Stationary distribution and extinction of stochastic coronavirus (COVID-19) epidemic model

Based on epidemiological parameter data, probe into a stochastically perturbed dominant variant of the COVID-19 pandemic model

During the COVID-19 pandemic, the SARS-CoV-2 gene mutation has been rapidly emerging and spreading all over the world. Experts worldwide regularly monitor genetic mutations and variants through genome-sequence-based surveillance, laboratory testing, outbreak investigation, and epidemiological probing. Clinical pathologists and medical laboratory scientists prefer developing or endorsing COVID-19 vaccines with a broader immune response involving various antibodies and cells to protect against mutations or new variants. Randomness plays an enormous role in pathology and epidemiology. Hence, based on epidemiological parameter data, we construct and probe a stochastically perturbed dominant variant of the coronavirus epidemic model with three nonlinear saturated incidence rates. We reveal the existence of a unique global positive solution to the constructed stochastic COVID-19 model. The Lyapunov function method is used to determine the presence of a stationary distribution of positive solutions. We derive sufficient conditions for the coronavirus to be eradicated. Eventually, numerical simulations validate the effectiveness of our theoretical outcomes.

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.

The dynamics of novel corona virus disease via stochastic epidemiological model with vaccination

During the past two years, the novel coronavirus pandemic has dramatically affected the world by producing 4.8 million deaths. Mathematical modeling is one of the useful mathematical tools which has been used frequently to investigate the dynamics of various infectious diseases. It has been observed that the nature of the novel disease of coronavirus transmission differs everywhere, implying that it is not deterministic while having stochastic nature. In this paper, a stochastic mathematical model has been investigated to study the transmission dynamics of novel coronavirus disease under the effect of fluctuated disease propagation and vaccination because effective vaccination programs and interaction of humans play a significant role in every infectious disease prevention. We develop the epidemic problem by taking into account the extended version of the susceptible-infected-recovered model and with the aid of a stochastic differential equation. We then study the fundamental axioms for existence and uniqueness to show that the problem is mathematically and biologically feasible. The extinction of novel coronavirus and persistency are examined, and sufficient conditions resulted from our investigation. In the end, some graphical representations support the analytical findings and present the effect of vaccination and fluctuated environmental variation.

Extinction and persistence of a stochastic delayed Covid-19 epidemic model

We formulated a Coronavirus (COVID-19) delay epidemic model with random perturbations, consisting of three different classes, namely the susceptible population, the infectious population, and the quarantine population. We studied the proposed problem to derive at least one unique solution in the positive feasweible region of the non-local solution. Sufficient conditions for the extinction and persistence of the proposed model are established. Our results show that the influence of Brownian motion and noise on the transmission of the epidemic is very large. We use the first-order stochastic Milstein scheme, taking into account the required delay of infected individuals.

Modelling and analysis of fractional-order vaccination model for control of COVID-19 outbreak using real data

In this paper, we construct the SV1V2EIR model to reveal the impact of two-dose vaccination on COVID-19 by using Caputo fractional derivative. The feasibility region of the proposed model and equilibrium points is derived. The basic reproduction number of the model is derived by using the next-generation matrix method. The local and global stability analysis is performed for both the disease-free and endemic equilibrium states. The present model is validated using real data reported for COVID-19 cumulative cases for the Republic of India from 1 January 2022 to 30 April 2022. Next, we conduct the sensitivity analysis to examine the effects of model parameters that affect the basic reproduction number. The Laplace Adomian decomposition method (LADM) is implemented to obtain an approximate solution. Finally, the graphical results are presented to examine the impact of the first dose of vaccine, the second dose of vaccine, disease transmission rate, and Caputo fractional derivatives to support our theoretical results.

Stochastic dynamical behavior of COVID-19 model based on secondary vaccination

This paper mainly studies the dynamical behavior of a stochastic COVID-19 model. First, the stochastic COVID-19 model is built based on random perturbations, secondary vaccination and bilinear incidence. Second, in the proposed model, we prove the existence and uniqueness of the global positive solution using random Lyapunov function theory, and the sufficient conditions for disease extinction are obtained. It is analyzed that secondary vaccination can effectively control the spread of COVID-19 and the intensity of the random disturbance can promote the extinction of the infected population. Finally, the theoretical results are verified by numerical simulations.

