Modeling the effect of random diagnoses on the spread of COVID-19 in Saudi Arabia

Salma M. Al-Tuwairqi; Sara K. Al-Harbi; Salma M. Al-Tuwairqi; Sara K. Al-Harbi

doi:10.3934/mbe.2022456

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 10: 9792-9824. doi: 10.3934/mbe.2022456

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Research article Special Issues

Modeling the effect of random diagnoses on the spread of COVID-19 in Saudi Arabia

Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

Academic Editor: Quentin Griette

Received: 20 May 2022 Revised: 16 June 2022 Accepted: 21 June 2022 Published: 08 July 2022

Saudi Arabia was among the countries that attempted to manage the COVID-19 pandemic by developing strategies to control the epidemic. Lockdown, social distancing and random diagnostic tests are among these strategies. In this study, we formulated a mathematical model to investigate the impact of employing random diagnostic tests to detect asymptomatic COVID-19 patients. The model has been examined qualitatively and numerically. Two equilibrium points were obtained: the COVID-19 free equilibrium and the COVID-19 endemic equilibrium. The local and global asymptotic stability of the equilibrium points depends on the control reproduction number $\mathcal{R}_{c}$ . The model was validated by employing the Saudi Ministry of Health COVID-19 dashboard data. Numerical simulations were conducted to substantiate the qualitative results. Further, sensitivity analysis was performed on $\mathcal{R}_{c}$ to scrutinize the significant parameters for combating COVID-19. Finally, different scenarios for implementing random diagnostic tests were explored numerically along with the control strategies applied in Saudi Arabia.

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Citation: Salma M. Al-Tuwairqi, Sara K. Al-Harbi. Modeling the effect of random diagnoses on the spread of COVID-19 in Saudi Arabia[J]. Mathematical Biosciences and Engineering, 2022, 19(10): 9792-9824. doi: 10.3934/mbe.2022456

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Abstract

A correction on

Numerical investigation and improvement of the aerodynamic performance of a modified elliptical-bladed Savonius-style wind turbine. By Sri Kurniati, Sudirman Syam and Arifin Sanusi. AIMS Energy, 2023, Volume 11, Issue 6: 1211–1230. Doi: 10.3934/energy.2023055

The authors would like to make the following corrections to the published paper [1].

On page 1213, we updated the contents of "one symbol statement: ρ" in section 2. The updated contents are as follows:

- ρ is the the density of air,

On page 1215, we updated the contents of "Eq 16" in section 2. The updated contents are as follows:

$\frac{{{\bf{∂}} {\bf{ \pmb{\mathsf{ ϕ}} }}}_{{\bf{ℓ}}}}{{\bf{∂}} \boldsymbol{t}}+{\bf{∇}} \left({{\varnothing }}_{{\bf{ℓ}}}\overrightarrow{\boldsymbol{V}}\right)-{\bf{∇}} \left({\bf{\Gamma }}_{{\bf{ℓ}}}\overrightarrow{\boldsymbol{V}}{{\varnothing }}_{{\bf{ℓ}}}\right) = {\boldsymbol{R}}_{{\bf{ℓ}}}$

(16)

On page 1216, we updated the contents of "Table 2" in section 2. The updated contents are as follows:

Table 2. The terms in the general transfer equation Eq 16.

$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \frac{{\partial {\rm{ \mathsf{ ϕ} }}}_{\ell }}{\partial t}+\nabla \left({\varnothing }_{\ell }\overrightarrow{V}\right)-\nabla \left({\mathrm{\Gamma }}_{\ell }\overrightarrow{V}{\varnothing }_{\ell }\right)={R}_{\ell } \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(16)$
$l$	${\varnothing }_{\ell }$	${\mathrm{\Gamma }}_{\ell }$
1	U	$vt$	$-\frac{1}{\rho }\frac{\partial \rho }{\partial x}+\frac{\partial }{\partial x}\left(vt\frac{\partial u}{\partial x}\right)+\frac{\partial }{\partial y}\left(vt\frac{\partial v}{\partial x}\right)+\frac{\partial }{\partial z}\left(vt\frac{\partial w}{\partial x}\right)+gx$
2	V	$vt$	$-\frac{1}{\rho }\frac{\partial \rho }{\partial y}+\frac{\partial }{\partial x}\left(vt\frac{\partial u}{\partial y}\right)+\frac{\partial }{\partial y}\left(vt\frac{\partial v}{\partial y}\right)+\frac{\partial }{\partial z}\left(vt\frac{\partial w}{\partial y}\right)+gy$
3	W	$vt$	$-\frac{1}{\rho }\frac{\partial \rho }{\partial z}+\frac{\partial }{\partial x}\left(vt\frac{\partial u}{\partial z}\right)+\frac{\partial }{\partial y}\left(vt\frac{\partial v}{\partial z}\right)+\frac{\partial }{\partial z}\left(vt\frac{\partial w}{\partial z}\right)+gz$
4	1	0	0
5	K	$vt/$	$G-\varepsilon$
6	$\varepsilon$	$vt/$	${C}_{1}\frac{\varepsilon }{k}G-{c}_{2}\frac{\varepsilon }{k}\varepsilon$

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Conflict of interest

All authors declare no conflicts of interest in this paper.

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