Theory and Modern Applications
From: A dynamic optimal control model for COVID-19 and cholera co-infection in Yemen
Parameters | Description | Value (range) | Source |
---|---|---|---|
\(I_{1}^{\mathrm{peak}}\) | Peak limit of COVID-19 | [104,105] | Assumed |
\(I_{2}^{\mathrm{peak}}\) | Peak limit of cholera | [105,5 × 105] | Assumed |
\(u_{1} ( t )\) | Time-dynamic function to measure the social distancing rate | [0.05,0.5] | [17] |
\(u_{2} ( t )\) | Time-dynamic function to measure the quarantining rate | [0.01,0.3] | [17] |
\(u_{3} ( t )\) | Time-dynamic function to measure the testing rate | [0.1,0.3] | [17] |
\(u_{4} ( t )\) | Time-dynamic function to measure the fraction of susceptible individuals who have access to CWT for water purification | [0.2,1] | [10] |
\(t_{\mathrm{latent}}^{-1}\) | Latent period of the virus | 0.5 days−1 | [17] |
\(\alpha _{c} ( t )\) | Direct transmission rate of cholera | \(5.5 e^{-7}\) | [11] |
β | Indirect transmission rate of cholera | 0.02325/week | Estimated |
\(K_{B}\) | Half saturation constant | 106 (cell/ml) | [11] |
\(\mu _{1}\) | Susceptible to COVID-19 after recovering | 0, | [17] |
\(\mu _{2} \) | Susceptible to cholera after recovering | 0.0003/week, | [11] |
\(\mu _{12}\) | Susceptible to both COVID-19 and cholera after recovering | 0 | Assumed |
ρ | Infectious period for subjects with unconfirmed infections | 0.1 days−1 | [17] |
\(\delta _{1}\) | Infection rate with cholera from COVID-19 patient | 0 | Estimated |
\(\beta _{1}\), \(\beta _{2}\) | Recovery rate from COVID-19 and cholera | 0.005, 1.5 | Estimated |
\(\lambda _{1}\) | Infected rate of cholera after recovery from COVID-19 | 0 | Estimated |
\(\upsilon _{1}\) | Recovery rate from COVID-19 and cholera sequentially | 0 | Estimated |
\(\omega _{1}\), \(\omega _{2}\), \(\omega _{12}\) | Death rate by COVID-19, cholera, and both | 0.0447, 0.0002, 0 | Estimated |
\(\alpha _{12}\) | Infected rate by both cholera and COVID-19 simultaneously | 0 | Estimated |
\(\delta _{2}\) | Infected rate with COVID-19 from cholera patient. | 0 | Estimated |
ξ | Shedding rate (infected) | 70 (cell/ml week−1 person−1) | [11] |
τ | Bacteria death rate | 0.233 /week | [11] |
\(\lambda _{2}\) | Infected rate by COVID-19 after recovering from cholera | 0 | Estimated |
\(\upsilon _{2}\) | Recovery rate from cholera and COVID-19 sequentially | 0 | Estimated |
\(\upsilon _{12}\) | Recovery rate from both COVID-19 and cholera simultaneously | 0 | Estimated |
k | Bacteria carrying capacity | \(K_{B} /2\) | [11] |
b | Allee threshold when τ = 0 | \(K_{B} /10\) | [11] |
r | Bacterial intrinsic growth rate | 1 | [11] |
Λ | A constant rate of the total population | 0.3 | Assumed |