A numerical study of COVID-19 epidemic model with vaccination and diffusion.

The coronavirus infectious disease (or COVID-19) is a severe respiratory illness. Although the infection incidence decreased significantly, still it remains a major panic for human health and the global economy. The spatial movement of the population from one region to another remains one of the major causes of the spread of the infection. In the literature, most of the COVID-19 models have been constructed with only temporal effects. In this paper, a vaccinated spatio-temporal COVID-19 mathematical model is developed to study the impact of vaccines and other interventions on the disease dynamics in a spatially heterogeneous environment. Initially, some of the basic mathematical properties including existence, uniqueness, positivity, and boundedness of the diffusive vaccinated models are analyzed. The model equilibria and the basic reproductive number are presented. Further, based upon the uniform and non-uniform initial conditions, the spatio-temporal COVID-19 mathematical model is solved numerically using finite difference operator-splitting scheme. Furthermore, detailed simulation results are presented in order to visualize the impact of vaccination and other model key parameters with and without diffusion on the pandemic incidence. The obtained results reveal that the suggested intervention with diffusion has a significant impact on the disease dynamics and its control.

Is it time for global adoption of endoscopic retrograde appendicitis therapy of acute appendicitis?

Acute appendicitis is a common abdominal surgical emergency worldwide. Abraham Groves performed the first documented open appendectomy in 1883. Although appendectomy is still the most effective treatment in cases of acute appendicitis, it causes a range of complications and carries the risk of negative appendectomy. In the awake of covid-19, the latest guidelines recommend antibiotic therapy as an acceptable first line treatment for acute appendicitis. However, patients treated with antibiotics have a recurrence risk of up to 30% at 1 year. Endoscopic retrograde appendicitis therapy (ERAT) has emerged as promising non-invasive treatment modality for acute uncomplicated appendicitis (AUA) which involves cannulation, appedicography, appendiceal stone extraction, appendiceal lumen irrigation, and stent insertion. ERAT aims to relieve the cause of appendicitis (e.g., obstruction or stenosis of the appendiceal lumen) and thus effectively prevent the recurrence of appendicitis. In addition, it can make a definitive diagnosis of acute appendicitis during endoscopic retrograde appendicography. Studies have shown that 93.8 to 95% of AUA patients did not have a recurrence following ERAT. In this study, we aim to summarize the current body of evidence on ERAT to situate it alongside currently established therapies for acute appendicitis, in particular, AUA.

The impact of vaccination on the modeling of COVID-19 dynamics: a fractional order model.

The coronavirus disease 2019 (COVID-19) is a recent outbreak of respiratory infections that have affected millions of humans all around the world. Initially, the major intervention strategies used to combat the infection were the basic public health measure, nevertheless, vaccination is an effective strategy and has been used to control the incidence of many infectious diseases. Currently, few safe and effective vaccines have been approved to control the inadvertent transmission of COVID-19. In this paper, the modeling approach is adopted to investigate the impact of currently available anti-COVID vaccines on the dynamics of COVID-19. A new fractional-order epidemic model by incorporating the vaccination class is presented. The fractional derivative is considered in the well-known Caputo sense. Initially, the proposed vaccine model for the dynamics of COVID-19 is developed via integer-order differential equations and then the Caputo-type derivative is applied to extend the model to a fractional case. By applying the least square method, the model is fitted to the reported cases in Pakistan and some of the parameters involved in the models are estimated from the actual data. The threshold quantity ( R 0 ) is computed by the Next-generation method. A detailed analysis of the fractional model, such as positivity of model solution, equilibrium points, and stabilities on both disease-free and endemic states are discussed comprehensively. An efficient iterative method is utilized for the numerical solution of the proposed model and the model is then simulated in the light of vaccination. The impact of important influential parameters on the pandemic dynamics is shown graphically. Moreover, the impact of different intervention scenarios on the disease incidence is depicted and it is found that the reduction in the effective contact rate (up to 30%) and enhancement in vaccination rate (up to 50%) to the current baseline values significantly reduced the disease new infected cases.

Application of fractional optimal control theory for the mitigating of novel coronavirus in Algeria.

