The impact of vaccination on the dynamics of the Omicron variant of SARS-CoV-2

In the context of vaccination, we develop a novel mathematical model to examine the Omicron type of coronavirus illness. The system's mathematical analysis based on its equilibrium points shall be obtained. The threshold quantity is used to investigate the system's local and global asymptotical analysis. The Omicron vaccination model shown to be stable locally asymptotically if R 0 v < 1 . The system is globally asymptotically stable at the disease-free equilibrium for a special case when η = 1 if R 0 v < 1 . We estimate the model parameters based on the observed data and show that the threshold is R 0 ≈ 2.4894 in the absence of vaccination. The model has the phenomenon of backward bifurcation under certain conditions. Herd immunity analysis is obtained and it turns out that the herd immunity threshold for the South African population is 74%. The impact of vaccination on disease dynamics is also shown and discussed. Further, we have given some graphical results showing the community's disease reduction. [ FROM AUTHOR] Copyright of Waves in Random & Complex Media is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

Numerical studies of implied volatility expansions under the gatheral model

The Gatheral model is a three factor model with mean-reverting stochastic volatility that reverts to a stochastic long run mean. This chapter reviews previous analytical results on the first and second order implied volatility expansions under this model. Using the Monte Carlo simulation as the benchmark method, numerical studies are conducted to investigate the accuracy and properties of these analytical expansions. The classical Black-Scholes option pricing model assumes that the underlying asset follows a geometric Brownian motion with constant volatility. The chapter discusses partial calibration procedure is proposed and synthetic and real data calibration. If a full calibration is desired, we can use the results from the partial calibration as inputs for the final local optimization over all model parameters. In implementing the calibration procedure, the effect of the Covid-19 pandemic on the model calibration is high. © ISTE Ltd 2022.

Epidemic Waves and Exact Solutions of a Sequence of Nonlinear Differential Equations Connected to the SIR Model of Epidemics.

The SIR model of epidemic spreading can be reduced to a nonlinear differential equation with an exponential nonlinearity. This differential equation can be approximated by a sequence of nonlinear differential equations with polynomial nonlinearities. The equations from the obtained sequence are treated by the Simple Equations Method (SEsM). This allows us to obtain exact solutions to some of these equations. We discuss several of these solutions. Some (but not all) of the obtained exact solutions can be used for the description of the evolution of epidemic waves. We discuss this connection. In addition, we use two of the obtained solutions to study the evolution of two of the COVID-19 epidemic waves in Bulgaria by a comparison of the solutions with the available data for the infected individuals.

A novel fractional order model of SARS-CoV-2 and Cholera disease with real data.

This study presents a novel approach to investigating COVID-19 and Cholera disease. In this situation, a fractional-order model is created to investigate the COVID-19 and Cholera outbreaks in Congo. The existence, uniqueness, positivity, and boundedness of the solution are studied. The equilibrium points and their stability conditions are achieved. Subsequently, the basic reproduction number (the virus transmission coefficient) is calculated that simply refers to the number of people, to whom an infected person can make infected, as R 0 = 6 . 7442389 e - 10 by using the next generation matrix method. Next, the sensitivity analysis of the parameters is performed according to R 0 . To determine the values of the parameters in the model, the least squares curve fitting method is beneficial. A total of 22 parameter values in the model are estimated by using real Cholera data from Congo. Finally, to find out the dynamic behavior of the system, numerical simulations are presented. The outcome of the study indicates that the severity of the Cholera epidemic cases will decrease with the decrease in cases of COVID-19, through the implementation and follow-up of safety measures that have been taken to reduce COVID-19 cases.

Numerical study of a nonlinear COVID-19 pandemic model by finite difference and meshless methods.

In this paper, a mathematical epidemiological model in the form of reaction diffusion is proposed for the transmission of the novel coronavirus (COVID-19). The next-generation method is utilized for calculating the threshold number R 0 while the least square curve fitting approach is used for estimating the parameter values. The mathematical epidemiological model without and with diffusion is simulated through the operator splitting approach based on finite difference and meshless methods. Further, for the graphical solution of the non-linear model, we have applied a one-step explicit meshless procedure. We study the numerical simulation of the proposed model under the effects of diffusion. The stability analysis of the endemic equilibrium point is investigated. The obtained numerical results are compared mutually since the exact solutions are not available.

