An optimal control strategy and Grünwald-Letnikov finite-difference numerical scheme for the fractional-order COVID-19 model

Haq, Ihtisham Ul; Ali, Nigar; Nisar, Kottakkaran Sooppy

doi:10.53391/mmnsa.2022.009

Cited by 13 publications

(7 citation statements)

References 30 publications

(35 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, several analytical solutions of SIR and SEIRD models obtained by different analytical methods are available in the literature. By comparing the proposed models in this paper with those previously introduced (see, e.g., previous studies [39][40][41][42]), the proposed models are more generalized with fractional-order derivatives. Further, most of the solutions for epidemic models are numerical (see, e.g., previous studies [43][44][45]), so analytical exact or approximate solutions are rarely available.…”

Section: Discussionmentioning

confidence: 95%

Conformable mathematical modeling of the COVID‐19 transmission dynamics: A more general study

Thabet

Kendre

2023

Math Methods in App Sciences

View full text Add to dashboard Cite

Many challenges are still faced in bridging the gap between mathematical modeling and biological sciences. Measuring population immunity to assess the epidemiology of health and disease is a challenging task and is currently an active area of research. However, to meet these challenges, mathematical modeling is an effective technique in shaping the population dynamics that can help disease control. In this paper, we introduce a susceptible–infected–recovered (SIR) model and a susceptible–exposed–infected–recovered–deceased (SEIRD) model based on conformable space‐time partial differential equations (PDEs) for the coronavirus disease 2019 (COVID‐19) pandemic. As efficient analytical tools, we present new modifications based on the fractional exponential rational function method (ERFM) and an analytical technique based on the Adomian decomposition method for obtaining the solutions for the proposed models. These analytical approaches are more efficacious for obtaining analytical solutions for nonlinear systems of PDEs with conformable derivatives. The interesting result of this paper is that it yields new exact and approximate solutions to the proposed COVID‐19 pandemic models with conformable space‐time partial derivatives.

show abstract

Section: Discussionmentioning

confidence: 95%

Conformable mathematical modeling of the COVID‐19 transmission dynamics: A more general study

Thabet

Kendre

2023

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…Mathematical models in epidemiology are great tools that can help us to understand the transmission dynamics of COVID-19 Ahmad et al (2022), Allegretti et al (2021), Biswas et al (2020), Erturk and Kumar (2020), Gao et al (2020), Kumar et al (2020), Naik et al (2020aNaik et al ( , 2020b, Rajagopal et al (2020), Sene (2020), Kumar and Erturk (2021), Naik et al (2021), Safare et al (2021), Sitthiwirattham et al (2021), Özköse et al (2022), , Karim et al (2022), Kurmi and Chouhan (2022), Pandey et al (2022), Guo and Li (2022), Haq et al (2022), Guo (2022a, 2022b), Pérez and Oluyori (2022), Swati (2022), Joshi et al (2023). It captures all the scenarios in a very compact form and by proper analysis of these models show, for example, (I) how the disease spreads worldwide, (II) how much population is affected, (III) how to constrain COVID-19.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of a non-singular fractional-order covid-19 model with nonlinear incidence and treatment rate

Joshi¹,

Yavuz

Townley

et al. 2023

Phys. Scr.

View full text Add to dashboard Cite

In this paper, a non-singular SIR model with the Mittag-Leffler law is proposed. The nonlinear Beddington-DeAngelis infection rate and Holling type II treatment rate are used. The qualitative properties of the SIR model are discussed in detail. The local and global stability of the model are analyzed. Moreover, some conditions are developed to guarantee local and global asymptotic stability. Finally, numerical simulations are provided to support the theoretical results and used to analyze the impact of face masks, social distancing, quarantine, lockdown, immigration, treatment rate of the disease, and limitation in treatment resources on COVID-19. The graphical results show that face masks, social distancing, quarantine, lockdown, immigration, and effective treatment rates significantly reduce the infected population over time. In contrast, limitation in the availability of treatment raises the infected population.

show abstract

“…The treatment of coinfection is indigent due to the dynamic behavior of COVID-19 and TB. An enormous amount of literature is available to understand the transmission dynamics of the COVID-19-only model [ 2 – 5 , 7 , 13 , 14 , 17 , 19 , 25 – 28 , 30 , 31 , 33 , 36 , 37 , 40 , 45 ], the TB-only model [ 1 , 11 , 29 , 41 , 46 , 47 , 53 ], and other models [ 12 , 32 , 35 , 44 , 48 ]. But to date, there is seldom evidence available to study the transmission dynamics of COVID-19 and TB coinfection.…”

Section: Introductionmentioning

confidence: 99%

Transition dynamics between a novel coinfection model of fractional-order for COVID-19 and tuberculosis via a treatment mechanism

Joshi¹,

Yavuz

2023

Eur. Phys. J. Plus

View full text Add to dashboard Cite

In this paper, a fractional-order coinfection model for the transmission dynamics of COVID-19 and tuberculosis is presented. The positivity and boundedness of the proposed coinfection model are derived. The equilibria and basic reproduction number of the COVID-19 sub-model, Tuberculosis sub-model, and COVID-19 and Tuberculosis coinfection model are derived. The local and global stability of both the COVID-19 and Tuberculosis sub-models are discussed. The equilibria of the coinfection model are locally asymptotically stable under certain conditions. Later, the impact of COVID-19 on TB and TB on COVID-19 is analyzed. Finally, the numerical simulation is carried out to assess the effect of various biological parameters in the transmission dynamics of COVID-19 and Tuberculosis coinfection.

show abstract

An optimal control strategy and Grünwald-Letnikov finite-difference numerical scheme for the fractional-order COVID-19 model

Cited by 13 publications

References 30 publications

Conformable mathematical modeling of the COVID‐19 transmission dynamics: A more general study

Conformable mathematical modeling of the COVID‐19 transmission dynamics: A more general study

Stability analysis of a non-singular fractional-order covid-19 model with nonlinear incidence and treatment rate

Transition dynamics between a novel coinfection model of fractional-order for COVID-19 and tuberculosis via a treatment mechanism

Contact Info

Product

Resources

About