Table 3 Description of model transitions and their rates.
# | Transition | Meaning | Transition rate |
|---|---|---|---|
1 | \({S}_{PAT}\to {S}_{PAT}+1\) | Entry of a non-contagious patient | \(\left(1-\phi \right){z}_{1}\) |
2 | \({I}_{PAT}\to {I}_{PAT}+1\) | Entry of a contagious patient | \(\phi {z}_{1}\) |
3 | \(\left({S}_{PAT},{E}_{PAT}\right)\to \left({S}_{PAT}-1,{E}_{PAT}+1\right)\) | Infection of a patient | \(\left({\beta }_{11}\frac{{I}_{1}}{{N}_{1}}+{\beta }_{12}\frac{{I}_{2}}{{N}_{2}}+{\beta }_{13}\frac{{I}_{3}}{{N}_{3}}\right){S}_{1}\) |
4 | \({S}_{PAT}\to {S}_{PAT}-1\) | Discharge of a susceptible patient | |
5 | \(\left({S}_{NUR},{E}_{NUR}\right)\to \left({S}_{NUR}-1,{E}_{NUR}+1\right)\) | Infection of a nurse | \(\left({\beta }_{21}\frac{{I}_{1}}{{N}_{1}}+{\beta }_{22}\frac{{I}_{2}}{{N}_{2}}+{\beta }_{23}\frac{{I}_{3}}{{N}_{3}}\right)\tau {S}_{2}\) |
6 | \(\left({S}_{MED},{E}_{MED}\right)\to \left({S}_{MED}-1,{E}_{MED}+1\right)\) | Infection of a medical doctor | \(\left({\beta }_{31}\frac{{I}_{1}}{{N}_{1}}+{\beta }_{32}\frac{{I}_{2}}{{N}_{2}}+{\beta }_{33}\frac{{I}_{3}}{{N}_{3}}\right){\tau S}_{3}\) |
7 | \(\left({E}_{PAT},{I}_{PAT}\right)\to \left({E}_{PAT}-1,{I}_{PAT}+1\right)\) | Infectivity of a patient | \({\sigma }_{1}{E}_{1}\) |
8 | \({E}_{PAT}\to {E}_{PAT}-1\) | Discharge of an infected but non contagious patient | \({z}_{1}\frac{{E}_{1}}{{N}_{1}}\) |
9 | \(\left({E}_{NUR},{I}_{NUR}\right)\to \left({E}_{NUR}-1,{I}_{NUR}+1\right)\) | Infectivity of a nurse | \({\sigma }_{2}{E}_{2}\) |
10 | \(\left({E}_{MED},{I}_{MED}\right)\to \left({E}_{MED}-1,{I}_{MED}+1\right)\) | Infectivity of a medical doctor | \({\sigma }_{3}{E}_{3}\) |
11 | \(\left({I}_{PAT},{R}_{PAT}\right)\to \left({I}_{PAT}-1,{R}_{PAT}+1\right)\) | Recovery of a patient | \({\gamma }_{1}{E}_{1}\) |
12 | \({I}_{PAT}\to {I}_{PAT}-1\) | Discharge of a contagious patient | \({z}_{1}\frac{{I}_{1}}{{N}_{1}}\) |
13 | \(\left({I}_{NUR},{R}_{NUR}\right)\to \left({I}_{NUR}-1,{R}_{NUR}+1\right)\) | Recovery of a nurse | \({\gamma }_{2}{E}_{2}\) |
14 | \(\left({I}_{MED},{R}_{MED}\right)\to \left({I}_{MED}-1,{R}_{MED}+1\right)\) | Recovery of a medical doctor | \({\gamma }_{3}{E}_{3}\) |
15 | \({R}_{PAT}\to {R}_{PAT}-1\) | Discharge of an immune patient | \({z}_{1}\frac{{R}_{1}}{{N}_{1}}\) |