On the Analysis of a Real Dataset of COVID-19 Patients in Alava

COVID-19 has been spread to many countries all over the world in a relatively short period, largely overwhelmed hospitals have been a direct consequence of the explosive increase of coronavirus cases. In this dire situation, the demand for the development of clinical decision support systems based on predictive algorithms has increased, since these predictive technologies may help to alleviate unmanageable stress on healthcare systems. We contribute to this effort by a comprehensive study over a real dataset of covid-19 patients from a local hospital. The collected dataset is representative of the local policies on data gathering implemented during the pandemic, showing high imabalance and large number of missing values. In this paper, we report a descriptive analysis of the data that points out the large disparity of data in terms of severity and age. Furthermore, we report the results of the principal component analysis (PCA) and Logistic Regression (LR) techniques to find out which variables are the most relevant and their respective weight. The results show that there are two very relevant variables for the detection of the most severe cases, yielding promissing results. One of our paper conclussions is a strong recommendation to the local authorities to improve the data gathering protocols. © 2022, Springer Nature Switzerland AG.

STOCHASTIC OPTIMAL CONTROL ANALYSIS FOR THE COVID-19 EPIDEMIC MODEL UNDER REAL STATISTICS

The COVID-19 pandemic started, a global effort to develop vaccines and make them available to the public, has prompted a turning point in the history of vaccine development. In this study, we formulate a stochastic COVID-19 epidemic mathematical model with a vaccination effect. First, we present the model equilibria and basic reproduction number. To indicate that our stochastic model is well-posed, we prove the existence and uniqueness of a positive solution at the beginning. The sufficient conditions of the extinction and the existence of a stationary probability measure for the disease are established. For controlling the transmission of the disease by the application of external sources, the theory of stochastic optimality is established. The nonlinear least-squares procedure is utilized to parametrize the model from actual cases reported in Pakistan. The numerical simulations are carried out to demonstrate the analytical results. [ FROM AUTHOR] Copyright of Fractals is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

Optimal control strategy to control pandemic Covid-19 using MSILIHR_V Model

Many researchers began doing studies about pandemic COVID-19 which began to spread from Wuhan, China in 2019 to all around the world and so far, numerous researches have been done around the world to control this contagious disease. In this paper, we proposed a MSIlIhR-V mathematical model to study the spreading of pandemic COVID-19. This paper is aimed to study the vaccination effect in the control of the disease propagation rate. Another goal of this paper is to find the maximum number of susceptible people, minimum number of infected people, and the best value for number of vaccination people. The Jacobian matrix was obtained in the virus absenteeism equilibrium point for the proposed dynamical system. The spectral radius method was applied to find the analytical formula for the reproductive number. Reproductive number is one of the most benefit and important tools to study of epidemic model's stability and instability. In the following, by adding a controller to the model and also using the optimal control strategy, model performance was improved. To validate of the proposed models with controller and without controller we use the real data of COVID-19 from 4 January, 2021 up to 14 June, 2021 in Iran. Maple and MATLAB software's will be used for programming. We will use Maple software for analytical parts and MATLAB software for numerical and simulation parts.

Fractional modeling of COVID-19 pandemic model with real data from Pakistan under the ABC operator

In this study, the COVID-19 epidemic model is established by incorporating quarantine and isolation compartments with Mittag-Leffler kernel. The existence and uniqueness of the solutions for the proposed fractional model are obtained. The basic reproduction number, equilibrium points, and stability analysis of the COVID-19 model are derived. Sensitivity analysis is carried out to elaborate the influential parameters upon basic reproduction number. It is obtained that the disease transmission parameter is the most dominant parameter upon basic reproduction number. A convergent iterative scheme is taken into account to simulate the dynamical behavior of the system. We estimate the values of variables with the help of the least square curve fitting tool for the COVID-19 cases in Pakistan from 04 March to May 10, 2020, by using MATLAB.

