Modeling and forecasting the spread of COVID-19 with stochastic and deterministic approaches: Africa and Europe

[Formula: see text] model for analyzing [Formula: see text]-19 pandemic process via [Formula: see text]-Caputo fractional derivative and numerical simulation

The objective of this study is to develop the [Formula: see text] epidemic model for [Formula: see text]-[Formula: see text] utilizing the [Formula: see text]-Caputo fractional derivative. The reproduction number ([Formula: see text]) is calculated utilizing the next generation matrix method. The equilibrium points of the model are computed, and both the local and global stability of the disease-free equilibrium point are demonstrated. Sensitivity analysis is discussed to describe the importance of the parameters and to demonstrate the existence of a unique solution for the model by applying a fixed point theorem. Utilizing the fractional Euler procedure, an approximate solution to the model is obtained. To study the transmission dynamics of infection, numerical simulations are conducted by using MatLab. Both numerical methods and simulations can provide valuable insights into the behavior of the system and help in understanding the existence and properties of solutions. By placing the values [Formula: see text], [Formula: see text] and [Formula: see text] instead of [Formula: see text], the derivatives of the Caputo and Caputo-Hadamard and Katugampola appear, respectively, to compare the results of each with real data. Besides, these simulations specifically with different fractional orders to examine the transmission dynamics. At the end, we come to the conclusion that the simulation utilizing Caputo derivative with the order of 0.95 shows the prevalence of the disease better. Our results are new which provide a good contribution to the current research on this field of research.

Cost-effectiveness analysis of COVID-19 intervention policies using a mathematical model: an optimal control approach

COVID-19 is an infectious disease that causes millions of deaths worldwide, and it is the principal leading cause of morbidity and mortality in all nations. Although the governments of developed and developing countries are enforcing their universal control strategies, more precise and cost-effective single or combination interventions are required to control COVID-19 outbreaks. Using proper optimal control strategies with appropriate cost-effectiveness analysis is important to simulate, examine, and forecast the COVID-19 transmission phase. In this study, we developed a COVID-19 mathematical model and considered two important features including direct link between vaccination and latently population, and practical healthcare cost by separation of infections into Mild and Critical cases. We derived basic reproduction numbers and performed mesh and contour plots to explore the impact of different parameters on COVID-19 dynamics. Our model fitted and calibrated with number of cases of the COVID-19 data in Bangladesh as a case study to determine the optimal combinations of interventions for particular scenarios. We evaluated the cost-effectiveness of varying single and combinations of three intervention strategies, including transmission control, treatment, and vaccination, all within the optimal control framework of the single-intervention policies; enhanced transmission control is the most cost-effective and prompt in declining the COVID-19 cases in Bangladesh. Our finding recommends that a three-intervention strategy that integrates transmission control, treatment, and vaccination is the most cost-effective compared to single and double intervention techniques and potentially reduce the overall infections. Other policies can be implemented to control COVID-19 depending on the accessibility of funds and policymakers' judgments.

A data-driven Markov process for infectious disease transmission

The 2019 coronavirus pandemic exudes public health and socio-economic burden globally, raising an unprecedented concern for infectious diseases. Thus, describing the infectious disease transmission process to design effective intervention measures and restrict its spread is a critical scientific issue. We propose a level-dependent Markov model with infinite state space to characterize viral disorders like COVID-19. The levels and states in this model represent the stages of outbreak development and the possible number of infectious disease patients. The transfer of states between levels reflects the explosive transmission process of infectious disease. A simulation method with heterogeneous infection is proposed to solve the model rapidly. After that, simulation experiments were conducted using MATLAB according to the reported data on COVID-19 published by Johns Hopkins. Comparing the simulation results with the actual situation shows that our proposed model can well capture the transmission dynamics of infectious diseases with and without imposed interventions and evaluate the effectiveness of intervention strategies. Further, the influence of model parameters on transmission dynamics is analyzed, which helps to develop reasonable intervention strategies. The proposed approach extends the theoretical study of mathematical modeling of infectious diseases and contributes to developing models that can describe an infinite number of infected persons.

A cyclic behavioral modeling aspect to understand the effects of vaccination and treatment on epidemic transmission dynamics

Evolutionary epidemiological models have played an active part in analyzing various contagious diseases and intervention policies in the biological sciences. The design in this effort is the addition of compartments for treatment and vaccination, so the system is designated as susceptible, vaccinated, infected, treated, and recovered (SVITR) epidemic dynamic. The contact of a susceptible individual with a vaccinated or an infected individual makes the individual either immunized or infected. Inventively, the assumption that infected individuals enter the treatment and recover state at different rates after a time interval is also deliberated through the presence of behavioral aspects. The rate of change from susceptible to vaccinated and infected to treatment is studied in a comprehensive evolutionary game theory with a cyclic epidemic model. We theoretically investigate the cyclic SVITR epidemic model framework for disease-free and endemic equilibrium to show stable conditions. Then, the embedded vaccination and treatment strategies are present using extensive evolutionary game theory aspects among the individuals in society through a ridiculous phase diagram. Extensive numerical simulation suggests that effective vaccination and treatment may implicitly reduce the community risk of infection when reliable and cheap. The results exhibited the dilemma and benefitted situation, in which the interplay between vaccination and treatment evolution and coexistence are investigated by the indicators of social efficiency deficit and socially benefited individuals.

