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Article: Analysis of a Covid-19 model: Optimal control, stability and simulations

Araz, Seda amp / Iacute, / ğret,

Alexandria Engineering Journal

Abstract: ... In this paper, we analyzed a mathematical model for the spread of COVID-19, we first start with stability ... analysis, present the optimal control for the system The model was extended to the concept of non-local ... Mathematical tools called differential and integral operators are used to model real world problems ...

Abstract	Mathematical tools called differential and integral operators are used to model real world problems in all fields of science as they are able to replicate some behaviors observed in real world like fading memory, long-range dependency, power law, random walk and many others Very recently the world has faced a serious challenge since the breakout of corona-virus started in Wuhan, China The deathly disease has killed about 1720000 and infected more than 2 millions humans around the globe since December 2019 to 21 of April 2020 In this paper, we analyzed a mathematical model for the spread of COVID-19, we first start with stability analysis, present the optimal control for the system The model was extended to the concept of non-local operators for each case, we presented the positiveness of the system solutions We presented numerical solutions are presented for different scenarios
Keywords	covid19
Publisher	WHO
Document type	Article
Note	WHO #Covidence: #836842
Database	COVID19

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Article ; Online: Optimal control analysis of COVID-19 vaccine epidemic model: a case study.

Khan, Arshad Alam / Ullah, Saif / Amin, Rohul

European physical journal plus

2022 Volume 137, Issue 1, Page(s) 156

Abstract: ... stability. In order to investigate the influence of model key parameters on the transmission and controlling ... is restructured to obtained optimal control model by introducing time-dependent control variables ... in controlling COVID-19 outbreak. We formulate the classical epidemic compartmental model by introducing ...

Abstract	The purpose of this research is to explore the complex dynamics and impact of vaccination in controlling COVID-19 outbreak. We formulate the classical epidemic compartmental model by introducing vaccination class. Initially, the proposed mathematical model is analyzed qualitatively. The basic reproductive number is computed and its numerical value is estimated using actual reported data of COVID-19 for Pakistan. The sensitivity analysis is performed to analyze the contribution of model embedded parameters in transmission of the disease. Further, we compute the equilibrium points and discussed its local and global stability. In order to investigate the influence of model key parameters on the transmission and controlling of the disease, we perform numerical simulations describing the impact of various scenarios of vaccine efficacy rate and other controlling measures. Further, on the basis of sensitivity analysis, the proposed model is restructured to obtained optimal control model by introducing time-dependent control variables
Language	English
Publishing date	2022-01-23
Publishing country	Germany
Document type	Journal Article
ISSN	2190-5444
ISSN (online)	2190-5444
DOI	10.1140/epjp/s13360-022-02365-8
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Analysis of a Covid-19 model

İğret Araz, Seda

Alexandria Engineering Journal ; ISSN 1110-0168

Optimal control, stability and simulations

2020

Keywords	General Engineering ; covid19
Language	English
Publisher	Elsevier BV
Publishing country	us
Document type	Article ; Online
DOI	10.1016/j.aej.2020.09.058
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: Bifurcation and optimal control analysis of HIV/AIDS and COVID-19 co-infection model with numerical simulation.

Kotola, Belela Samuel / Teklu, Shewafera Wondimagegnhu / Abebaw, Yohannes Fissha

PloS one

2023 Volume 18, Issue 5, Page(s) e0284759

Abstract: ... numerical simulations for both the deterministic model and the model incorporating optimal controls and ... In this paper, a mathematical model for the transmission dynamics of HIV/AIDS and COVID-19 co-infection ... of the optimal control problem applying the combinations of all the possible protection and treatment strategies ...

