RESUMO
In the current article, we aim to study in detail a novel coronavirus (2019-nCoV or COVID-19) mathematical model for different aspects under Caputo fractional derivative. First, from analysis point of view, existence is necessary to be investigated for any applied problem. Therefore, we used fixed point theorem's due to Banach's and Schaefer's to establish some sufficient results regarding existence and uniqueness of the solution to the proposed model. On the other hand, stability is important in respect of approximate solution, so we have developed condition sufficient for the stability of Ulam-Hyers and their different types for the considered system. In addition, the model has also been considered for semianalytical solution via Laplace Adomian decomposition method (LADM). On Matlab, by taking some real data about Pakistan, we graph the obtained results. In the last of the manuscript, a detail discussion and brief conclusion are provided.
RESUMO
This manuscript addressing the dynamics of fractal-fractional type modified SEIR model under Atangana-Baleanu Caputo (ABC) derivative of fractional order y and fractal dimension p for the available data in Pakistan. The proposed model has been investigated for qualitative analysis by applying the theory of non-linear functional analysis along with fixed point theory. The fractional Adams-bashforth iterative techniques have been applied for the numerical solution of the said model. The Ulam-Hyers (UH) stability techniques have been derived for the stability of the considered model. The simulation of all compartments has been drawn against the available data of covid-19 in Pakistan. The whole study of this manuscript illustrates that control of the effective transmission rate is necessary for stoping the transmission of the outbreak. This means that everyone in the society must change their behavior towards self-protection by keeping most of the precautionary measures sufficient for controlling covid-19.
