Table 1 Symbolic description of the model (Patient allocation method in major epidemics, China, 2022)
Ensemble | |
|---|---|
\(I\) | The point ensemble in the epidemic area with demand for treatment, \(I = \left\{ {i\left| {i = 1, \cdots ,N_{i} } \right.} \right\}\), where \(N_{i}\) is the total number of epidemic areas |
\(J\) | The ensemble of designated hospitals of patients, \(J = \left\{ {j\left| {j = 1, \cdots ,N_{j} } \right.} \right\}\), where \(N_{j}\) is the total number of designated hospitals |
\(P\) | The ensemble of patient states, \(P = \left\{ {p\left| {p = 1, \cdots ,N_{j} } \right.} \right\}\), where \(N_{p}\) is the the total number of patient's disease categories |
\(Q\) | The ensemble of designated hospital level, \(Q = \left\{ {q\left| {q = 1, \cdots ,N_{q} } \right.} \right\}\), where \(N_{q}\) is the the total number of designated hospital level |
\(K\) | The ensemble of medical resources, \(K = \left\{ {k\left| {k = 1, \cdots ,N_{k} } \right.} \right\}\), where \(N_{k}\) is the the total number of medical resources categories |
Parameters | |
|---|---|
\(C_{jqk}\) | Capacity of class k medical resources for hospital j of grade q |
\(A_{ip}\) | Number of patients with Category p in epidemic area i |
\(D_{ij}\) | Distance from epidemic area i to epidemic area j |
\(a_{pk}\) | The number of class k medical resources required per class p patient |
M | Unit allocation matching benefit matrix \(M = [m_{pq} ]_{{N_{p} \times N_{q} }}\), Where \(m_{pq}\) represents the allocation matching benefit coefficient for patients with Category p seen in q-level hospitals |
N | Infinite quantity |
Variables | |
|---|---|
\(r_{ip}\) | Number of patients with Category p admitted in epidemic area i |
\(A_{ip}^{{ \star }}\) | Number of patients in category P of epidemic area i waiting to receive treatment |
Decision variables | |
|---|---|
\(v_{ipjq}\) | Number of patients with Category p traveling from epidemic area i to q-level hospital j |
\(u_{ipj}\) | Number of patients with Category p traveling from epidemic area i to designated hospital j |
\(v_{ipjq}^{{ \star }}\) | Number of patients with Category p in epidemic area i assigned to q-level hospital j, and assigned to virtual capacity |
\(u_{ipj}^{{ \star }}\) | Number of patients with Category p in epidemic area i who are assigned to hospital j and assigned to the virtual capacity |