Abstract	HIV/AIDS and COVID-19 co-infection is a common global health and socio-economic problem. In this paper, a mathematical model for the transmission dynamics of HIV/AIDS and COVID-19 co-infection that incorporates protection and treatment for the infected (and infectious) groups is formulated and analyzed. Firstly, we proved the non-negativity and boundedness of the co-infection model solutions, analyzed the single infection models steady states, calculated the basic reproduction numbers using next generation matrix approach and then investigated the existence and local stabilities of equilibriums using Routh-Hurwiz stability criteria. Then using the Center Manifold criteria to investigate the proposed model exhibited the phenomenon of backward bifurcation whenever its effective reproduction number is less than unity. Secondly, we incorporate time dependent optimal control strategies, using Pontryagin's Maximum Principle to derive necessary conditions for the optimal control of the disease. Finally, we carried out numerical simulations for both the deterministic model and the model incorporating optimal controls and we found the results that the model solutions are converging to the model endemic equilibrium point whenever the model effective reproduction number is greater than unity, and also from numerical simulations of the optimal control problem applying the combinations of all the possible protection and treatment strategies together is the most effective strategy to drastically minimizing the transmission of the HIV/AIDS and COVID-19 co-infection in the community under consideration of the study.
MeSH term(s)	Humans ; Acquired Immunodeficiency Syndrome/epidemiology ; Coinfection/epidemiology ; COVID-19/epidemiology ; Computer Simulation ; Models, Theoretical ; Basic Reproduction Number
Language	English
Publishing date	2023-05-05
Publishing country	United States
Document type	Journal Article
ZDB-ID	2267670-3
ISSN	1932-6203 ; 1932-6203
ISSN (online)	1932-6203
ISSN	1932-6203
DOI	10.1371/journal.pone.0284759
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Dynamic behavior analysis of an SVIR epidemic model with two time delays associated with the COVID-19 booster vaccination time.

Lv, Zimeng / Liu, Xinyu / Ding, Yuting

Mathematical biosciences and engineering : MBE

2023 Volume 20, Issue 4, Page(s) 6030–6061

Abstract: ... the optimal time of booster vaccination and predict when the outbreak can be effectively controlled. ... Second, we theoretically analyze the existence and stability of equilibrium and further study the dynamic ... Since the outbreak of COVID-19, there has been widespread concern in the community, especially ...

Abstract	Since the outbreak of COVID-19, there has been widespread concern in the community, especially on the recent heated debate about when to get the booster vaccination. In order to explore the optimal time for receiving booster shots, here we construct an SVIR model with two time delays based on temporary immunity. Second, we theoretically analyze the existence and stability of equilibrium and further study the dynamic properties of Hopf bifurcation. Then, the statistical analysis is conducted to obtain two groups of parameters based on the official data, and numerical simulations are carried out to verify the theoretical analysis. As a result, we find that the equilibrium is locally asymptotically stable when the booster vaccination time is within the critical value. Moreover, the results of the simulations also exhibit globally stable properties, which might be more beneficial for controlling the outbreak. Finally, we propose the optimal time of booster vaccination and predict when the outbreak can be effectively controlled.
MeSH term(s)	Humans ; COVID-19/epidemiology ; COVID-19/prevention & control ; Epidemics ; Disease Outbreaks/prevention & control ; Research Design ; Vaccination
Language	English
Publishing date	2023-04-26
Publishing country	United States
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	2265126-3
ISSN	1551-0018 ; 1551-0018
ISSN (online)	1551-0018
ISSN	1551-0018
DOI	10.3934/mbe.2023261
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Article ; Online: Stability analysis and optimal control of COVID-19 with quarantine and media awareness.

Zhang, Jiajia / Qiao, Yuanhua / Zhang, Yan

Mathematical biosciences and engineering : MBE

2022 Volume 19, Issue 5, Page(s) 4911–4932

Abstract: In this paper, an improved COVID-19 model is given to investigate the influence of treatment and ... the given conditions. An object function is introduced to explore the optimal control strategy concerning treatment and ... awareness is given for prevention and treatment of COVID-19. ...

