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This research investigates the heat and mass transfer in 3-D MHD radiative flow of water based hybrid nanofluid over an extending sheet by employing the strength of numerical computing based Lobatto IIIA method. Nanoparticles of aluminum oxide (Al2O3) and silver (Ag) are being used with water (H2O) as base fluid. By considering the heat transfer phenomenon due to thermal radiation effects. The physical flow problem is then modeled into set of PDEs, which are then transmuted into equivalent set of nonlinear ODEs by utilizing the appropriate similarity transformations. The system of ODEs is solved by the computational strength of Lobatto IIIA method to get the various graphical and numerical results for analyzing the impact of various physical constraints on velocity and thermal profiles. Additionally, the heat transfers and skin friction analysis for the fluid flow dynamics is also investigated. The relative errors up to the accuracy level of 1e-15, established the worth and reliability of the computational technique. It is observed that heat transfer rate increases with the increase in magnetic effect, Biot number and rotation parameter.

Background: Mathematical modeling of vector-borne diseases and forecasting of epidemics outbreak are global challenges and big point of concern worldwide. The outbreaks depend on different social and demographic factors based on human mobility structured with the help of mathematical models for vector-borne disease transmission. In Dec 2019, an infectious disease is known as “coronavirus” (officially declared as COVID-19 by WHO) emerged in Wuhan (Capital city of Hubei, China) and spread quickly to all over the china with over 50,000 cases including more than 1000 death within a short period of one month. Multimodal modeling of robust dynamics system is a complex, challenging and fast growing area of the research. Objectives: The main objective of this proposed hybrid computing technique are as follows: The innovative design of the NAR-RBFs neural network paradigm is designed to construct the SITR epidemic differential equation (DE) model to ascertain the different features of the spread of COVID-19. The new set of transformations is introduced for nonlinear input to achieve with a higher level of accuracy, stability, and convergence analysis. Methods: Multimodal modeling of robust dynamics system is a complex, challenging and fast growing area of the research. In this research bimodal spread of COVID-19 is investigated with hybrid model based on nonlinear autoregressive with radial base function (NAR-RBFs) neural network for SITR model. Chaotic and stochastic data of the pandemic. A new class of transformation is presented for the system of ordinary differential equation (ODE) for fast convergence and improvement of desired accuracy level. The proposed transformations convert local optimum values to global values before implementation of bimodal paradigm. Results: This suggested NAR-RBFs model is investigated for the bi-module nature of SITR model with additional feature of fragility in modeling of stochastic variation ability for different cases and scenarios with constraints variation. Best agreement of the proposed bimodal paradigm with outstanding numerical solver is confirmed based on statistical results calculated from MSE, RMSE and MAPE with accuracy level based on mean square error up to 1E-25, which further validates the stability and consistence of bimodal proposed model. Conclusions: This computational technique is shown extraordinary results in terms of accuracy and convergence. The outcomes of this study will be useful in forecasting the progression of COVID-19, the influence of several deciding parameters overspread of COVID-19 and can help for planning, monitoring as well as preventing the spread of COVID-19.

that if there is no control (variables/interventios), 900 out 1000 susceptible individuals may be infected (exposed) in very short period. As such a circumstances no agency fighting against COVID-19 could be successful due to its limited resources.

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In this paper, novel computing paradigm by exploiting the strength of feed-forward artificial neural networks (ANNs) with Levenberg-Marquardt Method (LMM), and Bayesian Regularization Method (BRM) based backpropagation is presented to find the solutions of initial value problems (IVBs) of linear/nonlinear pantograph delay differential equations (LP/NP-DDEs). The dataset for training, testing and validation is created with reference to known standard solutions of LP/NP-DDEs. ANNs are implemented using the said dataset for approximate modeling of the system on mean squared error based merit functions, while learning of the adjustable parameters is conducted with efficacy of LMM (ANN-LMM) and BRMs (ANN-BRM). The performance of the designed algorithms ANN-LMM and ANN-BRM on IVPs of first, second and third order NP-FDEs are verified by attaining a good agreement with the available solutions having accuracy in the range from 10 -5 to 10 -8 and are further endorsed through error histograms and regression measures.

This work analyses thermal effect for a mixed convection flow of Maxwell nanofluid spinning motion produced by rotating and bidirectional stretching cylinder. Impacts of Joule heating and internal heat source/sink are also taken into account for current investigation. Moreover, the flow is exposed to a uniform magnetic field with convective boundary conditions. The modeled equations are converted to set of ODEs through group of similar variables and are then solved by using semi analytical technique HAM. It is observed in this study that, velocity grows up with enhancing values of Maxwell, mixed convection parameters and reduces with growing values of magnetic parameter. Temperature jumps up with increasing values of heat source, Eckert number, Brownian motion,thermophoresis parameter and jumps down with growing values of Prandtl number and heat sink. The concentration is a growing function of thermophoresis parameter and a reducing function of Brownian motion and Schmidt number.

We develop a new mathematical model by including the resistive class together with quarantine class and use it to investigate the transmission dynamics of the novel corona virus disease (COVID-19). Our developed model consists of four compartments, namely the susceptible class, the healthy (resistive) class, the infected class, and the quarantine class, . We derive basic properties like, boundedness and positivity, of our proposed model in a biologically feasible region. To discuss the local as well as the global behaviour of the possible equilibria of the model, we compute the threshold quantity. The linearization and Lyapunov function theory are used to derive conditions for the stability analysis of the possible equilibrium states. We present numerical simulations to support our investigations. The simulations are compared with the available real data for Wuhan city in China, where the infection was initially originated.