A fractional-order mathematical model for COVID-19 outbreak with the effect of symptomatic and asymptomatic transmissions

A bifurcation analysis and model of Covid-19 transmission dynamics with post-vaccination infection impact

SARS COV-2 (Covid-19) has imposed a monumental socio-economic burden worldwide, and its impact still lingers. We propose a deterministic model to describe the transmission dynamics of Covid-19, emphasizing the effects of vaccination on the prevailing epidemic. The proposed model incorporates current information on Covid-19, such as reinfection, waning of immunity derived from the vaccine, and infectiousness of the pre-symptomatic individuals into the disease dynamics. Moreover, the model analysis reveals that it exhibits the phenomenon of backward bifurcation, thus suggesting that driving the model reproduction number below unity may not suffice to drive the epidemic toward extinction. The model is fitted to real-life data to estimate values for some of the unknown parameters. In addition, the model epidemic threshold and equilibria are determined while the criteria for the stability of each equilibrium solution are established using the Metzler approach. A sensitivity analysis of the model is performed based on the Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficients (PRCCs) approaches to illustrate the impact of the various model parameters and explore the dependency of control reproduction number on its constituents parameters, which invariably gives insight on what needs to be done to contain the pandemic effectively. The foregoing notwithstanding, the contour plots of the control reproduction number concerning some of the salient parameters indicate that increasing vaccination coverage and decreasing vaccine waning rate would remarkably reduce the value of the reproduction number below unity, thus facilitating the possible elimination of the disease from the population. Finally, the model is solved numerically and simulated for different scenarios of disease outbreaks with the findings discussed.

Stochastic analysis of a COVID-19 model with effects of vaccination and different transition rates: Real data approach

This paper presents a stochastic model for COVID-19 that takes into account factors such as incubation times, vaccine effectiveness, and quarantine periods in the spread of the virus in symptomatically contagious populations. The paper outlines the conditions necessary for the existence and uniqueness of a global solution for the stochastic model. Additionally, the paper employs nonlinear analysis to demonstrate some results on the ergodic aspect of the stochastic model. The model is also simulated and compared to deterministic dynamics. To validate and demonstrate the usefulness of the proposed system, the paper compares the results of the infected class with actual cases from Iraq, Bangladesh, and Croatia. Furthermore, the paper visualizes the impact of vaccination rates and transition rates on the dynamics of infected people in the infected class.

A mathematical model for transmission dynamics of COVID-19 infection

In this paper, a mathematical model of COVID-19 has been proposed to study the transmission dynamics of infection by taking into account the role of symptomatic and asymptomatic infected individuals. The model has also considered the effect of non-pharmaceutical interventions (NPIs) in controlling the spread of virus. The basic reproduction number ( R 0 ) has been computed and the analysis shows that for R 0 < 1 , the disease-free state becomes globally stable. The conditions of existence and stability for two other equilibrium states have been obtained. Transcritical bifurcation occurs when basic reproduction number is one (i.e. R 0 = 1 ). It is found that when asymptomatic cases get increased, infection will persist in the population. However, when symptomatic cases get increased as compared to asymptomatic ones, the endemic state will become unstable and infection may eradicate from the population. Increasing NPIs decrease the basic reproduction number and hence, the epidemic can be controlled. As the COVID-19 transmission is subject to environmental fluctuations, the effect of white noise has been considered in the deterministic model. The stochastic differential equation model has been solved numerically by using the Euler-Maruyama method. The stochastic model gives large fluctuations around the respective deterministic solutions. The model has been fitted by using the COVID-19 data of three waves of India. A good match is obtained between the actual data and the predicted trajectories of the model in all three waves of COVID-19. The findings of this model may assist policymakers and healthcare professionals in implementing the most effective measures to prevent the transmission of COVID-19 in different settings.

