A fractional-order mathematical model based on vaccinated and infected compartments of SARS-CoV-2 with a real case study during the last stages of the epidemiological event.

In 2020 the world faced with a pandemic spread that affected almost everything of humans' social and health life. Regulations to decrease the epidemiological spread and studies to produce the vaccine of SARS-CoV-2 were on one side a hope to return back to the regular life, but on the other side there were also notable criticism about the vaccines itself. In this study, we established a fractional order differential equations system incorporating the vaccinated and re-infected compartments to a S I R frame to consider the expanded and detailed form as an S V I I v R model. We considered in the model some essential parameters, such as the protection rate of the vaccines, the vaccination rate, and the vaccine's lost efficacy after a certain period. We obtained the local stability of the disease-free and co-existing equilibrium points under specific conditions using the Routh-Hurwitz Criterion and the global stability in using a suitable Lyapunov function. For the numerical solutions we applied the Euler's method. The data for the simulations were taken from the World Health Organization (WHO) to illustrate numerically some scenarios that happened.

Modeling and Dynamics of the Fractional Order SARS-CoV-2 Epidemiological Model

We propose a theoretical study to investigate the spread of the SARS-CoV-2 virus, reported in Wuhan, China. We develop a mathematical model based on the characteristic of the disease and then use fractional calculus to fractionalize it. We use the Caputo-Fabrizio operator for this purpose. We prove that the considered model has positive and bounded solutions. We calculate the threshold quantity of the proposed model and discuss its sensitivity analysis to find the role of every epidemic parameter and the relative impact on disease transmission. The threshold quantity (reproductive number) is used to discuss the steady states of the proposed model and to find that the proposed epidemic model is stable asymptotically under some constraints. Both the global and local properties of the proposed model will be performed with the help of the mean value theorem, Barbalat’s lemma, and linearization. To support our analytical findings, we draw some numerical simulations to verify with graphical representations.

A mathematical model of COVID-19 and the multi fears of the community during the epidemiological stage.

Within two years, the world has experienced a pandemic phenomenon that changed almost everything in the macro and micro-environment; the economy, the community's social life, education, and many other fields. Governments started to collaborate with health institutions and the WHO to control the pandemic spread, followed by many regulations such as wearing masks, maintaining social distance, and home office work. While the virus has a high transmission rate and shows many mutated forms, another discussion appeared in the community: the fear of getting infected and the side effects of the produced vaccines. The community started to face uncertain information spread through some networks keeping the discussions of side effects on-trend. However, this pollution spread confused the community more and activated multi fears related to the virus and the vaccines. This paper establishes a mathematical model of COVID-19, including the community's fear of getting infected and the possible side effects of the vaccines. These fears appeared from uncertain information spread through some social sources. Our primary target is to show the psychological effect on the community during the pandemic stage. The theoretical study contains the existence and uniqueness of the IVP and, after that, the local stability analysis of both equilibrium points, the disease-free and the positive equilibrium point. Finally, we show the global asymptotic stability holds under specific conditions using a suitable Lyapunov function. In the end, we conclude our theoretical findings with some simulations.

Ensemble Classifiers for Arabic Sentiment Analysis of Social Network (Twitter Data) towards COVID-19-Related Conspiracy Theories

Sentiment analysis has recently become increasingly important with a massive increase in online content. It is associated with the analysis of textual data generated by social media that can be easily accessed, obtained, and analyzed. With the emergence of COVID-19, most published studies related to COVID-19’s conspiracy theories were surveys on the people's sentiments and opinions and studied the impact of the pandemic on their lives. Just a few studies utilized sentiment analysis of social media using a machine learning approach. These studies focused more on sentiment analysis of Twitter tweets in the English language and did not pay more attention to other languages such as Arabic. This study proposes a machine learning model to analyze the Arabic tweets from Twitter. In this model, we apply Word2Vec for word embedding which formed the main source of features. Two pretrained continuous bag-of-words (CBOW) models are investigated, and Naïve Bayes was used as a baseline classifier. Several single-based and ensemble-based machine learning classifiers have been used with and without SMOTE (synthetic minority oversampling technique). The experimental results show that applying word embedding with an ensemble and SMOTE achieved good improvement on average of F1 score compared to the baseline classifier and other classifiers (single-based and ensemble-based) without SMOTE.

