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 $R_0$ 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 $R_0$ 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.

In this article, the Caputo fractional derivative operator of different orders $ 0 < \alpha\leq1 $ is applied to formulate the fractional-order model of the COVID-19 pandemic. The existence and boundedness of the solutions of the model are investigated by using the Gronwall-Bellman inequality. Further, the uniqueness of the model solutions is established by using the fixed-point theory. The Laplace Adomian decomposition method is used to obtain an approximate solution of the nonlinear system of fractional-order differential equations of the model with a different fractional-order $ \alpha $ for every compartment in the model. Finally, graphical presentations are presented to show the effects of other fractional parameters $ \alpha $ on the obtained approximate solutions.

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.

In this article, a mathematical model of the COVID-19 pandemic with control parameters is introduced. The main objective of this study is to determine the most effective model for predicting the transmission dynamic of COVID-19 using a deterministic model with control variables. For this purpose, we introduce three control variables to reduce the number of infected and asymptomatic or undiagnosed populations in the considered model. Existence and necessary optimal conditions are also established. The Grünwald-Letnikov non-standard weighted average finite difference method (GL-NWAFDM) is developed for solving the proposed optimal control system. Further, we prove the stability of the considered numerical method. Graphical representations and analysis are presented to verify the theoretical results.

For the purpose of analyzing the Omicron pandemic, we build a novel S E I a I s I o H R mathematical model. The fundamental properties of the model are studied, including boundedness, uniqueness, and existence. The boundedness of the model’s solution is examined by solving the fractional Gronwall’s inequality using the Laplace transform method. Using the Picard-Lindelöf theorem, we verify the solution’s existence and uniqueness. The next-generation matrix is used to compute R o (the basic reproduction number), which is significant in the mathematical modeling of infectious diseases. It is demonstrated that both the endemic and disease-free equilibrium solutions are globally and locally asymptotically stable. We also conducted a sensitivity analysis of the parameters based on R o . Moreover, the model is extended by employing optimal control theory to examine the effects of certain control strategies. Finally, numerical simulations are performed to validate the model.

The SEIQHR model, introduced in this study, serves as a valuable tool for anticipating the emergence of various infectious diseases, such as COVID-19 and illnesses transmitted by insects. An analysis of the model’s qualitative features was conducted, encompassing the computation of the fundamental reproduction number, . It was observed that the disease-free equilibrium point remains singular and locally asymptotically stable when , while the endemic equilibrium point exhibits uniqueness when . Additionally, specific conditions were outlined to guarantee the local asymptotic stability of both equilibrium points. Employing numerical simulations, the graphical representation illustrated the influence of model parameters on disease dynamics and the potential for its eradication across different noninteger orders of the Caputo derivative. In essence, the adoption of a fractional epidemic model contributes to a deeper comprehension and enhanced biological insights into the dynamics of diseases.