Mathematical Model of COVID-19 Pandemic with Double Dose Vaccination

This paper is concerned with the formulation and analysis of an epidemic model of COVID-19 governed by an eight-dimensional system of ordinary differential equations, by taking into account the first dose and the second dose of vaccinated individuals in the population. The developed model is analyzed and the threshold quantity known as the control reproduction number [Formula: see text] is obtained. We investigate the equilibrium stability of the system, and the COVID-free equilibrium is said to be locally asymptotically stable when the control reproduction number is less than unity, and unstable otherwise. Using the least-squares method, the model is calibrated based on the cumulative number of COVID-19 reported cases and available information about the mass vaccine administration in Malaysia between the 24th of February 2021 and February 2022. Following the model fitting and estimation of the parameter values, a global sensitivity analysis was performed by using the Partial Rank Correlation Coefficient (PRCC) to determine the most influential parameters on the threshold quantities. The result shows that the effective transmission rate [Formula: see text], the rate of first vaccine dose [Formula: see text], the second dose vaccination rate [Formula: see text] and the recovery rate due to the second dose of vaccination [Formula: see text] are the most influential of all the model parameters. We further investigate the impact of these parameters by performing a numerical simulation on the developed COVID-19 model. The result of the study shows that adhering to the preventive measures has a huge impact on reducing the spread of the disease in the population. Particularly, an increase in both the first and second dose vaccination rates reduces the number of infected individuals, thus reducing the disease burden in the population.

A new fractional mathematical model to study the impact of vaccination on COVID-19 outbreaks

This study proposes a new fractional mathematical model to study the impact of vaccination on COVID-19 outbreaks by categorizing infected people into non-vaccinated, first dose-vaccinated, and second dose-vaccinated groups and exploring the transmission dynamics of the disease outbreaks. We present a non-linear integer order mathematical model of COVID-19 dynamics and modify it by introducing Caputo fractional derivative operator. We start by proving the good state of the model and then calculating its reproduction number. The Caputo fractional-order model is discretized by applying a reliable numerical technique. The model is proven to be stable. The classical model is fitted to the corresponding cumulative number of daily reported cases during the vaccination regime in India between 01 August 2021 and 21 July 2022. We explore the sensitivities of the reproduction number with respect to the model parameters. It is shown that the effective transmission rate and the recovery rate of unvaccinated infected individuals are the most sensitive parameters that drive the transmission dynamics of the pandemic in the population. Numerical simulations are used to demonstrate the applicability of the proposed fractional mathematical model via the memory index at different values of 0 . 7 , 0 . 8 , 0 . 9 and 1. We discuss the epidemiological significance of the findings and provide perspectives on future health policy tendencies. For instance, efforts targeting a decrease in the transmission rate and an increase in the recovery rate of non-vaccinated infected individuals are required to ensure virus-free population. This can be achieved if the population strictly adhere to precautionary measures, and prompt and adequate treatment is provided for non-vaccinated infectious individuals. Also, given the ongoing community spread of COVID-19 in India and almost the pandemic-affected countries worldwide, the need to scale up the effort of mass vaccination policy cannot be overemphasized in order to reduce the number of unvaccinated infections with a view to halting the transmission dynamics of the disease in the population.

Theoretical Analysis of a COVID-19 CF-Fractional Model to Optimally Control the Spread of Pandemic

In this manuscript, we formulate a mathematical model of the deadly COVID-19 pandemic to understand the dynamic behavior of COVID-19. For the dynamic study, a new SEIAPHR fractional model was purposed in which infectious individuals were divided into three sub-compartments. The purpose is to construct a more reliable and realistic model for a complete mathematical and computational analysis and design of different control strategies for the proposed Caputo–Fabrizio fractional model. We prove the existence and uniqueness of solutions by employing well-known theorems of fractional calculus and functional analyses. The positivity and boundedness of the solutions are proved using the fractional-order properties of the Laplace transformation. The basic reproduction number for the model is computed using a next-generation technique to handle the future dynamics of the pandemic. The local–global stability of the model was also investigated at each equilibrium point. We propose basic fixed controls through manipulation of quarantine rates and formulate an optimal control problem to find the best controls (quarantine rates) employed on infected, asymptomatic, and “superspreader” humans, respectively, to restrict the spread of the disease. For the numerical solution of the fractional model, a computationally efficient Adams–Bashforth method is presented. A fractional-order optimal control problem and the associated optimality conditions of Pontryagin maximum principle are discussed in order to optimally reduce the number of infected, asymptomatic, and superspreader humans. The obtained numerical results are discussed and shown through graphs.