In this paper, we investigate the dynamics of novel coronavirus infection (COVID-19) using a fractional mathematical model in Caputo sense. Based on the spread of COVID-19 virus observed in Algeria, we formulate the model by dividing the infected population into two sub-classes namely the reported and unreported infective individuals. The existence and uniqueness of the model solution are given by using the well-known Picard-Lindelöf approach. The basic reproduction number R 0 is obtained and its value is estimated from the actual cases reported in Algeria. The model equilibriums and their stability analysis are analyzed. The impact of various constant control parameters is depicted for integer and fractional values of α . Further, we perform the sensitivity analysis showing the most sensitive parameters of the model versus R 0 to predict the incidence of the infection in the population. Further, based on the sensitivity analysis, the Caputo model with constant controls is extended to time-dependent variable controls in order obtain a fractional optimal control problem. The associated four time-dependent control variables are considered for the prevention, treatment, testing and vaccination. The fractional optimality condition for the control COVID-19 transmission model is presented. The existence of the Caputo optimal control model is studied and necessary condition for optimality in the Caputo case is derived from Pontryagin's Maximum Principle. Finally, the effectiveness of the proposed control strategies are demonstrated through numerical simulations. The graphical results revealed that the implantation of time-dependent controls significantly reduces the number of infective cases and are useful in mitigating the infection.

Application of fractional optimal control theory for the mitigating of novel coronavirus in Algeria

In this paper, we investigate the dynamics of novel coronavirus infection (COVID-19) using a fractional mathematical model in Caputo sense. Based on the spread of COVID-19 virus observed in Algeria, we formulate the model by dividing the infected population into two sub-classes namely the reported and unreported infective individuals. The existence and uniqueness of the model solution are given by using the well-known Picard-Lindelöf approach. The basic reproduction number

Correction to: Optimal control analysis of COVID-19 vaccine epidemic model: a case study.

[This corrects the article DOI: 10.1140/epjp/s13360-022-02365-8.].

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 by u 1 ( t ) , u 2 ( t ) and u 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.

The dynamic nexus of E-Government, and sustainable development: Moderating role of multi-dimensional regional integration index in Belt and Road partner countries

This research primarily aims to determine how e-government resource utilization influences sustainable development (SD) while considering the multi-dimensional regional integration (MRII). The sample consists of year 2003–2018 for 64 Belt and Road countries. The study uses the untapped potential moderating role of MRII between the e-government, and the genuine savings index (GSI) for sustainable development. Further, governance composite (WGI), institutional quality (ICRG), government consumptions, macroeconomics conditions, information and communications technology (ICT) exports, and population size are the other important factors that drive sustainable development. The study's findings are estimated through a two-step system Generalized Method of Moments (GMM). Direct channel results of e-government level indicate a significant but negative impact on sustainable development as most countries in BRI are developing or under developing. While with regional integration, indirect channel e-government resources play a significant positive role in sustainable development path. Also, it is evident that in this Covid-19 pandemic period, a better technological system and innovation at the institutional level of countries like China may combat Covid-19 effectively in a more robust manner. At the same time, regional integration at a multi-dimensional level further enhances sustainable development path for neighboring and regionally interconnected countries. Therefore, regional integration can help to an extent in combating post-Covid-19 pandemic effects with the help of robust e-government system implementation. This study contributes to the e-government transformation in the multi-dimensional regional integration of BRI contexts, which boosts socio-economic growth.

Mathematical modeling and stability analysis of the COVID-19 with quarantine and isolation.

The present paper focuses on the modeling of the COVID-19 infection with the use of hospitalization, isolation and quarantine. Initially, we construct the model by spliting the entire population into different groups. We then rigorously analyze the model by presenting the necessary basic mathematical features including the feasible region and positivity of the problem solution. Further, we evaluate the model possible equilibria. The theoretical expression of the most important mathematical quantity of major public health interest called the basic reproduction number is presented. We are taking into account to study the disease free equilibrium by studying its local and global asymptotical analysis. We considering the cases of the COVID-19 infection of Pakistan population and find the parameters using the estimation with the help of nonlinear least square and have R 0 ≈ 1 . 95 . Further, to determine the influence of the model parameters on disease dynamics we perform the sensitivity analysis. Simulations of the model are presented using estimated parameters and the impact of various non-pharmaceutical interventions on disease dynamics is shown with the help of graphical results. The graphical interpretation justify that the effective utilization of keeping the social-distancing, making the quarantine of people (or contact-tracing policy) and to make hospitalization of confirmed infected people that dramatically reduces the number of infected individuals (enhancing the quarantine or contact-tracing by 50% from its baseline reduces 84% in the predicted number of confirmed infected cases). Moreover, it is observed that without quarantine and hospitalization the scenario of the disease in Pakistan is very worse and the infected cases are raising rapidly. Therefore, the present study suggests that still, a proper and effective application of these non-pharmaceutical interventions are necessary to curtail or minimize the COVID-19 infection in Pakistan.