Coupled simultaneous analysis of vaccine and self-awareness strategies on evolutionary dilemma aspect with various immunity

On evolutionary game theory (EGT), two intervention policies: vaccination and self-awareness, are considered to account for how human attitude impacts disease spreading. Although these interventions can impose, their implementation may depend on the various immunity systems such as shield immunity, innate immunity, waning immunity, natural immunity, and artificial immunity. This framework provides an epidemic SEIRVA (susceptible-exposed-infected-removed-vaccinated-aware) model and two EGT dynamics to analyze the interplay between the immunity system and social learning interventions. The prospect of exploring the individual's strategy and social dilemma for removing a disease could assist design an effective vaccine program and self-awareness policy. Also, we evaluated the indicator of social efficiency deficit (SED) for a social dual-dilemma to measure the presence of a dilemma situation. Extensive theoretical analysis displays that stability includes the reproduction number, conditions for positivity and uniqueness, and the strength number analyzed in the equilibria, including fundamental properties validated by numerical simulation of the discretization method that appraises a variety of graphs at adjusting parameters. We present extensive numerical studies investigating the affect of controlling parameters, individual vulnerability, optimal policies, and individual costs. It turns out that, even with the affordable vaccine, individuals may have very different behaviors; self-awareness strategy plays a vital role in controlling diseases.

Impact of information and Lévy noise on stochastic COVID-19 epidemic model under real statistical data

In this paper, we consider the dynamical behaviour of a stochastic coronavirus (COVID-19) susceptible-infected-removed epidemic model with the inclusion of the influence of information intervention and Lévy noise. The existence and uniqueness of the model positive solution are proved. Then, we establish a stochastic threshold as a sufficient condition for the extinction and persistence in mean of the disease. Based on the available COVID-19 data, the parameters of the model were estimated and we fit the model with real statistics. Finally, numerical simulations are presented to support our theoretical results.

Time-delayed modelling of the COVID-19 dynamics with a convex incidence rate

COVID-19 pandemic represents an unprecedented global health crisis which has an enormous impact on the world population and economy. Many scientists and researchers have combined efforts to develop an approach to tackle this crisis and as a result, researchers have developed several approaches for understanding the COVID-19 transmission dynamics and the way of mitigating its effect. The implementation of a mathematical model has proven helpful in further understanding the behaviour which has helped the policymaker in adopting the best policy necessary for reducing the spread. Most models are based on a system of equations which assume an instantaneous change in the transmission dynamics. However, it is believed that SARS-COV-2 have an incubation period before the tendency of transmission. Therefore, to capture the dynamics adequately, there would be a need for the inclusion of delay parameters which will account for the delay before an exposed individual could become infected. Hence, in this paper, we investigate the SEIR epidemic model with a convex incidence rate incorporated with a time delay. We first discussed the epidemic model as a form of a classical ordinary differential equation and then the inclusion of a delay to represent the period in which the susceptible and exposed individuals became infectious. Secondly, we identify the disease-free together with the endemic equilibrium state and examine their stability by adopting the delay differential equation stability theory. Thereafter, we carried out numerical simulations with suitable parameters choice to illustrate the theoretical result of the system and for a better understanding of the model dynamics. We also vary the length of the delay to illustrate the changes in the model as the delay parameters change which enables us to further gain an insight into the effect of the included delay in a dynamical system. The result confirms that the inclusion of delay destabilises the system and it forces the system to exhibit an oscillatory behaviour which leads to a periodic solution and it further helps us to gain more insight into the transmission dynamics of the disease and strategy to reduce the risk of infection.

A case study of 2019-nCoV in Russia using integer and fractional order derivatives

In this article, we define a mathematical model to analyze the outbreaks of the most deadly disease of the decade named 2019-nCoV by using integer and fractional order derivatives. For the case study, the real data of Russia is taken to perform novel parameter estimation by using the Trust Region Reflective (TRR) algorithm. First, we define an integer order model and then generalize it by using fractional derivatives. A novel optimal control problem is derived to see the impact of possible preventive measures against the spread of 2019-nCoV. We implement the forward-backward sweep method to numerically solve our proposed model and control problem. A number of graphs have been plotted to see the impact of the proposed control practically. The Russian data-based parameter estimation along with the proposal of a mathematical model in the sense of Caputo fractional derivative that contains the memory term in the system are the main novel features of this study.

A computational study of a stochastic fractal-fractional hepatitis B virus infection incorporating delayed immune reactions via the exponential decay

Recently, researchers have become interested in modelling, monitoring, and treatment of hepatitis B virus infection. Understanding the various connections between pathogens, immune systems, and general liver function is crucial. In this study, we propose a higher-order stochastically modified delay differential model for the evolution of hepatitis B virus transmission involving defensive cells. Taking into account environmental stimuli and ambiguities, we presented numerical solutions of the fractal-fractional hepatitis B virus model based on the exponential decay kernel that reviewed the hepatitis B virus immune system involving cytotoxic T lymphocyte immunological mechanisms. Furthermore, qualitative aspects of the system are analyzed such as the existence-uniqueness of the non-negative solution, where the infection endures stochastically as a result of the solution evolving within the predetermined system's equilibrium state. In certain settings, infection-free can be determined, where the illness settles down tremendously with unit probability. To predict the viability of the fractal-fractional derivative outcomes, a novel numerical approach is used, resulting in several remarkable modelling results, including a change in fractional-order δ with constant fractal-dimension ϖ, δ with changing ϖ, and δ with changing both δ and ϖ. White noise concentration has a significant impact on how bacterial infections are treated.

