Simulation of Impact of Migration Caused by the War in Ukraine on COVID-19 Epidemic Process in Moldova

The novel coronavirus pandemic has become a global challenge and has shown that health systems worldwide are unprepared for pandemics of this magnitude. The war in Ukraine, escalated by Russia on February 24, 2022, brought deaths and a humanitarian catastrophe and stimulated the spread of COVID-19. Most refugees who evacuated from the war crossed the border with other countries. At the end of July, almost 550 thousand people crossed the border with Moldova. This study is devoted to modeling the impact of migration processes on the dynamics of COVID-19 in Moldova. For this, a machine learning model was built based on the polynomial regression method. The forecast accuracy a month before the escalation of the war was from 98.77% to 96.37% for new cases and from 99.8% to 99.75% for fatal cases. The forecast accuracy for the first month after the escalation of the war was from 99.96% to 99.34% for new cases and from 99.91% to 99.88% for fatal cases. The high accuracy of the model, both before the war and with the start of its escalation, suggests that the migration flows of refugees from Ukraine to Moldova did not affect the dynamics of COVID-19. ©2022 Copyright for this paper by its authors.

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

In this manuscript, we formulate a mathematical model of the deadly COVID-19 pandemic to understand the dynamic behavior of COVID-19. For the dynamic study, a new SEIAPHR fractional model was purposed in which infectious individuals were divided into three sub-compartments. The purpose is to construct a more reliable and realistic model for a complete mathematical and computational analysis and design of different control strategies for the proposed Caputo–Fabrizio fractional model. We prove the existence and uniqueness of solutions by employing well-known theorems of fractional calculus and functional analyses. The positivity and boundedness of the solutions are proved using the fractional-order properties of the Laplace transformation. The basic reproduction number for the model is computed using a next-generation technique to handle the future dynamics of the pandemic. The local–global stability of the model was also investigated at each equilibrium point. We propose basic fixed controls through manipulation of quarantine rates and formulate an optimal control problem to find the best controls (quarantine rates) employed on infected, asymptomatic, and "superspreader” humans, respectively, to restrict the spread of the disease. For the numerical solution of the fractional model, a computationally efficient Adams–Bashforth method is presented. A fractional-order optimal control problem and the associated optimality conditions of Pontryagin maximum principle are discussed in order to optimally reduce the number of infected, asymptomatic, and superspreader humans. The obtained numerical results are discussed and shown through graphs. © 2023 by the authors.

Compartmental modelling in epidemic diseases: a comparison between SIR model with constant and time-dependent parameters

The compartmental modelling is one of the most widely used techniques in investigating the dynamics of infectious diseases. This modelling technique usually treats model parameters as constant. However, the parameters associated with infectious diseases randomly change following the changes in the conditions of disease transmission. As a result, the estimated parameters are often found over or under-determined by direct problems when some conditions change and the forecasting using direct problems often goes wrong. In this study, we estimate the model parameters over different time intervals by means of the inverse problem method and then solve the forward problem using these estimated parameters to compare them with the real epidemic data. We apply the method to estimate the parameters corresponding to Nipah virus, Measles and COVID-19 in the context of Bangladesh. The results suggest that the method helps to gain improved insights into epidemic scenarios corresponding to smaller time intervals. The results of the direct problem are found to fall apart fairly quickly from the real epidemic data as the length of the interval used in the inverse problem method increased. © 2023 The Author(s). Published by IOP Publishing Ltd.

Dynamical analysis of a discrete-time COVID-19 epidemic model.

In this paper, we explore local dynamics with topological classifications, bifurcation analysis, and chaos control in a discrete-time COVID-19 epidemic model in the interior of ℝ + 4 . It is explored that for all involved parametric values, discrete-time COVID-19 epidemic model has boundary equilibrium solution and also it has an interior equilibrium solution under definite parametric condition. We have explored the local dynamics with topological classifications about boundary and interior equilibrium solutions of the discrete-time COVID-19 epidemic model by linear stability theory. Further, for the discrete-time COVID-19 epidemic model, existence of periodic points and convergence rate are also investigated. It is also studied the existence of possible bifurcations about boundary and interior equilibrium solutions and proved that there exists no flip bifurcation about boundary equilibrium solution. Moreover, it is proved that about interior equilibrium solution, there exist Hopf and flip bifurcations, and we have studied these bifurcations by utilizing explicit criterion. Moreover, by feedback control strategy, chaos in the discrete COVID-19 epidemic model is also explored. Finally, theoretical results are verified numerically.

Analysis of a Fractional-Order COVID-19 Epidemic Model with Lockdown.

The outbreak of the coronavirus disease (COVID-19) has caused a lot of disruptions around the world. In an attempt to control the spread of the disease among the population, several measures such as lockdown, and mask mandates, amongst others, were implemented by many governments in their countries. To understand the effectiveness of these measures in controlling the disease, several mathematical models have been proposed in the literature. In this paper, we study a mathematical model of the coronavirus disease with lockdown by employing the Caputo fractional-order derivative. We establish the existence and uniqueness of the solution to the model. We also study the local and global stability of the disease-free equilibrium and endemic equilibrium solutions. By using the residual power series method, we obtain a fractional power series approximation of the analytic solution. Finally, to show the accuracy of the theoretical results, we provide some numerical and graphical results.