Bifurcation from an Epidemic Model in the Presence of Memory Effects

In this paper, we consider a fractional SIS epidemic system with logistic growth demographic and saturated incidence rate for susceptibles. First, we validate our model by proving the global existence, positivity as well as boundedness of solutions. Then, we give necessary and sufficient conditions for the extinction and persistence of the disease from the population. We also study the local asymptotic stability of the unique positive equilibrium point by analyzing the corresponding characteristic equation. We find that combining logistic growth and saturated incidence for susceptibles can lead the system dynamic behavior to exhibit stability switches. By choosing the growth rate and the carrying capacity of the population as the bifurcation parameters, the stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. Finally, numerical simulations are performed to verify the theoretical results, to fit real-time data from 10 June to 25 November of 2020 and also to predict the number of cumulative cases for COVID-19 in Morocco during 2021.

An HMM-ensemble approach to predict severity progression of ICU treatment for hospitalized COVID-19 patients

COVID-19-related pneumonia requires different modalities of Intensive Care Unit (ICU) interventions at different times to facilitate breathing, depending on severity progression. The ability for clinical staff to predict how patients admitted to hospital will require more or less ICU treatment on a daily basis is critical to ICU management. For real datasets that are sparse and incomplete and where the most important state transitions (dismissal, death) are rare, a standard Hidden Markov Model (HMM) approach is insufficient, as it is prone to overfitting. In this paper we propose a more sophisticated ensemble-based approach that involves training multiple HMMs, each specialized in a subset of the state transitions, and then selecting the more plausible predictions either by selecting or combining the models. We have validated the approach on a live dataset of about 1, 000 patients from a partner hospital. Our results show that rare events, as well as the transitions to the most severe treatments outperform state of the art approaches. © 2021 IEEE.

CCTV: A new network-based methodology for the analysis and visualization of COVID-19 data

The novel COVID-19 pandemic has posed unprecedented challenges to the society and the health sector all over the globe. Here, we present a new network-based methodology to analyze COVID-19 data measures and its application on a real dataset. The goal of the methodology is to analyze set of homogeneous datasets (i.e. COVID-19 data in several regions) using a statistical test to find similar/dissimilar dataset, mapping such similarity information on a graph and then using community detection algorithm to visualize and analyze the initial dataset. The methodology and its implementation as R function are publicly available at https://github.com/mmilano87/analyzeC19D. We evaluated diverse Italian COVID-19 data made publicly available by the Italian Protezione Civile Department at https://github.com/pcm-dpc/COVID-19/ © 2021 IEEE.

Fractional order modelling of omicron SARS-CoV-2 variant containing heart attack effect using real data from the United Kingdom.

In this study, a new approach to COVID-19 pandemic is presented. In this context, a fractional order pandemic model is developed to examine the spread of COVID-19 with and without Omicron variant and its relationship with heart attack using real data from the United Kingdom. In the model, heart attack is adopted by considering its relationship with the quarantine strategy. Then, the existence, uniqueness, positivity and boundedness of the solution are studied. The equilibrium points and their stability conditions are achieved. Subsequently, we calculate the basic reproduction number (the virus transmission coefficient) that simply refers to the number of people, to whom an infected person can make infected, as R 0 = 3.6456 by using the next generation matrix method. Next, we consider the sensitivity analysis of the parameters according to R 0 . In order to determine the values of the parameters in the model, the least squares curve fitting method, which is one of the leading methods in parameter estimation, is benefited. A total of 21 parameter values in the model are estimated by using real Omicron data from the United Kingdom. Moreover, in order to highlight the advantages of using fractional differential equations, applications related to memory trace and hereditary properties are given. Finally, the numerical simulations are presented to examine the dynamic behavior of the system. As a result of numerical simulations, an increase in the number of people who have heart attacks is observed when Omicron cases were first seen. In the future, it is estimated that the risk of heart attack will decrease as the cases of Omicron decrease.