Infectious disease modelling for SARS-CoV-2 in Africa to guide policy: A systematic review

Applied epidemiological models have played a critical role in understanding the transmission and control of disease outbreaks. Their utility and accuracy in decision-making on appropriate responses during public health emergencies is however a factor of their calibration to local data, evidence informing model assumptions, speed of obtaining and communicating their results, ease of understanding and willingness by policymakers to use their insights. We conducted a systematic review of infectious disease models focused on SARS-CoV-2 in Africa to determine: a) spatial and temporal patterns of SARS-CoV-2 modelling in Africa, b) use of local data to calibrate the models and local expertise in modelling activities, and c) key modelling questions and policy insights. We searched PubMed, Embase, Web of Science and MedRxiv databases following the PRISMA guidelines to obtain all SARS-CoV-2 dynamic modelling papers for one or multiple African countries. We extracted data on countries studied, authors and their affiliations, modelling questions addressed, type of models used, use of local data to calibrate the models, and model insights for guiding policy decisions. A total of 74 papers met the inclusion criteria, with nearly two-thirds of these coming from 6% (3) of the African countries. Initial papers were published 2 months after the first cases were reported in Africa, with most papers published after the first wave. More than half of all papers (53, 78%) and (48, 65%) had a first and last author affiliated to an African institution respectively, and only 12% (9) used local data for model calibration. A total of 60% (46) of the papers modelled assessment of control interventions. The transmission rate parameter was found to drive the most uncertainty in the sensitivity analysis for majority of the models. The use of dynamic models to draw policy insights was crucial and therefore there is need to increase modelling capacity in the continent.

Novel stochastic dynamics of a fractal-fractional immune effector response to viral infection via latently infectious tissues

In this paper, the global complexities of a stochastic virus transmission framework featuring adaptive response and Holling type II estimation are examined via the non-local fractal-fractional derivative operator in the Atangana-Baleanu perspective. Furthermore, we determine the existence-uniqueness of positivity of the appropriate solutions. Ergodicity and stationary distribution of non-negative solutions are carried out. Besides that, the infection progresses in the sense of randomization as a consequence of the response fluctuating within the predictive case's equilibria. Additionally, the extinction criteria have been established. To understand the reliability of the findings, simulation studies utilizing the fractal-fractional dynamics of the synthesized trajectory under the Atangana-Baleanu-Caputo derivative incorporating fractional-order α and fractal-dimension ℘ have also been addressed. The strength of white noise is significant in the treatment of viral pathogens. The persistence of a stationary distribution can be maintained by white noise of sufficient concentration, whereas the eradication of the infection is aided by white noise of high concentration.

Comparative study of artificial neural network versus parametric method in COVID-19 data analysis

Since the previous two years, a new coronavirus (COVID-19) has found a major global problem. The speedy pathogen over the globe was followed by a shockingly large number of afflicted people and a gradual increase in the number of deaths. If the survival analysis of active individuals can be predicted, it will help to contain the epidemic significantly in any area. In medical diagnosis, prognosis and survival analysis, neural networks have been found to be as successful as general nonlinear models. In this study, a real application has been developed for estimating the COVID-19 mortality rates in Italy by using two different methods, artificial neural network modeling and maximum likelihood estimation. The predictions obtained from the multilayer artificial neural network model developed with 9 neurons in the hidden layer were compared with the numerical results. The maximum deviation calculated for the artificial neural network model was -0.14% and the R value was 0.99836. The study findings confirmed that the two different statistical models that were developed had high reliability.

A vaccination model for COVID-19 in Gauteng, South Africa

The COVID-19 pandemic provides an opportunity to explore the impact of government mandates on movement restrictions and non-pharmaceutical interventions on a novel infection, and we investigate these strategies in early-stage outbreak dynamics. The rate of disease spread in South Africa varied over time as individuals changed behavior in response to the ongoing pandemic and to changing government policies. Using a system of ordinary differential equations, we model the outbreak in the province of Gauteng, assuming that several parameters vary over time. Analyzing data from the time period before vaccination gives the approximate dates of parameter changes, and those dates are linked to government policies. Unknown parameters are then estimated from available case data and used to assess the impact of each policy. Looking forward in time, possible scenarios give projections involving the implementation of two different vaccines at varying times. Our results quantify the impact of different government policies and demonstrate how vaccinations can alter infection spread.

