In this article, Coronavirus Disease COVID-19 transmission dynamics were studied to examine the utility of the SEIR compartmental model, using two non-singular kernel fractional derivative operators. This method was used to evaluate the complete memory effects within the model. The Caputo–Fabrizio (CF) and Atangana–Baleanu models were used predicatively, to demonstrate the possible long–term trajectories of COVID-19. Thus, the expression of the basic reproduction number using the next generating matrix was derived. We also investigated the local stability of the equilibrium points. Additionally, we examined the existence and uniqueness of the solution for both extensions of these models. Comparisons of these two epidemic modeling approaches (i.e. CF and ABC fractional derivative) illustrated that, for non-integer
value. The ABC approach had a significant effect on the dynamics of the epidemic and provided new perspective for its utilization as a tool to advance research in disease transmission dynamics for critical COVID-19 cases. Concurrently, the CF approach demonstrated promise for use in mild cases. Furthermore, the integer
value results of both approaches were identical.
Regardless of the existing governmental and public preventive actions for surveillance and controlling the air quality in several regions of the Chennai city in India, the air quality does not meet the desired standard. In this regard, this study employs an ARMA/ARIMA modelling approach for forecasting Respirable Suspended Particulate Matter (RSPM), Sulphur dioxide (SO 2) and Nitrogen dioxide (NO 2) concentration for three most polluted sites in Chennai city. A total of nine univariate linear stochastic models have been developed, three for each of the stations which includes one for each of the specific pollutants in order to forecasts the concentration of each pollutant. The evaluation of the model statistics R 2 values and index of agreement values evince that a significant level of real-time forecasting of the pollutants can be achieved by employing the developed ARMA/ARIMA models. Moreover, the comparisons of actual air pollutant concentration have been carried out with the permissible limit as prescribed by the National ambient air quality standards (NAAQS) of India for assessing the level of pollution of all three locations.
In this study, we report an explicit analytical solution of state-controlled cellular neural network (SC-CNN) based second-order nonautonomous system. The proposed system is modeled with an aid of a generalized two-state-controlled cellular neural network (CNN) equations and experimentally realized by imposing a suitable connection of simple two-state-controlled generalized CNN cells following the report of Swathi et al. [2014]. The chaotic and quasi-periodic dynamics observed from this system have been investigated through an analytical approach for the first time. The intriguing dynamics observed from the system where further substantiated by phase portraits, Poincaré map, power spectra, and “0−1 test.” We trace the transition of the system from periodic to chaos through analytical solutions, which are in good agreement with hardware experiments. Additionally, we show PSpice circuit simulation results for validating our analytical and experimental studies.
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