Stochastic modeling of the Monkeypox 2022 epidemic with cross-infection hypothesis in a highly disturbed environment

Monkeypox 2022, a new re-emerging disease, is caused by the Monkeypox virus. Structurally, this virus is related to the smallpox virus and infects the host in a similar way; however, the symptoms of Monkeypox are more severe. In this research work, a mathematical model for understanding the dynamics of Monkeypox 2022 is suggested that takes into account two modes of transmission: horizontal human dissemination and cross-infection between animals and humans. Due to lack of substantial knowledge about the virus diffusion and the effect of external perturbations, the model is extended to the probabilistic formulation with Lévy jumps. The proposed model is a two block compartmental system that requires the form of Itô-Lévy stochastic differential equations. Based on some assumptions and nonstandard analytical techniques, two principal asymptotic properties are proved: the eradication and continuation in the mean of Monkeypox 2022. The outcomes of the study reveals that the dynamical behavior of the proposed Monkeypox 2022 system is chiefly governed by some parameters that are precisely correlated with the noise intensities. To support the obtained theoretical finding, examples based on numerical simulations and real data are presented at the end of the study. The numerical simulations also exhibit the impact of the innovative adopted mathematical techniques on the findings of this work.

Application of piecewise fractional differential equation to COVID-19 infection dynamics

We proposed a new mathematical model to study the COVID-19 infection in piecewise fractional differential equations. The model was initially designed using the classical differential equations and later we extend it to the fractional case. We consider the infected cases generated at health care and formulate the model first in integer order. We extend the model into Caputo fractional differential equation and study its background mathematical results. We show that the fractional model is locally asymptotically stable whenR 0 < 1 at the disease-free case. ForR 0 ≤ 1 , we show the global asymptotical stability of the model. We consider the infected cases in Saudi Arabia and determine the parameters of the model. We show that for the real cases, the basic reproduction isR 0 ≈ 1 . 7372 . We further extend the Caputo model into piecewise stochastic fractional differential equations and discuss the procedure for its numerical simulation. Numerical simulations for the Caputo case and piecewise models are shown in detail.

Probabilistic Analysis of a Marine Ecological System with Intense Variability

This work seeks to simulate and examine the complex character of marine predation. By taking into account the interaction between phytoplankton and zooplankton, we present a sophisticated mathematical system with a general functional response describing the ecological competition. This system is disturbed by a novel category of perturbations in the hybrid form which simulates certain unstable climatic and environmental variations. We merge between the higher-order white noise and quadratic jumps to offer an excellent overview of the complexity induced in the ecosystem. Analytically, we offer a surrogate framework to get the sharp sill between stationarity and zooplankton eradication. Our analysis enriches and improves many works by proposing an unfamiliar form of perturbation and unifying the criteria of said asymptotic characteristics. Numerically, we probe the rigor of our sill in a non-standard case: cubic white noise and quadratic leaps. We demonstrate that the increased order of perturbation has a significant effect on the zooplankton living time. This result shows that the sources of intricate fluctuations carry out an active role in the transient dynamics of marine ecological systems.

Acute threshold dynamics of an epidemic system with quarantine strategy driven by correlated white noises and Lévy jumps associated with infinite measure

Several studies have previously been conducted on the dynamics of probabilistic epidemic models driven by Lévy disorder. All of these works have used the Poisson counting process with finite Lévy measures. However, this scope disregards a considerable category of correlated Lévy jump processes governed by an infinite Lévy measure. In this research, we take into consideration this general framework applied to an epidemic model with a quarantine strategy. Under an appropriate hypothetical setting, we infer the exact threshold value between the ergodicity and the disease disappearance. Our analysis completes the work presented by Privault and Wang (J Nonlinear Sci 31(1):1-28, 2021) and puts forward a novel analytical aspect to deal with other stochastic models in several areas. As a numerical application, we implement the algorithm of Rosinski (Stoch Process Appl 117:677-707, 2007) for tempered stable Lévy processes with an infinite Lévy measure.