Abstract	In this paper, an improved COVID-19 model is given to investigate the influence of treatment and media awareness, and a non-linear saturated treatment function is introduced in the model to lay stress on the limited medical conditions. Equilibrium points and their stability are explored. Basic reproduction number is calculated, and the global stability of the equilibrium point is studied under the given conditions. An object function is introduced to explore the optimal control strategy concerning treatment and media awareness. The existence, characterization and uniqueness of optimal solution are studied. Several numerical simulations are given to verify the analysis results. Finally, discussion on treatment and media awareness is given for prevention and treatment of COVID-19.
MeSH term(s)	Basic Reproduction Number ; COVID-19/prevention & control ; Communications Media ; Epidemics/prevention & control ; Humans ; Quarantine
Language	English
Publishing date	2022-04-16
Publishing country	United States
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	2265126-3
ISSN	1551-0018 ; 1551-0018
ISSN (online)	1551-0018
ISSN	1551-0018
DOI	10.3934/mbe.2022230
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Article ; Online: Dynamic analysis and optimal control considering cross transmission and variation of information.

Kang, Sida / Hou, Xilin / Hu, Yuhan / Liu, Hongyu

Scientific reports

2022 Volume 12, Issue 1, Page(s) 18104

Abstract: ... from the viral recombination and variation in COVID-19 transmission is applied to information transmission. Virus ... analysis and the sensitivity of the system towards certain control parameters. In particular, the results ... transmission. An S2I4MR model with information crossing and variation is constructed. Then, the local and ...

Abstract	Cross-transmission of information has a profound influence on the progress of science and technology and the discipline integration in the field of education. In this work, knowledge gained from the viral recombination and variation in COVID-19 transmission is applied to information transmission. Virus recombination and virus variation are similar to the crossing and information fusion phenomena in information transmission. An S2I4MR model with information crossing and variation is constructed. Then, the local and global asymptotic stabilities of the information-free equilibrium and information-existence equilibrium are analyzed. Additionally, the basic reproduction number [Formula: see text] of the model is calculated. As such, an optimal control strategy is hereby proposed to promote the cross-transmission of information and generate variant information. The numerical simulations support the results of the theoretical analysis and the sensitivity of the system towards certain control parameters. In particular, the results show that strengthening information crossing promotes the generation of variant information. Furthermore, encouraging information exchange and enhancing education improve the generation of information crossing and information variation.
MeSH term(s)	Humans ; COVID-19 ; Basic Reproduction Number ; Models, Biological
Language	English
Publishing date	2022-10-27
Publishing country	England
Document type	Journal Article
ZDB-ID	2615211-3
ISSN	2045-2322 ; 2045-2322
ISSN (online)	2045-2322
ISSN	2045-2322
DOI	10.1038/s41598-022-21774-4
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Article ; Online: Stability analysis and optimal control of covid-19 with convex incidence rate in Khyber Pakhtunkhawa (Pakistan).

Khan, Amir / Zarin, Rahat / Hussain, Ghulam / Ahmad, Noor Atinah / Mohd, Mohd Hafiz / Yusuf, Abdullahi

Results in physics

2020 Volume 20, Page(s) 103703

Abstract: ... First, we formulate the model without control and study all the basic properties and results including ... The dynamic of covid-19 epidemic model with a convex incidence rate is studied in this article ... we develop a model with suitable optimal control strategies. Our aim is to minimize the infection in the host ...

Abstract	The dynamic of covid-19 epidemic model with a convex incidence rate is studied in this article. First, we formulate the model without control and study all the basic properties and results including local and global stability. We show the global stability of disease free equilibrium using the method of Lyapunov function theory while for disease endemic, we use the method of geometrical approach. Furthermore, we develop a model with suitable optimal control strategies. Our aim is to minimize the infection in the host population. In order to do this, we use two control variables. Moreover, sensitivity analysis complemented by simulations are performed to determine how changes in parameters affect the dynamical behavior of the system. Taking into account the central manifold theory the bifurcation analysis is also incorporated. The numerical simulations are performed in order to show the feasibility of the control strategy and effectiveness of the theoretical results.
Language	English
Publishing date	2020-12-17
Publishing country	Netherlands
Document type	Journal Article
ZDB-ID	2631798-9
ISSN	2211-3797 ; 2211-3797
ISSN (online)	2211-3797
ISSN	2211-3797
DOI	10.1016/j.rinp.2020.103703
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Article ; Online: Dynamic analysis and optimal control considering cross transmission and variation of information

