Table 1 Parameters of the optimal control problem.
Parameter | Description | Unit | Value or range [ ] | Source |
|---|---|---|---|---|
Epidemiological parameters | ||||
\({{\text{R}}}_{0}\) | Basic reproduction number (in the absence of any control interventions) | – | 3.6 | Lit41 |
\({\beta }_{P}\) | Pre-symptomatic transmission rate | \(da{y}^{-1}\) | 0.3983 | |
\({\beta }_{I}\) | Symptomatic transmission rate | \(da{y}^{-1}\) | 0.6277 | |
\({\beta }_{A}\) | Asymptomatic transmission rate | \(da{y}^{-1}\) | 0.2828 | |
\({\delta }_{E}\) | Latency rate (\(1/{\delta }_{E}\) = mean latency period) | \(da{y}^{-1}\) | 1/3.32 | |
\({\delta }_{P}\) | Post-latency rate | \(da{y}^{-1}\) | 1/1.88 | Lit41 |
\(\sigma\) | Probability to manifest symptoms | – | 0.25 | |
\({\eta }_{I}\) | Detection rate of symptomatic people | \(da{y}^{-1}\) | 1/4.05 | Lit41 |
\({\eta }_{A}\) | Detection rate of asymptomatic people | \(da{y}^{-1}\) | \({\eta }_{I}/2\) | Lit41 |
\(\zeta\) | Probability of being hospitalized | – | 0.40 | |
\({\gamma }_{A}\) | Recovery rate of asymptomatic | \(da{y}^{-1}\) | 1/7 | |
\({\gamma }_{H}\) | Recovery rate of hospitalized people | \(da{y}^{-1}\) | 1/14 | Lit41 |
\({\gamma }_{I}\) | Recovery rate of symptomatic | \(da{y}^{-1}\) | 1/14 | Lit41 |
\({\gamma }_{Q}\) | Recovery rate of quarantined individuals | \(da{y}^{-1}\) | 1/14 | Lit41 |
\({\alpha }_{I}\) | death rate of symptomatic | \(da{y}^{-1}\) | 1/24 | Lit41 |
\({\alpha }_{H}\) | Death rate of hospitalized (H) people | \(da{y}^{-1}\) | 1/24 | Lit41 |
\({\alpha }_{U}\) | Death rate of untreated (U) people | \(da{y}^{-1}\) | \(\left(1+f\right){\alpha }_{H}, f>1\) | Free |
\({H}_{max}\) | Maximal capacity of hospitals | \(-\) | 195,000 | Italian NIH60 |
Social distancing & cost parameters | ||||
\(\theta\) | Adherence (Effectiveness) of social distancing | – | 0.7 [0–1] | Free |
\({L}_{max}\) | Upper bound of social distancing | – | 0.7 | Lit20 |
\(\Lambda\) | Prioritization to indirect costs | – | [0, 1] | Free |
\({t}_{s}\) | Intervention delay | days | [0, 150] | Free |
\(\omega\) | Average daily wage | $ | 32,500/365 | World Bank 2020 |
\(1/r\) | Numbers of life years lost by those dying of COVID | \(year\) | 20 | |
\(\tau\) | Availability of post-infection testing | – | 1 | Lit20 |
\({\alpha }_{1}\) | Average hospitalization cost per patient | $ | 2275.20 | Lit62 |
\({p}_{y}\) | Fraction of under-65 in deceased population | – | 0.151 | Lit60 |
\(vsl\) | Value of a Statistical Life (\(365\omega /r\)) | $ | 650,000 | Lit20 |
\(T\) | Horizon length | \(days\) | 365 | Fixed |
