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(searched for: doi:10.53391/mmnsa.2022.009)
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Published: 28 December 2022
by MDPI
Journal: Mathematics
Mathematics, Volume 11; https://doi.org/10.3390/math11010142

Abstract:
A mathematical model revealing the transmission mechanism of COVID-19 is produced and theoretically examined, which has helped us address the disease dynamics and treatment measures, such as vaccination for susceptible patients. The mathematical model containing the whole population was partitioned into six different compartments, represented by the SVEIQR model. Important properties of the model, such as the nonnegativity of solutions and their boundedness, are established. Furthermore, we calculated the basic reproduction number, which is an important parameter in infection models. The disease-free equilibrium solution of the model was determined to be locally and globally asymptotically stable. When the basic reproduction number R0 is less than one, the disease-free equilibrium point is locally asymptotically stable. To discover the approximative solution to the model, a general numerical approach based on the Haar collocation technique was developed. Using some real data, the sensitivity analysis of R0 was shown. We simulated the approximate results for various values of the quarantine and vaccination populations using Matlab to show the transmission dynamics of the Coronavirus-19 disease through graphs. The validation of the results by the Simulink software and numerical methods shows that our model and adopted methodology are appropriate and accurate and could be used for further predictions for COVID-19.
Published: 26 September 2022
by MDPI
Mathematical and Computational Applications, Volume 27; https://doi.org/10.3390/mca27050082

Abstract:
This article develops a within-host viral kinetics model of SARS-CoV-2 under the Caputo fractional-order operator. We prove the results of the solution’s existence and uniqueness by using the Banach mapping contraction principle. Using the next-generation matrix method, we obtain the basic reproduction number. We analyze the model’s endemic and disease-free equilibrium points for local and global stability. Furthermore, we find approximate solutions for the non-linear fractional model using the Modified Euler Method (MEM). To support analytical findings, numerical simulations are carried out.
, Nigar Ali, Shabir Ahmad
Mathematical Modelling and Control, Volume 2, pp 228-242; https://doi.org/10.3934/mmc.2022022

Abstract:
The Covid illness (COVID-19), which has emerged, is a highly infectious viral disease. This disease led to thousands of infected cases worldwide. Several mathematical compartmental models have been examined recently in order to better understand the Covid disease. The majority of these models rely on integer-order derivatives, which are incapable of capturing the fading memory and crossover behaviour observed in many biological phenomena. Similarly, the Covid disease is investigated in this paper by exploring the elements of COVID-19 pathogens using the non-integer Atangana-Baleanu-Caputo derivative. Using fixed point theory, we demonstrate the existence and uniqueness of the model's solution. All basic properties for the given model are investigated in addition to Ulam-Hyers stability analysis. The numerical scheme is based on Lagrange's interpolation polynomial developed to estimate the model's approximate solution. Using real-world data, we simulate the outcomes for different fractional orders in Matlab to illustrate the transmission patterns of the present Coronavirus-19 epidemic through graphs.
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