A fractional-order mathematical model for analyzing the pandemic trend of COVID-19

Many countries worldwide have been affected by the outbreak of the novel coronavirus (COVID-19) that was first reported in China. To understand and forecast the transmission dynamics of this disease, fractional-order derivative-based modeling can be beneficial. We propose in this paper a fractional-order mathematical model to examine the COVID-19 disease outbreak. This model outlines the multiple mechanisms of transmission within the dynamics of infection. The basic reproduction number and the equilibrium points are calculated from the model to assess the transmissibility of the COVID-19. Sensitivity analysis is discussed to explain the significance of the epidemic parameters. The existence and uniqueness of the solution to the proposed model have been proven using the fixed-point theorem and by helping the Arzela-Ascoli theorem. Using the predictor-corrector algorithm, we approximated the solution of the proposed model. The results obtained are represented by using figures that illustrate the behavior of the predicted model classes. Finally, the study of the stability of the numerical method is carried out using some results and primary lemmas.

Mathematical Analysis of Two Waves of COVID-19 Disease with Impact of Vaccination as Optimal Control

This paper is devoted to answering some questions using a mathematical model by analyzing India’s first and second phases of the COVID-19 pandemic. A new mathematical model is introduced with a nonmonotonic incidence rate to incorporate the psychological effect of COVID-19 in society. The paper also discusses the local stability and global stability of an endemic equilibrium and a disease-free equilibrium. The basic reproduction number is evaluated using the proposed COVID-19 model for disease spread in India based on the actual data sets. The study of nonperiodic solutions at a positive equilibrium point is also analyzed. The model is rigorously studied using MATLAB to alert the decision-making bodies to hinder the emergence of any other pandemic outbreaks or the arrival of subsequent pandemic waves. This paper shows the excellent prediction of the first wave and very commanding for the second wave. The exciting results of the paper are as follows: (i) psychological effect on the human population has an impact on propagation; (ii) lockdown is a suitable technique mathematically to control the COVID spread; (iii) different variants produce different waves; (iv) the peak value always crosses its past value.

Mathematical modelling of earlier stages of COVID-19 transmission dynamics in Ghana

In late 2019, a novel coronavirus, the SARS-CoV-2 outbreak was identified in Wuhan, China and later spread to every corner of the globe. Whilst the number of infection-induced deaths in Ghana, West Africa are minimal when compared with the rest of the world, the impact on the local health service is still significant. Compartmental models are a useful framework for investigating transmission of diseases in societies. To understand how the infection will spread and how to limit the outbreak. We have developed a modified SEIR compartmental model with nine compartments (CoVCom9) to describe the dynamics of SARS-CoV-2 transmission in Ghana. We have carried out a detailed mathematical analysis of the CoVCom9, including the derivation of the basic reproduction number, R 0 . In particular, we have shown that the disease-free equilibrium is globally asymptotically stable when R 0 < 1 via a candidate Lyapunov function. Using the SARS-CoV-2 reported data for confirmed-positive cases and deaths from March 13 to August 10, 2020, we have parametrised the CoVCom9 model. The results of this fit show good agreement with data. We used Latin hypercube sampling-rank correlation coefficient (LHS-PRCC) to investigate the uncertainty and sensitivity of R 0 since the results derived are significant in controlling the spread of SARS-CoV-2. We estimate that over this five month period, the basic reproduction number is given by R 0 = 3 . 110 , with the 95% confidence interval being 2 . 042 ≤ R 0 ≤ 3 . 240 , and the mean value being R 0 = 2 . 623 . Of the 32 parameters in the model, we find that just six have a significant influence on R 0 , these include the rate of testing, where an increasing testing rate contributes to the reduction of R 0 .

Investigating the transmission dynamics of SARS-CoV-2 in Nigeria: A SEIR modelling approach

This study was designed to investigate the transmission dynamics of the novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) to inform policy advisory vital for managing the spread of the virus in Nigeria. We applied the Susceptible-Exposed-Infectious-Recovered (SEIR)-type predictive model to discern the transmission dynamics of SARS-CoV-2 at different stages of the pandemic; incidence, during and after the lockdown from 27th March 2020 to 22nd September 2020 in Nigeria. Our model was calibrated with the COVID-19 data (obtained from the Nigeria Centre for Disease Control) using the "lsqcurvefit" package in MATLAB to fit the "cumulative active cases" and "cumulative death" data. We adopted the Latin hypercube sampling with a partial rank correlation coefficient index to determine the measure of uncertainty in our parameter estimation at a 99% confidence interval (CI). At the incidence of SARS-CoV-2 in Nigeria, the basic reproduction number (R0 ) was 6.860; 99%CI [6.003, 7.882]. R0 decreased by half (3.566; 99%CI [3.503, 3.613]) during the lockdown, and R0 was 1.238; 99%CI [1.215, 1.262] after easing the lockdown. If all parameters are maintained (as in after easing the lockdown), our model forecasted a gradual and perpetual surge through the next 12 months or more. In the light of our results and available data, evidence of human-to-human transmission at higher rates is still very likely. A timely, proactive, and well-articulated effort should help mitigate the transmission of SARS-CoV-2 in Nigeria.

