A new mathematical model of multi-faced COVID-19 formulated by fractional derivative chains

A new fractional mathematical model to study the impact of vaccination on COVID-19 outbreaks

This study proposes a new fractional mathematical model to study the impact of vaccination on COVID-19 outbreaks by categorizing infected people into non-vaccinated, first dose-vaccinated, and second dose-vaccinated groups and exploring the transmission dynamics of the disease outbreaks. We present a non-linear integer order mathematical model of COVID-19 dynamics and modify it by introducing Caputo fractional derivative operator. We start by proving the good state of the model and then calculating its reproduction number. The Caputo fractional-order model is discretized by applying a reliable numerical technique. The model is proven to be stable. The classical model is fitted to the corresponding cumulative number of daily reported cases during the vaccination regime in India between 01 August 2021 and 21 July 2022. We explore the sensitivities of the reproduction number with respect to the model parameters. It is shown that the effective transmission rate and the recovery rate of unvaccinated infected individuals are the most sensitive parameters that drive the transmission dynamics of the pandemic in the population. Numerical simulations are used to demonstrate the applicability of the proposed fractional mathematical model via the memory index at different values of 0 . 7 , 0 . 8 , 0 . 9 and 1. We discuss the epidemiological significance of the findings and provide perspectives on future health policy tendencies. For instance, efforts targeting a decrease in the transmission rate and an increase in the recovery rate of non-vaccinated infected individuals are required to ensure virus-free population. This can be achieved if the population strictly adhere to precautionary measures, and prompt and adequate treatment is provided for non-vaccinated infectious individuals. Also, given the ongoing community spread of COVID-19 in India and almost the pandemic-affected countries worldwide, the need to scale up the effort of mass vaccination policy cannot be overemphasized in order to reduce the number of unvaccinated infections with a view to halting the transmission dynamics of the disease in the population.

The effect of the Caputo fractional difference operator on a new discrete COVID-19 model

This study aims to generalize the discrete integer-order SEIR model to obtain the novel discrete fractional-order SEIR model of COVID-19 and study its dynamic characteristics. Here, we determine the equilibrium points of the model and discuss the stability analysis of these points in detail. Then, the non-linear dynamic behaviors of the suggested discrete fractional model for commensurate and incommensurate fractional orders are investigated through several numerical techniques, including maximum Lyapunov exponents, phase attractors, bifurcation diagrams and C 0 algorithm. Finally, we fitted the model with actual data to verify the accuracy of our mathematical study of the stability of the fractional discrete COVID-19 model.