Some novel mathematical analysis on the fractional-order 2019-nCoV dynamical model

Since December 2019, the whole world has been facing the big challenge of Covid-19 or 2019-nCoV. Some nations have controlled or are controlling the spread of this virus strongly, but some countries are in big trouble because of their poor control strategies. Nowadays, mathematical models are very effective tools to simulate outbreaks of this virus. In this research, we analyze a fractional-order model of Covid-19 in terms of the Caputo fractional derivative. First, we generalize an integer-order model to a fractional sense, and then, we check the stability of equilibrium points. To check the dynamics of Covid-19, we plot several graphs on the time scale of daily and monthly cases. The main goal of this content is to show the effectiveness of fractional-order models as compared to integer-order dynamics.

A new approach to modeling pre-symptomatic incidence and transmission time of imported COVID-19 cases evolving with SARS-CoV-2 variants

There is paucity of the statistical model that is specified for data on imported COVID-19 cases with the unique global information on infectious properties of SARS-CoV-2 variant different from local outbreak data used for estimating transmission and infectiousness parameters via the established epidemic models. To this end, a new approach with a four-state stochastic model was proposed to formulate these well-established infectious parameters with three new parameters, including the pre-symptomatic incidence rate, the median of pre-symptomatic transmission time (MPTT) to symptomatic state, and the incidence (proportion) of asymptomatic cases using imported COVID-19 data. We fitted the proposed stochastic model to empirical data on imported COVID-19 cases from D614G to Omicron with the corresponding calendar periods according to the classification GISAID information on the evolution of SARS-CoV-2 variant between March 2020 and Jan 2022 in Taiwan. The pre-symptomatic incidence rate was the highest for Omicron followed by Alpha, Delta, and D614G. The MPTT (in days) increased from 3.45 (first period) ~ 4.02 (second period) of D614G until 3.94-4.65 of VOC Alpha but dropped to 3.93-3.49 of Delta and 2 days (only first period) of Omicron. The proportion of asymptomatic cases increased from 29% of D-614G period to 59.2% of Omicron. Modeling data on imported cases across strains of SARS-CoV-2 not only bridges the link between the underlying natural infectious properties elucidated in the previous epidemic models and different disease phenotypes of COVID-19 but also provides precision quarantine and isolation policy for border control in the face of various emerging SRAS-CoV-2 variants globally.

Influence of Co-morbidities During SARS-CoV-2 Infection in an Indian Population

Background

Since the outbreak of COVID-19 pandemic the interindividual variability in the course of the disease has been reported, indicating a wide range of factors influencing it. Factors which were the most often associated with increased COVID-19 severity include higher age, obesity and diabetes. The influence of cytokine storm is complex, reflecting the complexity of the immunological processes triggered by SARS-CoV-2 infection. A modern challenge such as a worldwide pandemic requires modern solutions, which in this case is harnessing the machine learning for the purpose of analysing the differences in the clinical properties of the populations affected by the disease, followed by grading its significance, consequently leading to creation of tool applicable for assessing the individual risk of SARS-CoV-2 infection.

Methods

Biochemical and morphological parameters values of 5,000 patients (Curisin Healthcare (India) were gathered and used for calculation of eGFR, SII index and N/L ratio. Spearman's rank correlation coefficient formula was used for assessment of correlations between each of the features in the population and the presence of the SARS-CoV-2 infection. Feature importance was evaluated by fitting a Random Forest machine learning model to the data and examining their predictive value. Its accuracy was measured as the F1 Score.