A new study on two different vaccinated fractional-order COVID-19 models via numerical algorithms

The main purpose of this paper is to provide new vaccinated models of COVID-19 in the sense of Caputo-Fabrizio and new generalized Caputo-type fractional derivatives. The formulation of the given models is presented including an exhaustive study of the model dynamics such as positivity, boundedness of the solutions and local stability analysis. Furthermore, the unique solution existence for the proposed fractional order models is discussed via fixed point theory. Numerical solutions are also derived by using two-steps Adams-Bashforth algorithm for Caputo-Fabrizio operator, and modified Predictor-Corrector method for generalised Caputo fractional derivative. Our analysis allow to show that the given fractional-order models exemplify the dynamics of COVID-19 much better than the classical ones. Also, the analysis on the convergence and stability for the proposed methods are performed. By this study, we see that how the vaccine availability plays an important role in the control of COVID-19 infection.

Prediction intervals of the COVID-19 cases by HAR models with growth rates and vaccination rates in top eight affected countries: Bootstrap improvement

This paper is devoted to modeling and predicting COVID-19 confirmed cases through a multiple linear regression. Especially, prediction intervals of the COVID-19 cases are extensively studied. Due to long-memory feature of the COVID-19 data, a heterogeneous autoregression (HAR) is adopted with Growth rates and Vaccination rates; it is called HAR-G-V model. Top eight affected countries are taken with their daily confirmed cases and vaccination rates. Model criteria results such as root mean square error (RMSE), mean absolute error (MAE), R 2 , AIC and BIC are reported in the HAR models with/without the two rates. The HAR-G-V model performs better than other HAR models. Out-of-sample forecasting by the HAR-G-V model is conducted. Forecast accuracy measures such as RMSE, MAE, mean absolute percentage error and root relative square error are computed. Furthermore, three types of prediction intervals are constructed by approximating residuals to normal and Laplace distributions, as well as by employing bootstrap procedure. Empirical coverage probability, average length and mean interval score are evaluated for the three prediction intervals. This work contributes three folds: a novel trial to combine both growth rates and vaccination rates in modeling COVID-19; construction and comparison of three types of prediction intervals; and an attempt to improve coverage probability and mean interval score of prediction intervals via bootstrap technique.

Optimal control and comprehensive cost-effectiveness analysis for COVID-19

Cost-effectiveness analysis is a mode of determining both the cost and economic health outcomes of one or more control interventions. In this work, we have formulated a non-autonomous nonlinear deterministic model to study the control of COVID-19 to unravel the cost and economic health outcomes for the autonomous nonlinear model proposed for the Kingdom of Saudi Arabia. We calculated the strength number and noticed the strength number is less than zero, meaning the proposed model does not capture multiple waves, hence to capture multiple wave new compartmental model may require for the Kingdom of Saudi Arabia. We proposed an optimal control problem based on a previously studied model and proved the existence of the proposed optimal control model. The optimality system associated with the non-autonomous epidemic model is derived using Pontryagin's maximum principle. The optimal control model captures four time-dependent control functions, thus,u 1 -practising physical or social distancing protocols;u 2 -practising personal hygiene by cleaning contaminated surfaces with alcohol-based detergents;u 3 -practising proper and safety measures by exposed, asymptomatic and symptomatic infected individuals;u 4 -fumigating schools in all levels of education, sports facilities, commercial areas and religious worship centres. We have performed numerical simulations to investigate extensive cost-effectiveness analysis for fourteen optimal control strategies. Comparing the control strategies, we noticed that; Strategy 1 (practising physical or social distancing protocols) is the most cost-saving and most effective control intervention in Saudi Arabia in the absence of vaccination. But, in terms of the infection averted, we saw that strategy 6, strategy 11, strategy 12, and strategy 14 are just as good in controlling COVID-19.

Modeling the dynamics of COVID-19 using fractal-fractional operator with a case study

This research study consists of a newly proposed Atangana-Baleanu derivative for transmission dynamics of the coronavirus (COVID-19) epidemic. Taking the advantage of non-local Atangana-Baleanu fractional-derivative approach, the dynamics of the well-known COVID-19 have been examined and analyzed with the induction of various infection phases and multiple routes of transmissions. For this purpose, an attempt is made to present a novel approach that initially formulates the proposed model using classical integer-order differential equations, followed by application of the fractal fractional derivative for obtaining the fractional COVID-19 model having arbitrary order Ψ and the fractal dimension Ξ . With this motive, some basic properties of the model that include equilibria and reproduction number are presented as well. Then, the stability of the equilibrium points is examined. Furthermore, a novel numerical method is introduced based on Adams-Bashforth fractal-fractional approach for the derivation of an iterative scheme of the fractal-fractional ABC model. This in turns, has helped us to obtained detailed graphical representation for several values of fractional and fractal orders Ψ and Ξ , respectively. In the end, graphical results and numerical simulation are presented for comprehending the impacts of the different model parameters and fractional order on the disease dynamics and the control. The outcomes of this research would provide strong theoretical insights for understanding mechanism of the infectious diseases and help the worldwide practitioners in adopting controlling strategies.

