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. 2025 Mar 4;15(1):7587.
doi: 10.1038/s41598-025-90915-2.

Dynamical analysis and numerical assessment of the 2019-nCoV virus transmission with optimal control

Shuo Li  1 , Tahir Khan  2 , Qasem M Al-Mdallal  3 , Fuad A Awwad  4 , Gul Zaman  5
Affiliations

Dynamical analysis and numerical assessment of the 2019-nCoV virus transmission with optimal control

Shuo Li et al. Sci Rep. .

Abstract

In this article, we discuss the qualitative analysis and develop an optimal control mechanism to study the dynamics of the novel coronavirus disease (2019-nCoV) transmission using an epidemiological model. With the help of a suitable mathematical model, health officials often can take positive measures to control the infection. To develop the model, we assume two disease transmission sources (humans and reservoirs) keeping in view the characteristics of novel coronavirus transmission. We formulate the model to study the temporal dynamics and determine an optimal control mechanism to minimize the infected population and control the spreading of the novel coronavirus disease propagation. In addition, to understand the significance of each model parameter, we compute the threshold quantity and perform the sensitivity analysis of the basic reproductive number. Based on the temporal dynamics of the model and sensitivity analysis of the threshold parameter, we develop a control mechanism to identify the best control policy for eradicating the disease. We then conduct numerical experiments using large-scale numerical simulations to validate the theoretical findings.

Keywords: Epidemiological model; Numerical simulation; Optimal control theory; Stability analysis; Threshold parameter.

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Conflict of interest statement

Declarations. Competing interests: The authors declare no competing interests.

Figures

Figure 1
Figure 1
The schematic diagram for the transmission of 2019-nCoV.
Figure 2
Figure 2
Estimated values of the threshold quantity formula image) for the 2019-nCoV virus in China.
Figure 3
Figure 3
The graphical results show the sensitivity analysis of the threshold quantity (formula image) and its relative impact against the variations of various epidemic parameters formula image. For this analysis, the numerical values of the parameters used are formula image formula image, formula image, formula image, formula image, formula image, formula image, formula image.
Figure 4
Figure 4
The graphical results show the sensitivity analysis of the threshold quantity (formula image) and its relative impact against the variation of various epidemic parameters formula image. We use the numerical values of other parameters formula image, formula image, formula image, formula image.
Figure 5
Figure 5
The dynamics of the model in the case whenever formula image and formula image. For this, we use the value of the parameters: formula image, formula image, formula image, formula image, formula image, formula image, formula image and formula image.
Figure 6
Figure 6
The dynamics of the model compartmental population in the case whenever formula image and formula image. For this, we use the value of the parameters are formula image, formula image, formula image, formula image, formula image, formula image, formula image and formula image.
Figure 7
Figure 7
The graphical visualization of the control problem with and without controls.
Figure 8
Figure 8
The plots visualizes the dynamics of time dependent controls measures.
See this image and copyright information in PMC

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