Neural Networks Architecture for COVID-19 Early Detection

Coronavirus fight seems far from being won. Governments are trying to balance the necessity to enforce restrictions on travel outside the home and the impact of these restrictions on the economy. Healthcare workers are overloaded, a considerable number of unnecessary and costly PCR tests are performed to serve as a certificate to go to work. At this stage, going back to everyday life safely requires the companies and public places to adopt AI-based solutions to assist the public authorities and the hospitals with the COVID detection. The most important issue that we tackle in this paper is the prediction to be very accurate. As a result, we propose an AI system based on Neural Networks (NN) method to predict whether a person has caught COVID19 disease or not. In this study, we used a real data set of 9416 patients tested for COVID19 at a hospital in Dubai. After training the NN model, the average error function of the neural network was equal to 0.01, and the accuracy of the prediction of whether a person has COVID or not was 97.6%. © 2021 IEEE.

Modified SIQR model for the COVID-19 outbreak in several countries.

In this paper, we propose a modified Susceptible-Infected-Quarantine-Recovered (mSIQR) model, for the COVID-19 pandemic. We start by proving the well-posedness of the model and then compute its reproduction number and the corresponding sensitivity indices. We discuss the values of these indices for epidemiological relevant parameters, namely, the contact rate, the proportion of unknown infectious, and the recovering rate. The mSIQR model is simulated, and the outputs are fit to COVID-19 pandemic data from several countries, including France, US, UK, and Portugal. We discuss the epidemiological relevance of the results and provide insights on future patterns, subjected to health policies.

Mathematical modeling and optimal control of the COVID-19 dynamics.

We are considering a new COVID-19 model with an optimal control analysis when vaccination is present. Firstly, we formulate the vaccine-free model and present the associated mathematical results involved. Stability results for R 0 < 1 are shown. In addition, we frame the model with the vaccination class. We look at the mathematical results with the details of the vaccine model. Additionally, we are considering setting controls to minimize infection spread and control. We consider four different controls, such as prevention, vaccination control, rapid screening of people in the exposed category, and people who are identified as infected without screening. Using the suggested controls, we develop an optimal control model and derive mathematical results from it. In addition, the mathematical model with control and without control is resolved by the forward-backward Runge-Kutta method and presents the results graphically. The results obtained through optimal control suggest that controls can be useful for minimizing infected individuals and improving population health.

Significant Decrease in Annual Cancer Diagnoses in Spain during the COVID-19 Pandemic: A Real-Data Study.

The COVID-19 pandemic has caused a profound change in health organizations at both the primary and hospital care levels. This cross-sectional study aims to investigate the impact of the COVID-19 pandemic in the annual rate of new cancer diagnosis in two university-affiliated hospitals. This study includes all the patients with a pathological diagnosis of cancer attended in two hospitals in Málaga (Spain) during the first year of pandemic. This study population was compared with the patients diagnosed during the previous year 2019. To analyze whether the possible differences in the annual rate of diagnoses were due to the pandemic or to other causes, the patients diagnosed during 2018 and 2017 were also compared. There were 2340 new cancer diagnosis compared to 2825 patients in 2019 which represented a decrease of -17.2% (p = 0.0001). Differences in the number of cancer patients diagnosed between 2018 and 2019 (2840 new cases; 0.5% increase) or 2017 and 2019 (2909 new cases; 3% increase) were not statistically significant. The highest number of patients lost from diagnosis in 2020 was in breast cancer (-26.1%), colorectal neoplasms (-16.9%), and head and neck tumors (-19.8%). The study of incidence rates throughout the first year of the COVID-19 pandemic shows that the diagnosis of new cancer patients has been significantly impaired. Health systems must take the necessary measures to restore pre-pandemic diagnostic procedures and to recover lost patients who have not been diagnosed.

Stability analysis and simulation of the novel Corornavirus mathematical model via the Caputo fractional-order derivative: A case study of Algeria.