A delayed plant disease model with Caputo fractional derivatives

We analyze a time-delay Caputo-type fractional mathematical model containing the infection rate of Beddington-DeAngelis functional response to study the structure of a vector-borne plant epidemic. We prove the unique global solution existence for the given delay mathematical model by using fixed point results. We use the Adams-Bashforth-Moulton P-C algorithm for solving the given dynamical model. We give a number of graphical interpretations of the proposed solution. A number of novel results are demonstrated from the given practical and theoretical observations. By using 3-D plots we observe the variations in the flatness of our plots when the fractional order varies. The role of time delay on the proposed plant disease dynamics and the effects of infection rate in the population of susceptible and infectious classes are investigated. The main motivation of this research study is examining the dynamics of the vector-borne epidemic in the sense of fractional derivatives under memory effects. This study is an example of how the fractional derivatives are useful in plant epidemiology. The application of Caputo derivative with equal dimensionality includes the memory in the model, which is the main novelty of this study.

A new mathematical model of multi-faced COVID-19 formulated by fractional derivative chains

It has been reported that there are seven different types of coronaviruses realized by individuals, containing those responsible for the SARS, MERS, and COVID-19 epidemics. Nowadays, numerous designs of COVID-19 are investigated using different operators of fractional calculus. Most of these mathematical models describe only one type of COVID-19 (infected and asymptomatic). In this study, we aim to present an altered growth of two or more types of COVID-19. Our technique is based on the ABC-fractional derivative operator. We investigate a system of coupled differential equations, which contains the dynamics of the diffusion between infected and asymptomatic people. The consequence is accordingly connected with a macroscopic rule for the individuals. In this analysis, we utilize the concept of a fractional chain. This type of chain is a fractional differential-difference equation combining continuous and discrete variables. The existence of solutions is recognized by formulating a matrix theory. The solution of the approximated system is shown to have a minimax point at the origin.

Dynamical analysis of coronavirus disease with crowding effect, and vaccination: a study of third strain

Countries affected by the coronavirus epidemic have reported many infected cases and deaths based on world health statistics. The crowding factor, which we named "crowding effects," plays a significant role in spreading the diseases. However, the introduction of vaccines marks a turning point in the rate of spread of coronavirus infections. Modeling both effects is vastly essential as it directly impacts the overall population of the studied region. To determine the peak of the infection curve by considering the third strain, we develop a mathematical model (susceptible-infected-vaccinated-recovered) with reported cases from August 01, 2021, till August 29, 2021. The nonlinear incidence rate with the inclusion of both effects is the best approach to analyze the dynamics. The model's positivity, boundedness, existence, uniqueness, and stability (local and global) are addressed with the help of a reproduction number. In addition, the strength number and second derivative Lyapunov analysis are examined, and the model was found to be asymptotically stable. The suggested parameters efficiently control the active cases of the third strain in Pakistan. It was shown that a systematic vaccination program regulates the infection rate. However, the crowding effect reduces the impact of vaccination. The present results show that the model can be applied to other countries' data to predict the infection rate.

Mathematical assessment of constant and time-dependent control measures on the dynamics of the novel coronavirus: An application of optimal control theory

The coronavirus infectious disease (COVID-19) is a novel respiratory disease reported in 2019 in China. The COVID-19 is one of the deadliest pandemics in history due to its high mortality rate in a short period. Many approaches have been adopted for disease minimization and eradication. In this paper, we studied the impact of various constant and time-dependent variable control measures coupled with vaccination on the dynamics of COVID-19. The optimal control theory is used to optimize the model and set an effective control intervention for the infection. Initially, we formulate the mathematical epidemic model for the COVID-19 without variable controls. The model basic mathematical assessment is presented. The nonlinear least-square procedure is utilized to parameterize the model from actual cases reported in Pakistan. A well-known technique based on statistical tools known as the Latin-hypercube sampling approach (LHS) coupled with the partial rank correlation coefficient (PRCC) is applied to present the model global sensitivity analysis. Based on global sensitivity analysis, the COVID-19 vaccine model is reformulated to obtain a control problem by introducing three time dependent control variables for isolation, vaccine efficacy and treatment enhancement represented byu 1 ( t ) ,u 2 ( t ) andu 3 ( t ) , respectively. The necessary optimality conditions of the control problem are derived via the optimal control theory. Finally, the simulation results are depicted with and without variable controls using the well-known Runge-Kutta numerical scheme. The simulation results revealed that time-dependent control measures play a vital role in disease eradication.

A new lifetime family of distributions: Theoretical developments and analysis of COVID 19 data

In parametric statistical modeling and inference, it is critical to develop generalizations of existing statistical distributions to make them more flexible in modeling real data sets. Thus , this paper contributes to the subject by investigating a new flexible and versatile generalized family of distributions defined from the alliance of the families known as beta-G and Topp-Leone generated (TL-G), inspiring the name of BTL-G family. The characteristics of this new family are studied through analytical, graphical and numerical approaches. Statistical features of the family such as expansion of density function (pdf), cumulative function (cdf), moments (MOs), incomplete moments (IMOs), mean deviation (MDE), and entropy (ENT) are calculated. The model parameters' maximum likelihood estimates (MaxLEs) and Bayesian estimates (BEs) are provided. Symmetric and Asymmetric Bayesian Loss function have been discussed. A complete simulation study is proposed to illustrate their numerical efficiency. The considered model is also applied to analyze two different kinds of genuine COVID 19 data sets. We show that it outperforms other well-known models defined with the same baseline distribution, proving its high level of adaptability in the context of data analysis.