Results

The parameters which showed the highest correlation coefficient were age, random serum glucose, serum urea, gender and serum cholesterol, whereas the highest inverse correlation coefficient was assessed for alanine transaminase, red blood cells count and serum creatinine. The accuracy of created model for differentiating positive from negative SARS-CoV-2 cases was 97%. Features of highest importance were age, alanine transaminase, random serum glucose and red blood cells count.

Conclusion

The current analysis indicates a number of parameters available for a routine screening in clinical setting. It also presents a tool created on the basis of these parameters, useful for assessing the individual risk of developing COVID-19 in patients. The limitation of the study is the demographic specificity of the studied population, which might restrict its general applicability.

Modeling the impact of the vaccine on the COVID-19 epidemic transmission via fractional derivative

To achieve the goal of ceasing the spread of COVID-19 entirely it is essential to understand the dynamical behavior of the proliferation of the virus at an intense level. Studying this disease simply based on experimental analysis is very time consuming and expensive. Mathematical modeling might play a worthy role in this regard. By incorporating the mathematical frameworks with the available disease data it will be beneficial and economical to understand the key factors involved in the spread of COVID-19. As there are many vaccines available globally at present, henceforth, by including the effect of vaccination into the model will also support to understand the visible influence of the vaccine on the spread of COVID-19 virus. There are several ways to mathematically formulate the effect of disease on the population like deterministic modeling, stochastic modeling or fractional order modeling etc. Fractional order derivative modeling is one of the fundamental methods to understand real-world problems and evaluate accurate situations. In this article, a fractional order epidemic modelS p E p I p E r p R p D p Q p V p on the spread of COVID-19 is presented.S p E p I p E r p R p D p Q p V p consists of eight compartments of population namely susceptible, exposed, infective, recovered, the quarantine population, recovered-exposed, and dead population. The fractional order derivative is considered in the Caputo sense. For the prophecy and tenacity of the epidemic, we compute the reproduction number R 0 . Using fixed point theory, the existence and uniqueness of the solutions of fractional order derivative have been studied. Furthermore, we are using the generalized Adams-Bashforth-Moulton method, to obtain the approximate solution of the fractional-order COVID-19 model. Finally, numerical results and illustrative graphic simulation are given. Our results suggest that to reduce the number of cases of COVID-19 we should reduce the contact rate of the people if the population is not fully vaccinated. However, to tackle the issue of reducing the social distancing and lock down, which have very negative impact on the economy as well as on the mental health of the people, it is much better to increase the vaccine rate and get the whole nation to be fully vaccinated.

Mathematical modelling of unemployment as the effect of COVID-19 pandemic in middle-income countries

WHO (World Health Organization) has stamped Coronavirus disease 2019 (COVID-19) as a pandemic. This disease has affected most of the population in every aspect. One of those main aspects is the economical burden on the middle class and poor people. To overcome these issues, there should be multi-stage precautions, and awareness was required apart from these, there should be a multi-level posterior effort on facing the challenges that were much needed. In that way, to join the dealing of facing the posterior challenges of this disease, we try to help the society in our way of modelling approach, so that we developed a mathematical model to identify the complexities of the virus and its actual phenomena along with its economical oriented effects and perspectives. During the time of the COVID-19 pandemic situation, millions of employees lost their jobs irrespective of age consideration. More youngsters in many countries have been looking for a new jobs even after facing so much of struggles as the effect of this pandemic. In these facts, a system of ordinary differential equations (ODEs) model is constructed and analysed the outbreak of COVID-19 and its effects on employment. The basic reproduction number R 0 has determined using the next-generation matrix technique. If R 0 ≤ 1 disease-free equilibrium is globally asymptotically stable. If R 0 ≥ 1 , the endemic equilibrium is global asymptotic stability is achieved. To show the analytic findings, numerical simulations were performed. We hope that this work is suitable to control unemployment for all kinds of income populations.