Mathematical Modeling to Determine the Fifth Wave of COVID-19 in South Africa.

The aim of this study is to predict the COVID-19 infection fifth wave in South Africa using the Gaussian mixture model for the available data of the early four waves for March 18, 2020-April 13, 2022. The quantification data is considered, and the time unit is used in days. We give the modeling of COVID-19 in South Africa and predict the future fifth wave in the country. Initially, we use the Gaussian mixture model to characterize the coronavirus infection to fit the early reported cases of four waves and then to predict the future wave. Actual data and the statistical analysis using the Gaussian mixture model are performed which give close agreement with each other, and one can able to predict the future wave. After that, we fit and predict the fifth wave in the country and it is predicted to be started in the last week of May 2022 and end in the last week of September 2022. It is predicted that the peak may occur on the third week of July 2022 with a high number of 19383 cases. The prediction of the fifth wave can be useful for the health authorities in order to prepare themselves for medical setup and other necessary measures. Further, we use the result obtained from the Gaussian mixture model in the new model formulated in terms of differential equations. The differential equations model is simulated for various values of the model parameters in order to determine the disease's possible eliminations.

On nonlinear dynamics of COVID-19 disease model corresponding to nonsingular fractional order derivative.

This manuscript is devoted to investigate the mathematical model of fractional-order dynamical system of the recent disease caused by Corona virus. The said disease is known as Corona virus infectious disease (COVID-19). Here we analyze the modified SEIR pandemic fractional order model under nonsingular kernel type derivative introduced by Atangana, Baleanu and Caputo ([Formula: see text]) to investigate the transmission dynamics. For the validity of the proposed model, we establish some qualitative results about existence and uniqueness of solution by using fixed point approach. Further for numerical interpretation and simulations, we utilize Adams-Bashforth method. For numerical investigations, we use some available clinical data of the Wuhan city of China, where the infection initially had been identified. The disease free and pandemic equilibrium points are computed to verify the stability analysis. Also we testify the proposed model through the available data of Pakistan. We also compare the simulated data with the reported real data to demonstrate validity of the numerical scheme and our analysis.

The generalized viscosity explicit rules for a family of strictly pseudo-contractive mappings in a q-uniformly smooth Banach space.

In this paper, we construct an iterative method by a generalized viscosity explicit rule for a countable family of strictly pseudo-contractive mappings in a q-uniformly smooth Banach space. We prove strong convergence theorems of proposed algorithm under some mild assumption on control conditions. We apply our results to the common fixed point problem of convex combination of family of mappings and zeros of accretive operator in Banach spaces. Furthermore, we also give some numerical examples to support our main results.