Open Data Resources on COVID-19 in Six European Countries: Issues and Opportunities

Since the beginning of the COVID-19 pandemic in March 2020, national and international authorities started to develop and update datasets to provide data to researchers, journalists and health care providers as well as public opinion. These data became one of the most important sources of information, which are updated daily and analysed by scientists in order to investigate and predict the spread of this epidemic. Despite this positive reaction from both national and international authorities in providing aggregated information on the diffusion of COVID-19, different challenges have been underlined in previously published studies. Different papers have discussed strengths and weaknesses of these types of datasets by focusing on different quality perspectives, which include the statistical methods adopted to analyse them; the lack of standards and models in the adoption of data for their management and distribution; and the analysis of different data quality characteristics. These studies have analysed datasets at the general level or by focusing the attention on specific indicators such as the number of cases or deaths. This paper further investigates issues and opportunities in the diffusion of these datasets under two main perspectives. At the general level, it analyses how data are organized and distributed to scientific and non-scientific communities. Moreover, it further explores the indicators adopted to describe the spread of the COVID-19 epidemic while also highlighting the level of detail used to describe them in terms of gender, age ranges and territorial units. The paper focuses on six European countries: Belgium, France, Germany, Italy, Spain and UK.

A secondary approach with conventional medicines and supplements to recuperate current COVID-19 status

Novel coronavirus 2019 (COVID-19) is a zoonosis that revised the global economic and societal progress since early 2020. The SARS-CoV-2 has been recognized as the responsible pathogen for COVID-19 with high infection and mortality rate potential. It has spread in 192 countries and infected about 1.5% of the world population, and still, a proper therapeutic approach is not unveiled. COVID-19 indication starts with fever to shortness of breathing, leading to ICU admission with the ventilation support in severe conditions. Besides the symptomatic mainstay clinical therapeutic approach, only Remdesivir has been approved by the FDA. Several pharmaceutical companies claimed different vaccines with exceptionally high efficacy (90-95%) against COVID-19; how long these vaccines can protect and long-term safety with the new variants are unpredictable. After the worldwide spread of the COVID-19 pandemic, numerous clinical trials with different phases are being performed to find the most appropriate solution to this condition. Some of these trials with old FDA-approved drugs showed promising results. In this review, we have precisely compiled the efforts to curb the disease and discussed the clinical findings of Ivermectin, Doxycycline, Vitamin-D, Vitamin-C, Zinc, and cannabidiol and their combinations. Additionally, the correlation of these molecules on the prophylactic and diseased ministration against COVID-19 has been explored.

Modeling and forecasting the COVID-19 pandemic with heterogeneous autoregression approaches: South Korea

This paper deals with time series analysis for COVID-19 in South Korea. We adopt heterogeneous autoregressive (HAR) time series models and discuss the statistical inference for various COVID-19 data. Seven data sets such as cumulative confirmed (CC) case, cumulative recovered (CR) case and cumulative death (CD) case as well as recovery rate, fatality rate and infection rates for 14 and 21 days are handled for the statistical analysis. In the HAR models, model selections of orders are conducted by evaluating root mean square error (RMSE) and mean absolute error (MAE) as well asR 2 , AIC, and BIC. As a result of estimation, we provide coefficients estimates, standard errors and 95% confidence intervals in the HAR models. Our results report that fitted values via the HAR models are not only well-matched with the real cumulative cases but also differenced values from the fitted HAR models are well-matched with real daily cases. Additionally, because the CC and the CD cases are strongly correlated, we use a bivariate HAR model for the two data sets. Out-of-sample forecastings are carried out with the COVID-19 data sets to obtain multi-step ahead predicted values and 95% prediction intervals. As for the forecasting performances, four accuracy measures such as RMSE, MAE, mean absolute percentage error (MAPE) and root relative square error (RRSE) are evaluated. Contributions of this work are three folds: First, it is shown that the HAR models fit well to cumulative numbers of the COVID-19 data along with good criterion results. Second, a variety of analysis are studied for the COVID-19 series: confirmed, recovered, death cases, as well as the related rates. Third, forecast accuracy measures are evaluated as small values of errors, and thus it is concluded that the HAR model provides a good prediction model for the COVID-19.

Analysis of a discrete mathematical COVID-19 model

To describe the main propagation of the COVID-19 and has to find the control for the rapid spread of this viral disease in real life, in current manuscript a discrete form of the SEIR model is discussed. The main aim of this is to describe the viral disease in simplest way and the basic properties that are related with the nature of curves for susceptible and infected individuals are discussed here. The elementary numerical examples are given by using the real data of India and Algeria.

A novel mathematical model for COVID-19 with remedial strategies

Coronavirus (COVID-19) outbreak from Wuhan, Hubei province in China and spread out all over the World. In this work, a new mathematical model is proposed. The model consists the system of ODEs. The developed model describes the transmission pathways by employing non constant transmission rates with respect to the conditions of environment and epidemiology. There are many mathematical models purposed by many scientists. In this model, "α E " and "α I ", transmission coefficients of the exposed cases to susceptible and infectious cases to susceptible respectively, are included. " δ " as a governmental action and restriction against the spread of coronavirus is also introduced. The RK method of order four (RK4) is employed to solve the model equations. The results are presented for four countries i.e., Pakistan, Italy, Japan, and Spain etc. The parametric study is also performed to validate the proposed model.

