Skip to main content

Theory and Modern Applications

Table 2 Descriptions and values of model parameters

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