A novel mathematical model for COVID-19 with remedial strategies

Model Development and Prediction of Covid-19 Pandemic in Bangladesh with Nonlinear Incident

We introduce a SEIRD compartmental model to analyze the dynamics of the pandemic in Bangladesh. The multi-wave patterns of the new infective in Bangladesh from the day of the official confirmation to August 15, 2021, are simulated in the proposed SEIRD model. To solve the model equations numerically, we use the RK-45 method. Primarily, we establish some theorems including local and global stability for the proposed model. The analysis shows that the death curve simulated by the model provides a very good agreement with the officially confirmed death data for the Covid-19 pandemic in Bangladesh. Furthermore, the proposed model estimates the duration and peaks of Covid-19 in Bangladesh which are compared with the real data.

The fractional-order discrete COVID-19 pandemic model: stability and chaos

This paper presents and investigates a new fractional discrete COVID-19 model which involves three variables: the new daily cases, additional severe cases and deaths. Here, we analyze the stability of the equilibrium point at different values of the fractional order. Using maximum Lyapunov exponents, phase attractors, bifurcation diagrams, the 0-1 test and approximation entropy (ApEn), it is shown that the dynamic behaviors of the model change from stable to chaotic behavior by varying the fractional orders. Besides showing that the fractional discrete model fits the real data of the pandemic, the simulation findings also show that the numbers of new daily cases, additional severe cases and deaths exhibit chaotic behavior without any effective attempts to curb the epidemic.

A Novel Fractional-Order Discrete SIR Model for Predicting COVID-19 Behavior

During the broadcast of Coronavirus across the globe, many mathematicians made several mathematical models. This was, of course, in order to understand the forecast and behavior of this epidemic’s spread precisely. Nevertheless, due to the lack of much information about it, the application of many models has become difficult in reality and sometimes impossible, unlike the simple SIR model. In this work, a simple, novel fractional-order discrete model is proposed in order to study the behavior of the COVID-19 epidemic. Such a model has shown its ability to adapt to the periodic change in the number of infections. The existence and uniqueness of the solution for the proposed model are examined with the help of the Picard Lindelöf method. Some theoretical results are established in view of the connection between the stability of the fixed points of this model and the basic reproduction number. Several numerical simulations are performed to verify the gained results.

Fractional-Order Discrete-Time SIR Epidemic Model with Vaccination: Chaos and Complexity

This research presents a new fractional-order discrete-time susceptible-infected-recovered (SIR) epidemic model with vaccination. The dynamical behavior of the suggested model is examined analytically and numerically. Through using phase attractors, bifurcation diagrams, maximum Lyapunov exponent and the 0−1 test, it is verified that the newly introduced fractional discrete SIR epidemic model vaccination with both commensurate and incommensurate fractional orders has chaotic behavior. The discrete fractional model gives more complex dynamics for incommensurate fractional orders compared to commensurate fractional orders. The reasonable range of commensurate fractional orders is between γ = 0.8712 and γ = 1, while the reasonable range of incommensurate fractional orders is between γ2 = 0.77 and γ2 = 1. Furthermore, the complexity analysis is performed using approximate entropy (ApEn) and C0 complexity to confirm the existence of chaos. Finally, simulations were carried out on MATLAB to verify the efficacy of the given findings.

Numerical Investigations through ANNs for Solving COVID-19 Model

The current investigations of the COVID-19 spreading model are presented through the artificial neuron networks (ANNs) with training of the Levenberg-Marquardt backpropagation (LMB), i.e., ANNs-LMB. The ANNs-LMB scheme is used in different variations of the sample data for training, validation, and testing with 80%, 10%, and 10%, respectively. The approximate numerical solutions of the COVID-19 spreading model have been calculated using the ANNs-LMB and compared viably using the reference dataset based on the Runge-Kutta scheme. The obtained performance of the solution dynamics of the COVID-19 spreading model are presented based on the ANNs-LMB to minimize the values of fitness on mean square error (M.S.E), along with error histograms, regression, and correlation analysis.

Automated image classification of chest X-rays of COVID-19 using deep transfer learning

INTRODUCTION

In December 2019, the city of Wuhan, located in the Hubei province of China became the epicentre of an outbreak of a pandemic called COVID-19 by the World Health Organisation. The detection of this virus by rRTPCR (Real-Time Reverse Transcription-Polymerase Chain Reaction) tests reported high false negative rate. The manifestations of CXR (Chest X-Ray) images contained salient features of the virus. The objective of this paper is to establish the application of an early automated screening model that uses low computational power coupled with raw radiology images to assist the physicians and radiologists in the early detection and isolation of potential positive COVID-19 patients, to stop the rapid spread of the virus in vulnerable countries with limited hospital capacities and low doctor to patient ratio in order to prevent the escalating death rates.

MATERIALS AND METHODS

Our database consists of 447 and 447 CXR images of COVID-19 and Nofindings respectively, a total of 894 CXR images. They were then divided into 4 parts namely training, validation, testing and local/Aligarh dataset. The 4th (local/Aligarh) folder of the dataset was created to retest the diagnostics efficacy of our model on a developing nation such as India (Images from J.N.M.C., Aligarh, Uttar Pradesh, India). We used an Artificial Intelligence technique called CNN (Convolutional Neural Network). The architecture based on CNN used was MobileNet. MobileNet makes it faster than the ordinary convolutional model, while substantially decreasing the computational cost.

RESULTS

The experimental results of our model show an accuracy of 96.33%. The F1-score is 93% and 96% for the 1st testing and 2nd testing (local/Aligarh) datasets (Tables 3.3 and 3.4). The false negative (FN) value, for the validation dataset is 6 (Fig. 3.6), for the testing dataset is 0 (Fig. 3.7) and that for the local/Aligarh dataset is 2 . The recall/sensitivity of the classifier is 93% and 96% for the 1st testing and 2nd testing (local/Aligarh) datasets (Tables 3.3 and 3.4). The recall/sensitivity for the detection of specifically COVID-19 (+) for the testing dataset is 88% and for the locally acquired dataset from India is 100%. The False Negative Rate (FNR) is 12% for the testing dataset and 0% for the locally acquired dataset (local/Aligarh). The execution time for the model to predict the input images and classify them is less than 0.1 s.

DISCUSSION AND CONCLUSION

The false negative rate is much lower than the standard rRT-PCR tests and even 0% on the locally acquired dataset. This suggests that the established model with end-to-end structure and deep learning technique can be employed to assist radiologists in validating their initial screenings of Chest X-Ray images of COVID-19 in developed and developing nations. Further research is needed to test the model to make it more robust, employ it on multiclass classification and also try sensitise it to identify new strains of COVID-19. This model might help cultivate tele-radiology.