Optimal control analysis of COVID-19 vaccine epidemic model: a case study

The purpose of this research is to explore the complex dynamics and impact of vaccination in controlling COVID-19 outbreak. We formulate the classical epidemic compartmental model by introducing vaccination class. Initially, the proposed mathematical model is analyzed qualitatively. The basic reproductive number is computed and its numerical value is estimated using actual reported data of COVID-19 for Pakistan. The sensitivity analysis is performed to analyze the contribution of model embedded parameters in transmission of the disease. Further, we compute the equilibrium points and discussed its local and global stability. In order to investigate the influence of model key parameters on the transmission and controlling of the disease, we perform numerical simulations describing the impact of various scenarios of vaccine efficacy rate and other controlling measures. Further, on the basis of sensitivity analysis, the proposed model is restructured to obtained optimal control model by introducing time-dependent control variables

Modeling the dynamics of coronavirus with super-spreader class: A fractal-fractional approach.

Super-spreaders of the novel coronavirus disease (or COVID-19) are those with greater potential for disease transmission to infect other people. Understanding and isolating the super-spreaders are important for controlling the COVID-19 incidence as well as future infectious disease outbreaks. Many scientific evidences can be found in the literature on reporting and impact of super-spreaders and super-spreading events on the COVID-19 dynamics. This paper deals with the formulation and simulation of a new epidemic model addressing the dynamics of COVID-19 with the presence of super-spreader individuals. In the first step, we formulate the model using classical integer order nonlinear differential system composed of six equations. The individuals responsible for the disease transmission are further categorized into three sub-classes, i.e., the symptomatic, super-spreader and asymptomatic. The model is parameterized using the actual infected cases reported in the kingdom of Saudi Arabia in order to enhance the biological suitability of the study. Moreover, to analyze the impact of memory index, we extend the model to fractional case using the well-known Caputo-Fabrizio derivative. By making use of the Picard-Lindelöf theorem and fixed point approach, we establish the existence and uniqueness criteria for the fractional-order model. Furthermore, we applied the novel fractal-fractional operator in Caputo-Fabrizio sense to obtain a more generalized model. Finally, to simulate the models in both fractional and fractal-fractional cases, efficient iterative schemes are utilized in order to present the impact of the fractional and fractal orders coupled with the key parameters (including transmission rate due to super-spreaders) on the pandemic peaks.

Combined application of biochar and nitrogen fertilizer promotes the activity of starch metabolism enzymes and the expression of related genes in rice in a dual cropping system.

BACKGROUND: Overuse of chemical fertilizer highly influences grain filling rate and quality of rice grain. Biochar is well known for improving plant growth and grain yield under lower chemical fertilization. Therefore field trials were conducted in the early and late seasons of 2019 at Guangxi University, China to investigate the effects of combined biochar (B) and nitrogen (N) application on rice yield and yield components. There were a total of eight treatments: N1B0, 135 kg N ha- 1+ 0 t B ha- 1; N2B0,180 kg N ha- 1+ 0 t B ha- 1; N1B1,135 kg N ha- 1+ 10 t B ha- 1; N1B2,135kg N ha- 1+ 20 t B ha- 1; N1B3,135 kg N ha- 1+ 30 t B ha- 1; N2B1,180 kg N ha- 1+ 10 t B ha- 1; N2B2,180 kg N ha- 1+ 20 t B ha- 1; and N2B3,180 kg N ha- 1+ 30 t B ha- 1. RESULTS: Biochar application at 30 t ha- 1combined with low N application (135 kg ha- 1) increased the activity of starch-metabolizing enzymes (SMEs) during the early and late seasons compared with treatments without biochar. The grain yield, amylose concentration, and starch content of rice were increased in plots treated with 30 t B ha-1and low N. RT-qPCR analysis showed that biochar addition combined with N fertilizer application increased the expression of AGPS2b, SSS1, GBSS1, and GBSE11b, which increased the activity of SMEs during the grain-filling period. CONCLUSION: Our results suggest that the use of 20 to 30 t B ha- 1coupled with 135 kg N ha- 1 is optimal for improving the grain yield and quality of rice.