Dynamics of a stochastic HBV infection model with drug therapy and immune response

Hepatitis B is a disease that damages the liver, and its control has become a public health problem that needs to be solved urgently. In this paper, we investigate analytically and numerically the dynamics of a new stochastic HBV infection model with antiviral therapies and immune response represented by CTL cells. Through using the theory of stochastic differential equations, constructing appropriate Lyapunov functions and applying Itô's formula, we prove that the disease-free equilibrium of the stochastic HBV model is stochastically asymptotically stable in the large, which reveals that the HBV infection will be eradicated with probability one. Moreover, the asymptotic behavior of globally positive solution of the stochastic model near the endemic equilibrium of the corresponding deterministic HBV model is studied. By using the Milstein's method, we provide the numerical simulations to support the analysis results, which shows that sufficiently small noise will not change the dynamic behavior, while large noise can induce the disappearance of the infection. In addition, the effect of inhibiting virus production is more significant than that of blocking new infection to some extent, and the combination of two treatment methods may be the better way to reduce HBV infection and the concentration of free virus.

Threshold Dynamics and the Density Function of the Stochastic Coronavirus Epidemic Model

Since November 2019, each country in the world has been affected by COVID-19, which has claimed more than four million lives. As an infectious disease, COVID-19 has a stronger transmission power and faster propagation speed. In fact, environmental noise is an inevitable important factor in the real world. This paper mainly gives a new random infectious disease system under infection rate environmental noise. We give the existence and uniqueness of the solution of the system and discuss the ergodic stationary distribution and the extinction conditions of the system. The probability density function of the stochastic system is studied. Some digital simulations are used to demonstrate the probability density function and the extinction of the system.

Dynamics of a stochastic COVID-19 epidemic model considering asymptomatic and isolated infected individuals

Coronavirus disease (COVID-19) has a strong influence on the global public health and economics since the outbreak in 2020. In this paper, we study a stochastic high-dimensional COVID-19 epidemic model which considers asymptomatic and isolated infected individuals. Firstly we prove the existence and uniqueness for positive solution to the stochastic model. Then we obtain the conditions on the extinction of the disease as well as the existence of stationary distribution. It shows that the noise intensity conducted on the asymptomatic infections and infected with symptoms plays an important role in the disease control. Finally numerical simulation is carried out to illustrate the theoretical results, and it is compared with the real data of India.

Fractional-Order Discrete-Time SIR Epidemic Model with Vaccination: Chaos and Complexity

This research presents a new fractional-order discrete-time susceptible-infected-recovered (SIR) epidemic model with vaccination. The dynamical behavior of the suggested model is examined analytically and numerically. Through using phase attractors, bifurcation diagrams, maximum Lyapunov exponent and the 0−1 test, it is verified that the newly introduced fractional discrete SIR epidemic model vaccination with both commensurate and incommensurate fractional orders has chaotic behavior. The discrete fractional model gives more complex dynamics for incommensurate fractional orders compared to commensurate fractional orders. The reasonable range of commensurate fractional orders is between γ = 0.8712 and γ = 1, while the reasonable range of incommensurate fractional orders is between γ2 = 0.77 and γ2 = 1. Furthermore, the complexity analysis is performed using approximate entropy (ApEn) and C0 complexity to confirm the existence of chaos. Finally, simulations were carried out on MATLAB to verify the efficacy of the given findings.

Dynamics and optimal control of a stochastic coronavirus (COVID-19) epidemic model with diffusion

In view of the facts in the infection and propagation of COVID-19, a stochastic reaction-diffusion epidemic model is presented to analyse and control this infectious diseases. Stationary distribution and Turing instability of this model are discussed for deriving the sufficient criteria for the persistence and extinction of disease. Furthermore, the amplitude equations are derived by using Taylor series expansion and weakly nonlinear analysis, and selection of Turing patterns for this model can be determined. In addition, the optimal quarantine control problem for reducing control cost is studied, and the differences between the two models are compared. By applying the optimal control theory, the existence and uniqueness of the optimal control and the optimal solution are obtained. Finally, these results are verified and illustrated by numerical simulation.