Sida Kang / Xilin Hou / Yuhan Hu / Hongyu Liu

Scientific Reports, Vol 12, Iss 1, Pp 1-

2022 Volume 18

Abstract: ... As such, an optimal control strategy is hereby proposed to promote the cross-transmission of information and generate ... from the viral recombination and variation in COVID-19 transmission is applied to information transmission. Virus ... transmission. An S2I4MR model with information crossing and variation is constructed. Then, the local and ...

Abstract	Abstract Cross-transmission of information has a profound influence on the progress of science and technology and the discipline integration in the field of education. In this work, knowledge gained from the viral recombination and variation in COVID-19 transmission is applied to information transmission. Virus recombination and virus variation are similar to the crossing and information fusion phenomena in information transmission. An S2I4MR model with information crossing and variation is constructed. Then, the local and global asymptotic stabilities of the information-free equilibrium and information-existence equilibrium are analyzed. Additionally, the basic reproduction number $$R_0$$ R 0 of the model is calculated. As such, an optimal control strategy is hereby proposed to promote the cross-transmission of information and generate variant information. The numerical simulations support the results of the theoretical analysis and the sensitivity of the system towards certain control parameters. In particular, the results show that strengthening information crossing promotes the generation of variant information. Furthermore, encouraging information exchange and enhancing education improve the generation of information crossing and information variation.
Keywords	Medicine ; R ; Science ; Q
Subject code	306
Language	English
Publishing date	2022-10-01T00:00:00Z
Publisher	Nature Portfolio
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: Projections and fractional dynamics of COVID-19 with optimal control analysis

Nabi, K. N.

Abstract: ... fractional derivatives. In addition, optimal control problem for fractional system has been designed and ... When the entire world is eagerly waiting for a safe, effective and widely available COVID-19 ... understanding about the future dynamics of COVID-19, a compartmental mathematical model has been proposed ...

Abstract	When the entire world is eagerly waiting for a safe, effective and widely available COVID-19 vaccine, unprecedented spikes of new cases are evident in numerous countries. To gain a deeper understanding about the future dynamics of COVID-19, a compartmental mathematical model has been proposed in this paper incorporating all possible non-pharmaceutical intervention policies. Model parameters have been calibrated using sophisticated trust-region-reflective algorithm and short-term projection results have been illustrated for Argentina, Bangladesh, Brazil, Colombia and India. Control reproduction numbers (Rc) have been calculated in order to get insights about the current epidemic scenario in the above-mentioned countries. Forecasting results depict that the aforesaid countries are having downward trends in daily COVID-19 cases. However, it is highly recommended to use efficacious face coverings and maintain strict physical distancing, as the pandemic is not over in any country. Global sensitivity analysis enlightens the fact that efficacy of face coverings is the most significant parameter, which could significantly control the transmission dynamics of the novel coronavirus compared to other non-pharmaceutical measures. In addition, reduction in effective contact rate with isolated patients is also essential in bringing down the epidemic threshold (Rc) below unity. All necessary graphical simulations have been performed with the help of Caputo-Fabrizio fractional derivatives. In addition, optimal control problem for fractional system has been designed and the existence of unique solution has also been showed by using Picard-Lindelof technique. Finally, the unconditionally stability of the given fractional numerical technique has been proved.
Keywords	covid19
Publisher	MedRxiv; WHO
Document type	Article ; Online
DOI	10.1101/2020.11.17.20233031
Database	COVID19

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