Mathematical assessment of the dynamics of novel coronavirus infection with treatment: A fractional study.

In this paper, a mathematical model is formulated to study the transmission dynamics of the novel coronavirus infection under the effect of treatment. The compartmental model is firstly formulated using a system of nonlinear ordinary differential equations. Then, with the help of Caputo operator, the model is reformulated in order to obtain deeper insights into disease dynamics. The basic mathematical features of the time fractional model are rigorously presented. The nonlinear least square procedure is implemented in order to parameterize the model using COVID-19 cumulative cases in Saudi Arabia for the selected time period. The important threshold parameter called the basic reproduction number is evaluated based on the estimated parameters and is found R 0 ≈ 1.60 . The fractional Lyapunov approach is used to prove the global stability of the model around the disease free equilibrium point. Moreover, the model in Caputo sense is solved numerically via an efficient numerical scheme known as the fractional Adamas-Bashforth-Molten approach. Finally, the model is simulated to present the graphical impact of memory index and various intervention strategies such as social-distancing, disinfection of the virus from environment and treatment rate on the pandemic peaks. This study emphasizes the important role of various scenarios in these intervention strategies in curtailing the burden of COVID-19.

Numerical simulation of a Caputo fractional epidemic model for the novel coronavirus with the impact of environmental transmission

The coronavirus infectious disease (COVID-19) is a novel respiratory disease reported in 2019 in China. The infection is very destructive to human lives and caused millions of deaths. Various approaches have been made recently to understand the complex dynamics of COVID-19. The mathematical modeling approach is one of the considerable tools to study the disease spreading pattern. In this article, we develop a fractional order epidemic model for COVID-19 in the sense of Caputo operator. The model is based on the effective contacts among the population and environmental impact to analyze the disease dynamics. The fractional models are comparatively better in understanding the disease outbreak and providing deeper insights into the infectious disease dynamics. We first consider the classical integer model studied in recent literature and then we generalize it by introducing the Caputo fractional derivative. Furthermore, we explore some fundamental mathematical analysis of the fractional model, including the basic reproductive number R0 and equilibria stability utilizing the Routh-Hurwitz and the Lyapunov function approaches. Besides theoretical analysis, we also focused on the numerical solution. To simulate the model, we use the well-known generalized Adams-Bashforth Moulton Scheme. Finally, the influence of some of the model essential parameters on the dynamics of the disease is demonstrated graphically.

Behavioral response of population on transmissibility and saturation incidence of deadly pandemic through fractional order dynamical system.

The world entered in another wave of the SARS-CoV-2 due to non-compliance of standard operating procedures appropriately, initiated by respective governments. Apparently, measures like using face masks and social distancing were not observed by populace that ultimately worsens the situation. The behavioral response of the population induces a change in the dynamical outcomes of the pandemic, which is documented in this paper for all intents and purposes. The innovative perception is executed through a compartmental model with the incorporation of fractional calculus and saturation incident rate. In the first instance, the epidemiological model is designed with proportional fractional definition considering the compartmental individuals of susceptible, social distancing, exposed, quarantined, infected, isolated and recovered populations. By virtue of proportional fractional derivative, effective dynamical outcomes of equilibrium states and basic reproduction number are successfully elaborated with memory effect. The expansion of this derivative greatly simplifies the model to integer order while remaining in the fractional context. Subsequently, the memory effects on the asymptotic profiles are demonstrated through various graphical plots and tabulated values. In addition, the inclusion of saturation incident rate further explains the transmissibility of infection for different behavior of susceptible individuals. Mathematically, the results are also validated through comparative analysis of values with the solutions attained from fractional fourth order Runge-Kutta method (FRK4).

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.

A fractional-order model describing the dynamics of the novel coronavirus (COVID-19) with nonsingular kernel.