Impact of information intervention on stochastic hepatitis B model and its variable-order fractional network

This paper aims at analyzing the dynamical behavior of a SIR hepatitis B epidemic stochastic model via a novel approach by incorporating the effect of information interventions and random perturbations. Initially, we demonstrate the positivity and global existence of the solutions. Afterward, we derive the stochastic threshold parameter R s , followed by the fact that this number concludes the transmission of hepatitis B from the population. By increasing the intensity of noise, we get R s less than one, inferring that ultimately hepatitis B will lapse. While decreasing the intensity of noise to a sufficient level, we have R s > 1 . For the case R s > 1 , adequate results for the presence of stationary distribution are achieved, showing the prevalence of hepatitis B. The present study also involves the derivation of the necessary conditions for the persistence of the epidemic. Finally, the main theoretical solutions are plotted through simulations. Discussion on theoretical and numerical results shows that utilizing random perturbations and information interventions have a pronounced impact on the syndrome's dynamics. Furthermore, since most communities interact with each other, and the disease spread rate is affected by this factor, a new variable-order fractional network of the stochastic hepatitis B model is offered. Subsequently, this study will provide a robust theoretical basis for comprehending worldwide SIR stochastic and variable-order fractional network-related case studies.

Caputo fractional-order SEIRP model for COVID-19 Pandemic

We propose a Caputo-based fractional compartmental model for the dynamics of the novel COVID-19 pandemic. The newly proposed nonlinear fractional order model is an extension of a recently formulated integer-order COVID-19 mathematical model. Using basic concepts such as continuity and Banach fixed-point theorem, existence and uniqueness of the solution to the proposed model were shown. Furthermore, we analyze the stability of the model in the context of Ulam-Hyers and generalized Ulam-Hyers stability criteria. The concept of next-generation matrix was used to compute the basic reproduction number R0, a number that determines the spread or otherwise of the disease into the general population. We also investigated the local asymptotic stability for the derived disease-free equilibrium point. Numerical simulation of the constructed epidemic model was carried out using the fractional Adam-Bashforth-Moulton method to validate the obtained theoretical results.

Extinction and stationary distribution of a stochastic COVID-19 epidemic model with time-delay

We reformulate a stochastic epidemic model consisting of four human classes. We show that there exists a unique positive solution to the proposed model. The stochastic basic reproduction number R0s is established. A stationary distribution (SD) under several conditions is obtained by incorporating stochastic Lyapunov function. The extinction for the proposed disease model is obtained by using the local martingale theorem. The first order stochastic Runge-Kutta method is taken into account to depict the numerical simulations.

Hybrid Method for Simulation of a Fractional COVID-19 Model with Real Case Application

In this research, we provide a mathematical analysis for the novel coronavirus responsible for COVID-19, which continues to be a big source of threat for humanity. Our fractional-order analysis is carried out using a non-singular kernel type operator known as the Atangana-Baleanu-Caputo (ABC) derivative. We parametrize the model adopting available information of the disease from Pakistan in the period 9 April to 2 June 2020. We obtain the required solution with the help of a hybrid method, which is a combination of the decomposition method and the Laplace transform. Furthermore, a sensitivity analysis is carried out to evaluate the parameters that are more sensitive to the basic reproduction number of the model. Our results are compared with the real data of Pakistan and numerical plots are presented at various fractional orders.

Tailored Pharmacokinetic model to predict drug trapping in long-term anesthesia

Introduction

In long-term induced general anesthesia cases such as those uniquely defined by the ongoing Covid-19 pandemic context, the clearance of hypnotic and analgesic drugs from the body follows anomalous diffusion with afferent drug trapping and escape rates in heterogeneous tissues. Evidence exists that drug molecules have a preference to accumulate in slow acting compartments such as muscle and fat mass volumes. Currently used patient dependent pharmacokinetic models do not take into account anomalous diffusion resulted from heterogeneous drug distribution in the body with time varying clearance rates.