A fractional-order model of COVID-19 considering the fear effect of the media and social networks on the community.

Since December 2019, the world has experienced from a virus, known as Covid-19, that is highly transmittable and is now spread worldwide. Many mathematical models and studies have been implemented to work on the infection and transmission risks. Besides the virus's transmission effect, another discussion appears in the community: the fear effect. People who have never heard about coronavirus, face every day uncertain and different information regarding the effect of the virus and the daily death rates from sources like the media, the medical institutions or organizations. Thus, the fear of the virus in the community can possibly reach the point that people become scared and confused about information polluted from different networks with long-term trend discussions. In this work, we use the Routh-Hurwitz Criteria to analyze the local stability of two essential critical points: the disease-free and the co-existing critical point. Using the discretization process, our analysis have shown that one should distinguish between the spread of "awareness" or "fear" in the community through the media and others to control the virus's transmission. Finally, we conclude our theoretical findings with numerical simulations.

Analysis of the outbreak of the novel coronavirus COVID-19 dynamic model with control mechanisms.

The mathematical models of infections are essential tools in understanding the dynamical behavior of disease transmission. In this paper, we establish a model of differential equations with piecewise constant arguments that explores the outbreak of Covid-19 including the control mechanisms such as health organizations and police supplements for the sake of controlling the pandemic spread and protecting the susceptible population. The local asymptotic stability of the equilibrium points, the disease-free equilibrium point, the apocalypse equilibrium point and the co-existing equilibrium point are analyzed by the aide of Schur-Cohn criteria. Furthermore and by incorporating the Allee function at time t, we consider the extinction case of the outbreak to analyze the conditions for a strong Allee Effect. Our study has demonstarted that the awareness of the police personal and the management of professional health organizations play a vital role to protect the susceptible class and to prevent the spreading. Numerical simulations are presented to support our theoretical findings. We end the paper by a describtive conclusion.

An optimal control analysis of a COVID-19 model

This paper aims to explore the optimal control of the novel pandemic COVID-19 using non-clinical approach. We formulate a mathematical model to analyze the transmission of the infection through different human compartments. By applying a sensitivity test, we obtain the sensitivity indexes of the parameters involved in the transmission of the disease. We demonstrate the most active/sensitive parameters to analyze the spread of the coronavirus COVID-19. The most active transmission parameters are interposed by introducing control variables. The control intervention is in the form of smart lockdown, frequent handwash, control of the disease’s side effects, face mask, and sanitizer. We Formulate Hamilton and Lagrangian to investigate the existence of the optimal control. Pontryagin’s Maximum Principle describes the control variables in the optimal control model. The objective function is designed to reduce both the infection and the cost of interventions. We use numerical simulation to verify the results of the control variables by Matlab 2019.

A mathematical model of the evolution and spread of pathogenic coronaviruses from natural host to human host.

Coronaviruses are highly transmissible and are pathogenic viruses of the 21st century worldwide. In general, these viruses are originated in bats or rodents. At the same time, the transmission of the infection to the human host is caused by domestic animals that represent in the habitat the intermediate host. In this study, we review the currently collected information about coronaviruses and establish a model of differential equations with piecewise constant arguments to discuss the spread of the infection from the natural host to the intermediate, and from them to the human host, while we focus on the potential spillover of bat-borne coronaviruses. The local stability of the positive equilibrium point of the model is considered via the Linearized Stability Theorem. Besides, we discuss global stability by employing an appropriate Lyapunov function. To analyze the outbreak in early detection, we incorporate the Allee effect at time t and obtain stability conditions for the dynamical behavior. Furthermore, it is shown that the model demonstrates the Neimark-Sacker Bifurcation. Finally, we conduct numerical simulations to support the theoretical findings.