In this paper, we investigate an epidemic model of the novel coronavirus disease or COVID-19 using the Caputo-Fabrizio derivative. We discuss the existence and uniqueness of solution for the model under consideration, by using the the Picard-Lindelöf theorem. Further, using an efficient numerical approach we present an iterative scheme for the solutions of proposed fractional model. Finally, many numerical simulations are presented for various values of the fractional order to demonstrate the impact of some effective and commonly used interventions to mitigate this novel infection. From the simulation results we conclude that the fractional order epidemic model provides more insights about the disease dynamics.

A fractional order mathematical model for COVID-19 dynamics with quarantine, isolation, and environmental viral load.

COVID-19 or coronavirus is a newly emerged infectious disease that started in Wuhan, China, in December 2019 and spread worldwide very quickly. Although the recovery rate is greater than the death rate, the COVID-19 infection is becoming very harmful for the human community and causing financial loses to their economy. No proper vaccine for this infection has been introduced in the market in order to treat the infected people. Various approaches have been implemented recently to study the dynamics of this novel infection. Mathematical models are one of the effective tools in this regard to understand the transmission patterns of COVID-19. In the present paper, we formulate a fractional epidemic model in the Caputo sense with the consideration of quarantine, isolation, and environmental impacts to examine the dynamics of the COVID-19 outbreak. The fractional models are quite useful for understanding better the disease epidemics as well as capture the memory and nonlocality effects. First, we construct the model in ordinary differential equations and further consider the Caputo operator to formulate its fractional derivative. We present some of the necessary mathematical analysis for the fractional model. Furthermore, the model is fitted to the reported cases in Pakistan, one of the epicenters of COVID-19 in Asia. The estimated value of the important threshold parameter of the model, known as the basic reproduction number, is evaluated theoretically and numerically. Based on the real fitted parameters, we obtained R 0 ≈ 1.50 . Finally, an efficient numerical scheme of Adams-Moulton type is used in order to simulate the fractional model. The impact of some of the key model parameters on the disease dynamics and its elimination are shown graphically for various values of noninteger order of the Caputo derivative. We conclude that the use of fractional epidemic model provides a better understanding and biologically more insights about the disease dynamics.

A robust study on 2019-nCOV outbreaks through non-singular derivative.

The new coronavirus disease is still a major panic for people all over the world. The world is grappling with the second wave of this new pandemic. Different approaches are taken into consideration to tackle this deadly disease. These approaches were suggested in the form of modeling, analysis of the data, controlling the disease spread and clinical perspectives. In all these suggested approaches, the main aim was to eliminate or decrease the infection of the coronavirus from the community. Here, in this paper, we focus on developing a new mathematical model to understand its dynamics and possible control. We formulate the model first in the integer order and then use the Atangana-Baleanu derivative concept with a non-singular kernel for its generalization. We present some of the necessary mathematical aspects of the fractional model. We use a nonlinear fractional Lyapunov function in order to present the global asymptotical stability of the model at the disease-free equilibrium. In order to solve the model numerically in the fractional case, we use an efficient modified Adams-Bashforth scheme. The resulting iterative scheme is then used to demonstrate the detailed simulation results of the ABC mathematical model to examine the importance of the memory index and model parameters on the transmission and control of COVID-19 infection.

The Role of E-Governance in Combating COVID-19 and Promoting Sustainable Development: A Comparative Study of China and Pakistan

This study’s aim is to investigate the role of e-governance in combating COVID-19 by integrating the implications of the China–Pakistan Economic Corridor (CPEC). We discuss and analyze the E-Government Development Index (EGDI) reports and rankings issued by the United Nations and big data implications during the COVID-19 pandemic. We used the Origin-pro 2018 application for the analysis and discussion. Overall, China’s EGDI ranking has improved from 74 to 65 out of 193 countries, while Pakistan’s ranking has gradually declined from 137 to 148. 5G and other big data technology and e-governance implications have helped to combat the COVID-19 pandemic. In this pandemic scenario, sustainable socioeconomic development in Pakistan needs significant improvement, similar to what has been done by China. We conclude that CPEC can help combat the COVID-19 pandemic because both countries are working together to mitigate social and economic problems. Pakistan should adapt and learn from the Government of China’s experience of successful and proficient e-governance model of technological advancement. This effort will ensure successful CPEC regional extension and help combat the COVID-19 pandemic to ensure Pakistan’s sustainable development.