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    Modelling and analysis of fractional-order vaccination model for control of COVID-19 outbreak using real data
    (Amer Inst Mathematical Sciences-Aims, 2023) Joshi, Hardik; Jha, Brajesh Kumar; Yavuz, Mehmet
    In this paper, we construct the SV1V2EIR model to reveal the impact of two-dose vaccination on COVID-19 by using Caputo fractional derivative. The feasibility region of the proposed model and equilibrium points is derived. The basic reproduction number of the model is derived by using the next-generation matrix method. The local and global stability analysis is performed for both the disease-free and endemic equilibrium states. The present model is validated using real data reported for COVID-19 cumulative cases for the Republic of India from 1 January 2022 to 30 April 2022. Next, we conduct the sensitivity analysis to examine the effects of model parameters that affect the basic reproduction number. The Laplace Adomian decomposition method (LADM) is implemented to obtain an approximate solution. Finally, the graphical results are presented to examine the impact of the first dose of vaccine, the second dose of vaccine, disease transmission rate, and Caputo fractional derivatives to support our theoretical results.
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    Numerical Analysis of Compound Biochemical Calcium Oscillations Process in Hepatocyte Cells
    (Wiley-V C H Verlag Gmbh, 2024) Joshi, Hardik; Yavuz, Mehmet
    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 G(alpha) 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 G(alpha) 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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    Stability analysis of a non-singular fractional-order covid-19 model with nonlinear incidence and treatment rate
    (Iop Publishing Ltd, 2023) Joshi, Hardik; Yavuz, Mehmet; Townley, Stuart; Jha, Brajesh Kumar
    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.
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    Transition dynamics between a novel coinfection model of fractional-order for COVID-19 and tuberculosis via a treatment mechanism
    (Springer Heidelberg, 2023) Joshi, Hardik; Yavuz, Mehmet
    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.