Objectives

This paper proposes a mathematical framework for drug trapping estimation in PK models for estimating optimal drug infusion rates to maintain long-term anesthesia in Covid-19 patients. We also propose a protocol for measuring and calibrating PK models, along with a methodology to minimize blood sample collection.

Methods

We propose a framework enabling calibration of the models during the follow up of Covid-19 patients undergoing anesthesia during their treatment and recovery period in ICU. The proposed model can be easily updated with incoming information from clinical protocols on blood plasma drug concentration profiles. Already available pharmacokinetic and pharmacodynamic models can be then calibrated based on blood plasma concentration measurements.

Results

The proposed calibration methodology allow to minimize risk for potential over-dosing as clearance rates are updated based on direct measurements from the patient.

Conclusions

The proposed methodology will reduce the adverse effects related to over-dosing, which allow further increase of the success rate during the recovery period.

The numerical solution of high dimensional variable-order time fractional diffusion equation via the singular boundary method

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The 3D variable-order time fractional variable-order time fractional diffusion is generated.

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An efficient meshless method is proposed for numerical solution of the new problem.

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The proposed approach is established upon the singular boundary method.

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The method accuracy is examined by some numerical examples on various geometries.

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The method can be extended for other types of variable-order fractional problems.

Introduction

This study describes a novel meshless technique for solving one of common problem within cell biology, computer graphics, image processing and fluid flow. The diffusion mechanism has extremely depended on the properties of the structure.

Objectives

The present paper studies why diffusion processes not following integer-order differential equations, and present novel meshless method for solving. diffusion problem on surface numerically.

Methods

The variable- order time fractional diffusion equation (VO-TFDE) is developed along with sense of the Caputo derivative for (0<α(t)<1). An efficient and accurate meshfree method based on the singular boundary method (SBM) and dual reciprocity method (DRM) in concomitant with finite difference scheme is proposed on three-dimensional arbitrary geometry. To discrete of the temporal term, the finite diffract method (FDM) is utilized. In the spatial variation domain; the proposal method is constructed two part. To evaluating first part, fundamental solution of (VO-TFDE) is transformed into inhomogeneous Helmholtz-type to implement the SBM approximation and other part the DRM is utilized to compute the particular solution.

Results

The stability and convergent of the proposed method is numerically investigated on high dimensional domain. To verified the reliability and the accuracy of the present approach on complex geometry several examples are investigated.

Conclusions

The result of study provides a rapid and practical scheme to capture the behavior of diffusion process.

Lung cancer dynamics using fractional order impedance modeling on a mimicked lung tumor setup

Introduction

As pulmonary dysfunctions are prospective factors for developing cancer, efforts are needed to solve the limitations regarding applications in lung cancer. Fractional order respiratory impedance models can be indicative of lung cancer dynamics and tissue heterogeneity.

Objective

The purpose of this study is to investigate how the existence of a tumorous tissue in the lung modifies the parameters of the proposed models. The first use of a prototype forced oscillations technique (FOT) device in a mimicked lung tumor setup is investigated by comparing and interpreting the experimental findings.

Methods

The fractional order model parameters are determined for the mechanical properties of the healthy and tumorous lung. Two protocols have been performed for a mimicked lung tumor setup in a laboratory environment. A low frequency evaluation of respiratory impedance model and nonlinearity index were assessed using the forced oscillations technique.

Results

The viscoelastic properties of the lung tissue change, results being mirrored in the respiratory impedance assessment via FOT. The results demonstrate significant differences among the mimicked healthy and tumor measurements, (p-values < 0.05) for impedance values and also for heterogeneity index. However, there was no significant difference in lung function before and after immersing the mimicked lung in water or saline solution, denoting no structural changes.

Conclusion

Simulation tests comparing the changes in impedance support the research hypothesis. The impedance frequency response is effective in non-invasive identification of respiratory tissue abnormalities in tumorous lung, analyzed with appropriate fractional models.

