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

Joshi, Hardik; Yavuz, Mehmet; Townley, Stuart; Jha, Brajesh Kumar

doi:10.1088/1402-4896/acbe7a

Cited by 33 publications

(16 citation statements)

References 51 publications

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“…The integer order differential equation is a local operator in nature and is not capable of characterizing the problems related to biomedicine and biology. [62][63][64][65][66][67][68] The fractional order differential equation is a nonlocal operator and hence well describes the calcium oscillation and bursting in a cellular process. Thus, by considering this fact the present hepatocytes model can be recast in the form of fractional order as…”

Section: And [Ca 2+mentioning

confidence: 99%

“…The integer order differential equation is a local operator in nature and is not capable of characterizing the problems related to biomedicine and biology. [ 62–68 ] The fractional order differential equation is a non‐local operator and hence well describes the calcium oscillation and bursting in a cellular process. Thus, by considering this fact the present hepatocytes model can be recast in the form of fractional order as

\begin{matrix} \begin{matrix} true \\ right_{0}^{C} D_{t}^{ϑ} [G_{α}] & left badbreak= k_{1} goodbreak+ k_{2} \cdot G_{α} goodbreak- k_{3} ((), \frac{G_{α} \cdot P L C}{G_{α} + k_{4}}) goodbreak- k_{5} ((), \frac{G_{α} \cdot C a^{2 +}}{G_{α} + k_{6}}) \\ right_{0}^{C} D_{t}^{ϑ} [P L C] & left badbreak= k_{7} \cdot G_{α} goodbreak- k_{8} ((), \frac{P L C}{P L C + k_{9}}) \\ right_{0}^{C} D_{t}^{ϑ} [C a^{2 +}] & left badbreak= k_{10} ((), \frac{P L C \cdot C a^{2 +} \cdot C a_{E R}^{2 +}}{C a_{E R}^{2 +} + k_{11}}) goodbreak+ k_{12} \cdot P L C goodbreak+ k_{13} \cdot G_{α} \\ left badbreak- k_{14} ((), \frac{C a^{2 +}}{C a^{2 +} + k_{15}}) goodbreak- k_{16} ((), \frac{C a^{2 +}}{C a^{2 +} + k_{17}}) \\ right_{0}^{C...} \end{matrix} \end{matrix}

…”

Section: Mathematical Model For Hepatocytesmentioning

confidence: 99%

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Numerical Analysis of Compound Biochemical Calcium Oscillations Process in Hepatocyte Cells

Joshi,

Yavuz

2024

Advanced Biology

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The hepatocyte cells regulate the wide range of liver function by moderating cellular activities such as lipid, protein metabolism, carbohydrate, and interact with other cells for proliferation and maintenance. In hepatocyte cells, the concentration of calcium uptake is quite extensive from various agonists such as active subunit, active phospholipase C, free calcium in the cytosol, and endoplasmic reticulum. The overproduction and degradation of calcium signals can cause homeostasis, liver inflammation, and liver diseases. The spatiotemporal behavior of calcium oscillation reveals the physiological role of these cellular entities in understanding the process of production and degradation. No computational attempt has been registered to date on the compound calcium regulation of these cellular entities including the memory of cells. Hence, the authors proposed a fractional order compartmental model that systematically simulates the exchange of calcium intake in cellular entities. The nonlinear equations of the rate of changes in the active subunit, active phospholipase C, free calcium in the cytosol, and endoplasmic reticulum are coupled to form a nonlinear fractional order initial value problem. The existence and uniqueness, stability analysis of the model is performed that validate the theoretical results and explore the dynamic behaviour of calcium oscillation in each compartment.

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Section: And [Ca 2+mentioning

confidence: 99%

\begin{matrix} \begin{matrix} true \\ right_{0}^{C} D_{t}^{ϑ} [G_{α}] & left badbreak= k_{1} goodbreak+ k_{2} \cdot G_{α} goodbreak- k_{3} ((), \frac{G_{α} \cdot P L C}{G_{α} + k_{4}}) goodbreak- k_{5} ((), \frac{G_{α} \cdot C a^{2 +}}{G_{α} + k_{6}}) \\ right_{0}^{C} D_{t}^{ϑ} [P L C] & left badbreak= k_{7} \cdot G_{α} goodbreak- k_{8} ((), \frac{P L C}{P L C + k_{9}}) \\ right_{0}^{C} D_{t}^{ϑ} [C a^{2 +}] & left badbreak= k_{10} ((), \frac{P L C \cdot C a^{2 +} \cdot C a_{E R}^{2 +}}{C a_{E R}^{2 +} + k_{11}}) goodbreak+ k_{12} \cdot P L C goodbreak+ k_{13} \cdot G_{α} \\ left badbreak- k_{14} ((), \frac{C a^{2 +}}{C a^{2 +} + k_{15}}) goodbreak- k_{16} ((), \frac{C a^{2 +}}{C a^{2 +} + k_{17}}) \\ right_{0}^{C...} \end{matrix} \end{matrix}

…”

Section: Mathematical Model For Hepatocytesmentioning

confidence: 99%

Numerical Analysis of Compound Biochemical Calcium Oscillations Process in Hepatocyte Cells

Joshi,

Yavuz

2024

Advanced Biology

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“…The impact of the environment on the transmission dynamics of COVID-19 patterns has been studied in the given literature [16,17]. The impact of quarantine and social distancing on the transmission dynamics of COVID-19 is explored in the given literature [18,19]. The impact of vaccination on the transmission dynamics of COVID-19 is explored in the given literature [20,21].…”

Section: Introductionmentioning

confidence: 99%

Mechanistic insights of COVID-19 dynamics by considering the influence of neurodegeneration and memory trace

Joshi

2024

Phys. Scr.

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COVID-19 has been declared a global pandemic as it disturbs education, society, agriculture, the economy, poverty, death rate, social development, mental psychology, and many more. Neurodegenerative disease is a brain disorder associated with several pathological factors along with mental psychology. This paper introduces a mathematical model to inspect mechanistic insights into COVID-19 dynamics by considering the influence of neurodegeneration and memory trace. The analysis of the proposed model and the existence and uniqueness of the model are derived using the ﬁxed-point criteria. A numerical experiment is presented to validate the theoretical results and examine the impact of various biological parameters, the influence of neurodegeneration, and memory trace on the transmission dynamics of COVID-19.

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“…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

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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.

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

Cited by 33 publications

References 51 publications

Numerical Analysis of Compound Biochemical Calcium Oscillations Process in Hepatocyte Cells

Numerical Analysis of Compound Biochemical Calcium Oscillations Process in Hepatocyte Cells

Mechanistic insights of COVID-19 dynamics by considering the influence of neurodegeneration and memory trace

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

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