml+1ml+2, … , ml+k}
Qitp Available amount of relief p in EMRC i in time period t
Wit Available transportation capacity in EMRC i in time period t
Ct Maximum budget in time period t
cijtp Unit distribution cost of relief p from EMRC i to area j in time period t
θp Demand of medical relief p needed per unit time per demander
αp Mortality increase caused by unit dissatisfaction of medical relief p,pMt
βp Infection rate increase caused by unit dissatisfaction of medical relief p,pMp
αM The highest mortality rate that can be withstood
βM The highest infection rate that can be withstood
Sjc(t),Sjvt Numbers of common and vulnerable susceptible people in area j at moment t
Ejct,Ejvt Numbers of common and vulnerable exposed people in area j at moment t
Ijct,Ijvt Numbers of common and vulnerable infectious people in area j at moment t
Rjct,Rjvt Numbers of common and vulnerable recovered people in area j at moment t
Sjtc,Sjtv The approximate average numbers of common and vulnerable susceptible people in area j in time period t
Ejtc,Ejtv The approximate average numbers of common and vulnerable exposed people in area j in time period t
Ijtc,Ijtv The approximate average numbers of common and vulnerable infectious people in area j in time period t
Ajc,Ajv Constant net input of common and vulnerable people to area j
βjc,βjv Common and vulnerable infection rate in area j
δj Contact coefficient in area j
ε Exposure rate (the rate at which exposed individuals become infectious)
γjc,γjv Common and vulnerable recovery rate in area j
μj Diagnosis rate in area j
djc,djv Natural mortality rate of common and vulnerable people in area j
αjc,αjv Disease mortality rate of common and vulnerable people in area j
Djtp Demand for medical relief p in area j in time period t
Invjtp The inventory of relief p in area j at the beginning of time period t
xijtp The amount of medical relief p sent from EMRC i to area j in time period t