Self organizing maps for the parametric analysis of COVID-19 SEIRS delayed model

Since 2019, entire world is facing the accelerating threat of Corona Virus, with its third wave on its way, although accompanied with several vaccination strategies made by world health organization. The control on the transmission of the virus is highly desired, even though several key measures have already been made, including masks, sanitizing and disinfecting measures. The ongoing research, though devoted to this pandemic, has certain flaws, due to which no permanent solution has been discovered. Currently different data based studies have emerged but unfortunately, the pandemic fate is still unrevealed. During this research, we have focused on a compartmental model, where delay is taken into account from one compartment to another. The model depicts the dynamics of the disease relative to time and constant delays in time. A deep learning technique called "Self Organizing Map" is used to extract the parametric values from the data repository of COVID-19. The input we used for SOM are the attributes on which, the variables are dependent. Different grouping/clustering of patients were achieved with 2- dimensional visualization of the input data ( h t t p s : / / c r e a t i v e c o m m o n s . o r g / l i c e n s e s / b y / 2.0 / ). Extensive stability analysis and numerical results are presented in this manuscript which can help in designing control measures.

Modeling the dynamic of COVID-19 with different types of transmissions

In this paper, we propose a new epidemiological mathematical model for the spread of the COVID-19 disease with a special focus on the transmissibility of individuals with severe symptoms, mild symptoms, and asymptomatic symptoms. We compute the basic reproduction number and we study the local stability of the disease-free equilibrium in terms of the basic reproduction number. Numerical simulations were employed to illustrate our results. Furthermore, we study the present model in case we took into consideration the vaccination of a portion of susceptible individuals to predict the impact of the vaccination program.

Modified SIRD Model for COVID-19 Spread Prediction for Northern and Southern States of India

The Severe Acute Respiratory Syndrome Coronavirus 2 (SAR-CoV-2) is the strain of coronavirus that causes coronavirus disease (COVID-19), the respiratory illness that resulted in COVID-19 pandemic in early December 2019. Due to lack of knowledge of the epidemiological cycle and absence of any type of vaccine or medications, the Government issued various non-pharmacological measures to end the COVID-19 pandemic. Several researchers applied the Susceptible-Infected-Recovered-Deceased (SIRD) compartmental epidemiology process model to identifying the effect of different governments intervention methods enforced to mollify the spread of COVID-19 epidemic. In this paper, we aim to provide a modified SIRD model for COVID-19 spread prediction. We have analyzed the data of the Northern and Southern states of India from January 30, 2020, to October 24, 2020 using the proposed SIRD model and existing SIRD model. We have made the predictions with reasonable assumptions based on real data, considering that the precise course of an epidemic is highly dependent on how and when quarantine, isolation, and precautionary measures were imposed. The proposed method gives better approximation values of new cases, R0 (Reproductive Number), daily deaths, daily infectious, transmission rate, and recovered individuals.Through the analysis of the reported results, the proposed SIRD model can be an effective method for investigating the effect of government interventions on COVID-19 associated transmission and mortality rate at the time of epidemic.

Modeling the dynamics of novel coronavirus (COVID-19) via stochastic epidemic model

In this article we propose a stochastic model to discuss the dynamics of novel corona virus disease. We formulate the model to study the long run behavior in varying population environment. For this purposes we divided the total human population into three epidemiological compartments: the susceptible, covid-19 infected, recovered and recovered along with one class of reservoir. The existence and uniqueness of the newly formulated model will be studied to show the well-possedness of the model. Moreover, we investigate the extinction analysis as well as the persistence analysis to find the disease extinction and disease persistence conditions. At the end we perform simulation to justify the investigation of analytical work with the help of graphical representations.

Mathematical analysis of a stochastic model for spread of Coronavirus

This paper is associated to investigate a stochastic SEIAQHR model for transmission of Coronavirus disease 2019 that is a recent great crisis in numerous societies. This stochastic pandemic model is established due to several safety protocols, for instance social-distancing, mask and quarantine. Three white noises are added to three of the main parameters of the system to represent the impact of randomness in the environment on the considered model. Also, the unique solvability of the presented stochastic model is proved. Moreover, a collocation approach based on the Legendre polynomials is presented to obtain the numerical solution of this system. Finally, some simulations are provided to survey the obtained results of this pandemic model and to identify the theoretical findings.