The novel coronavirus infectious disease (or COVID-19) almost spread widely around the world and causes a huge panic in the human population. To explore the complex dynamics of this novel infection, several mathematical epidemic models have been adopted and simulated using the statistical data of COVID-19 in various regions. In this paper, we present a new nonlinear fractional order model in the Caputo sense to analyze and simulate the dynamics of this viral disease with a case study of Algeria. Initially, after the model formulation, we utilize the well-known least square approach to estimate the model parameters from the reported COVID-19 cases in Algeria for a selected period of time. We perform the existence and uniqueness of the model solution which are proved via the Picard-Lindelöf method. We further compute the basic reproduction numbers and equilibrium points, then we explore the local and global stability of both the disease-free equilibrium point and the endemic equilibrium point. Finally, numerical results and graphical simulation are given to demonstrate the impact of various model parameters and fractional order on the disease dynamics and control.

Discrete and continuum models of COVID-19 virus, formal solutions, stability and comparison with real data.

Very recently, various mathematical models, for the dynamics of COVID-19 with main contribution of suspected-exposed-infected-recovered people have been proposed. Some models that account for the deceased, quarantined or social distancing functions were also presented. However, in any local space the real data reveals that the effects of lock-down and traveling are significant in decreasing and increasing the impact of this virus respectively. Here, discrete and continuum models for the dynamics of this virus are suggested. The continuum dynamical model is studied in detail. The present model deals with exposed, infected, recovered and deceased individuals (EIRD), which accounts for the health isolation and travelers (HIT) effects. Up to now no exact solutions of the parametric-dependent, nonlinear dynamical system NLDS were found. In this work, our objective is to find the exact solutions of a NLDS. To this issue, a novel approach is presented where a NLDS is recast to a linear dynamical system LDS. This is done by implementing the unified method (UM), with auxiliary equations, which are taken coupled linear ODE's (LDS). Numerical results of the exact solutions are evaluated, which can be applied to data in a local space (or anywhere) when the initial data for the IRD are known. Here, as an example, initial conditions for the components in the model equation of COVID-19, are taken from the real data in Egypt. The results of susceptible, infected, recovered and deceased people are computed. The comparison between the computed results and the real data shows an agreement up to a relative error 1 0 - 3 . On the other hand it is remarked that locking-down plays a dominant role in decreasing the number of infected people. The equilibrium states are determined and it is found that they are stable. This reveals a relevant result that the COVID-19 can be endemic in the case of a disturbance in the number of the exposed people. A disturbance in the form of an increase in the exposed number, leads to an increase in the number of infected people. This result is, globally, valid. Furthermore, initial states control is analyzed, where region of initial conditions for infected and exposed is determined. We developed a software tool to interact with the model and facilitate applying various data of different local spaces.

Mathematical modeling and analysis of the novel Coronavirus using Atangana-Baleanu derivative.

The novel Coronavirus infection disease is becoming more complex for the humans society by giving death and infected cases throughout the world. Due to this infection, many countries of the world suffers from great economic loss. The researchers around the world are very active to make a plan and policy for its early eradication. The government officials have taken full action for the eradication of this virus using different possible control strategies. It is the first priority of the researchers to develop safe vaccine against this deadly disease to minimize the infection. Different approaches have been made in this regards for its elimination. In this study, we formulate a mathematical epidemic model to analyze the dynamical behavior and transmission patterns of this new pandemic. We consider the environmental viral concentration in the model to better study the disease incidence in a community. Initially, the model is constructed with the derivative of integer-order. The classical epidemic model is then reconstructed with the fractional order operator in the form of Atangana-Baleanu derivative with the nonsingular and nonlocal kernel in order to analyze the dynamics of Coronavirus infection in a better way. A well-known estimation approach is used to estimate model parameters from the COVID-19 cases reported in Saudi Arabia from March 1 till August 20, 2020. After the procedure of parameters estimation, we explore some basic mathematical analysis of the fractional model. The stability results are provided for the disease free case using fractional stability concepts. Further, the uniqueness and existence results will be shown using the Picard-Lendelof approach. Moreover, an efficient numerical scheme has been proposed to obtain the solution of the model numerically. Finally, using the real fitted parameters, we depict many simulation results in order to demonstrate the importance of various model parameters and the memory index on disease dynamics and possible eradication.