Fractional dynamic system simulating the growth of microbe

There are different approaches that indicate the dynamic of the growth of microbe. In this research, we simulate the growth by utilizing the concept of fractional calculus. We investigate a fractional system of integro-differential equations, which covers the subtleties of the diffusion between infected and asymptomatic cases. The suggested system is applicable to distinguish the presentation of growth level of the infection and to approve if its mechanism is positively active. An optimal solution under simulation mapping assets is considered. The estimated numerical solution is indicated by employing the fractional Tutte polynomials. Our methodology is based on the Atangana-Baleanu calculus (ABC). We assess the recommended system by utilizing real data.

A case study of 2019-nCOV cases in Argentina with the real data based on daily cases from March 03, 2020 to March 29, 2021 using classical and fractional derivatives

In this study, our aim is to explore the dynamics of COVID-19 or 2019-nCOV in Argentina considering the parameter values based on the real data of this virus from March 03, 2020 to March 29, 2021 which is a data range of more than one complete year. We propose a Atangana-Baleanu type fractional-order model and simulate it by using predictor-corrector (P-C) method. First we introduce the biological nature of this virus in theoretical way and then formulate a mathematical model to define its dynamics. We use a well-known effective optimization scheme based on the renowned trust-region-reflective (TRR) method to perform the model calibration. We have plotted the real cases of COVID-19 and compared our integer-order model with the simulated data along with the calculation of basic reproductive number. Concerning fractional-order simulations, first we prove the existence and uniqueness of solution and then write the solution along with the stability of the given P-C method. A number of graphs at various fractional-order values are simulated to predict the future dynamics of the virus in Argentina which is the main contribution of this paper.

A two diffusion stochastic model for the spread of the new corona virus SARS-CoV-2

We propose a refined version of the stochastic SEIR model for epidemic of the new corona virus SARS-Cov-2, causing the COVID-19 disease, taking into account the spread of the virus due to the regular infected individuals (transmission coefficient β ), hospitalized individuals (transmission coefficient l β , l > 0 ) and superspreaders (transmission coefficient β ' ). The model is constructed from the corresponding ordinary differential model by introducing two independent environmental white noises in transmission coefficients for above mentioned classes - one noise for infected and hospitalized individuals and the other for superspreaders. Therefore, the model is defined as a system of stochastic differential equations driven by two independent standard Brownian motions. Existence and uniqueness of the global positive solution is proven, and conditions under which extinction and persistence in mean hold are given. The theoretical results are illustrated via numerical simulations.

Dynamics and bifurcation analysis of a state-dependent impulsive SIS model

Recently, considering the susceptible population size-guided implementations of control measures, several modelling studies investigated the global dynamics and bifurcation phenomena of the state-dependent impulsive SIR models. In this study, we propose a state-dependent impulsive model based on the SIS model. We firstly recall the complicated dynamics of the ODE system with saturated treatment. Based on the dynamics of the ODE system, we firstly discuss the existence and the stability of the semi-trivial periodic solution. Then, based on the definition of the Poincaré map and its properties, we systematically investigate the bifurcations near the semi-trivial periodic solution with all the key control parameters; consequently, we prove the existence and stability of the positive periodic solutions.

Investigation of the dynamics of COVID-19 with a fractional mathematical model: A comparative study with actual data

One of the greatest challenges facing the humankind nowadays is to confront that emerging virus, which is the Coronavirus (COVID-19), and therefore all organizations have to unite in order to tackle that the transmission risk of this virus. From this standpoint, the scientific researchers have to find good mathematical models that do describe the transmission of such virus and contribute to reducing it in one way or another, where the study of COVID-19 transmission dynamics by mathematical models is very important for analyzing and controlling this disease propagation. Thus, in the current work, we present a new fractional-order mathematical model that describes the dynamics of COVID-19. In the proposed model, the total population is divided into eight classes, in addition to three compartments used to estimate the parameters and initial values. The effective reproduction number ( R 0 ) is derived by next generation matrix (NGM) method and all possible equilibrium points and their stability are investigated in details. We used the reported data (from January 23, 2020, to November 21, 2020) from the National Health Commission (NHC) of China to estimate the parameters and initial conditions (ICs) which suggested for our model. Simulation outcomes demonstrate that the fractional order model (FOM) represents behaviors that follow the real data more accurately than the integer-order model. The current work enhances the recent reported results of Zu et al. published in THE LANCET (doi:10.2139/ssrn.3539669).

Sensitivity analysis and optimal control of COVID-19 dynamics based on SEIQR model

It is of great curiosity to observe the effects of prevention methods and the magnitudes of the outbreak including epidemic prediction, at the onset of an epidemic. To deal with COVID-19 Pandemic, an SEIQR model has been designed. Analytical study of the model consists of the calculation of the basic reproduction number and the constant level of disease absent and disease present equilibrium. The model also explores number of cases and the predicted outcomes are in line with the cases registered. By parameters calibration, new cases in Pakistan are also predicted. The number of patients at the current level and the permanent level of COVID-19 cases are also calculated analytically and through simulations. The future situation has also been discussed, which could happen if precautionary restrictions are adopted.