A Two-Phase Stochastic Dynamic Model for COVID-19 Mid-Term Policy Recommendations in Greece: A Pathway towards Mass Vaccination

From 7 November 2020, Greece adopted a second nationwide lockdown policy to mitigate the transmission of SARS-CoV-2 (the first took place from 23 March to 4 May 2020), just as the second wave of COVID-19 was advancing, as did other European countries. To secure the full benefits of mass vaccination, which started in early January 2021, it is of utmost importance to complement it with mid-term non-pharmaceutical interventions (NPIs). The objective was to minimize human losses and to limit social and economic costs. In this paper a two-phase stochastic dynamic network compartmental model (a pre-vaccination SEIR until 15 February 2021 and a post-vaccination SVEIR from 15 February 2021 to 30 June 2021) is developed. Three scenarios are assessed for the first phase: (a) A baseline scenario, which lifts the national lockdown and all NPIs in January 2021; (b) a "semi-lockdown" scenario with school opening, partial retail sector operation, universal mask wearing, and social distancing/teleworking in January 2021; and (c) a "rolling lockdown" scenario combining a partial lifting of measures in January 2021 followed by a third nationwide lockdown in February 2021. In the second phase three scenarios with different vaccination rates are assessed. Publicly available data along with some first results of the SHARE COVID-19 survey conducted in Greece are used as input. The results regarding the first phase indicate that the "semi-lockdown" scenario clearly outperforms the third lockdown scenario (5.7% less expected fatalities); the second phase is extremely sensitive on the availability of sufficient vaccine supplies and high vaccination rates.

Suggesting a framework for preparedness against the pandemic outbreak based on medical informatics solutions: a thematic analysis

Background

When an outbreak emerged, each country needs a coherent and preventive plan to deal with epidemics. In the era of technology, adopting informatics‐based solutions is essential. The main objective of this study is to propose a conceptual framework to provide a rapid and responsive surveillance system against pandemics.

Methods

A three‐step approach was employed in this research to develop a conceptual framework. These three steps comprise (1) literature review, (2) extracting and coding concepts, and determining main themes based on thematic analysis using ATLAS.ti® software, and (3) mapping concepts. Later, all of the results synthesized under expert consultation to design a conceptual framework based on the main themes and identified strategies related to medical informatics.

Results

In the literature review phase, 65 articles were identified as eligible studies for analysis. Through line by line coding in thematic analysis, more than 46 themes were extracted as potential foremost themes. Based on the key themes and strategies were employed by studies, the proposed framework designed in three main components. The most appropriate strategies that can be used in each section were identified based on the demands of each part and the available solutions. These solutions were employed in the final framework.

Conclusion

The presented model in this study can be the first step for a better understanding of the potential of medical informatics solutions in promoting epidemic disease management. It can be applied as a reference model for designing intelligent surveillance systems to prepare for probable future pandemics.

On a new conceptual mathematical model dealing the current novel coronavirus-19 infectious disease

The present paper describes a three compartment mathematical model to study the transmission of the current infection due to the novel coronavirus (2019-nCoV or COVID-19). We investigate the aforesaid dynamical model by using Atangana, Baleanu and Caputo (ABC) derivative with arbitrary order. We derive some existence results together with stability of Hyers-Ulam type. Further for numerical simulations, we use Adams-Bashforth (AB) method with fractional differentiation. The mentioned method is a powerful tool to investigate nonlinear problems for their respective simulation. Some discussion and future remarks are also given.

On modeling of coronavirus-19 disease under Mittag-Leffler power law

This paper investigates a new model on coronavirus-19 disease (COVID-19) with three compartments including susceptible, infected, and recovered class under Mittag-Leffler type derivative. The mentioned derivative has been introduced by Atangana, Baleanu, and Caputo abbreviated as ( ABC ) . Upon utilizing fixed point theory, we first prove the existence of at least one solution for the considered model and its uniqueness. Also, some results about stability of Ulam-Hyers type are also established. By applying a numerical technique called fractional Adams-Bashforth (AB) method, we develop a scheme for the approximate solutions to the considered model. Using some real available data, we perform the concerned numerical simulation corresponding to different values of fractional order.