MULTISTAGE VARIATIONAL ITERATION METHOD FOR A SEIQR COVID-19 EPIDEMIC MODEL WITH ISOLATION CLASS

The SEIQR COVID-19 epidemic model is in the form of the system of first-order nonlinear differential equations. In this paper we propose multistage versions of the variational iteration method (VIM) to solve this COVID-19 epidemic model. The idea of multistage version is to divide the entire time domain into a finite number of subintervals and then implementing the VIM piecewisely on each subinterval. There are two kinds of multistage methods discussed in this paper, where the difference between the two methods lies in the number of restricted variations used in the correction functional. The multistage methods generally give more accurate solutions on longer time intervals than the classical versions. The multistage VIM with less number of restricted variations has the best performance among all types of variational iteration methods discussed in this paper. The accuracy of multistage VIM solution can be increased by using smaller size of subinterval or by implementing more iterations in each subinterval.

The epidemic COVID-19 model via Caputo–Fabrizio fractional operator

In this article, we analyze and identify the optimum values for a deeper sense of the mathematical model of the COVID-19 epidemic from the reservoir to humans by using a powerful fractional homotopy perturbation transform method with Caputo–Fabrizio fractional derivative. We receive simulations of this propagation under high parameters. Although the results show the efficacy of the theoretic framework considered for the governing structure. The obtained results also provide lighting on the dynamic behavior of the COVID-19 model. We gave a few numerical approximations to explain the efficiency of the proposed method for various values of fractional order, which correspond to the process. Finally, we graphically demonstrate the obtained outcome. [ FROM AUTHOR] Copyright of Waves in Random & Complex Media is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

Dynamics of COVID-19 Epidemic Model with Asymptomatic Infection, Quarantine, Protection and Vaccination

We discuss the dynamics of new COVID-19 epidemic model by considering asymptomatic infections and the policies such as quarantine, protection (adherence to health protocols), and vaccination. The proposed model contains nine subpopulations: Susceptible (S), exposed (E), symptomatic infected (I), asymptomatic infected (A), recovered (R), death (D), protected (P), quarantined (Q), and vaccinated (V). We first show the non-negativity and boundedness of solutions. The equilibrium points, basic reproduction number, and stability of equilibrium points, both locally and globally, are also investigated analytically. The proposed model has disease-free equilibrium point and endemic equilibrium point. The disease-free equilibrium point always exists and is globally asymptotically stable if basic reproduction number is less than one. The endemic equilibrium point exists uniquely and is globally asymptotically stable if the basic reproduction number is greater than one. These properties have been confirmed by numerical simulations using the fourth order Runge-Kutta method. Numerical simulations show that the disease transmission rate of asymptomatic infection, quarantine rates, protection rate, and vaccination rates affect the basic reproduction number and hence also influence the stability of equilibrium points. © 2021 Published by Indonesian Biomathematical Society.

Fractal fractional based transmission dynamics of COVID-19 epidemic model.

We investigate the dynamical behavior of Coronavirus (COVID-19) for different infections phases and multiple routes of transmission. In this regard, we study a COVID-19 model in the context of fractal-fractional order operator. First, we study the COVID-19 dynamics with a fractal fractional-order operator in the framework of Atangana-Baleanu fractal-fractional operator. We estimated the basic reduction number and the stability results of the proposed model. We show the data fitting to the proposed model. The system has been investigated for qualitative analysis. Novel numerical methods are introduced for the derivation of an iterative scheme of the fractal-fractional Atangana-Baleanu order. Finally, numerical simulations are performed for various orders of fractal-fractional dimension.

Multi-Agent modeling of the spread of diseases using the example of coronavirus disease COVID-19

Throughout the history of humanity, large-scale epidemics and pandemics have repeatedly erupted. Athenian ulcer, several plague and cholera pandemics, Spanish flu, Avian influenza, Swine influenza, HIV/AIDS-millions of people have died due to lack of medicines and medical knowledge. In the 21st century, it would seem that world medicine is ready and capable of preventing many diseases, but by the beginning of 2020, a new pandemic of the coronavirus disease COVID-19 caused by the SARS-CoV-2 virus broke out. The paper provided a brief systematic overview of modeling methods in epidemiology. A modified SEIRD simulation model of epidemic spread is presented. The proposed model was implemented in the AnyLogic system. © 2021 IEEE.

Discrete-time COVID-19 epidemic model with bifurcation and control.

The local dynamics with different topological classifications, bifurcation analysis and chaos control in a discrete-time COVID-19 epidemic model are investigated in the interior of $ \mathbb{R}_+^3 $. It is proved that discrete-time COVID-19 epidemic model has boundary equilibrium solution for all involved parameters, but it has an interior equilibrium solution under definite parametric condition. Then by linear stability theory, local dynamics with different topological classifications are investigated about boundary and interior equilibrium solutions of the discrete-time COVID-19 epidemic model. Further for the discrete-time COVID-19 epidemic model, existence of periodic points and convergence rate are also investigated. It is also investigated the existence of possible bifurcations about boundary and interior equilibrium solutions, and proved that there exists no flip bifurcation about boundary equilibrium solution. Moreover, it is proved that about interior equilibrium solution there exists hopf and flip bifurcations, and we have studied these bifurcations by utilizing explicit criterion. Next by feedback control strategy, chaos in the discrete COVID-19 epidemic model is also explored. Finally numerically verified theoretical results.

Investigation of interactions between COVID-19 and diabetes with hereditary traits using real data: A case study in Turkey.

In the present paper, interactions between COVID-19 and diabetes are investigated using real data from Turkey. Firstly, a fractional order pandemic model is developed both to examine the spread of COVID-19 and its relationship with diabetes. In the model, diabetes with and without complications are adopted by considering their relationship with the quarantine strategy. Then, the existence and uniqueness of solution are examined by using the fixed point theory. The dynamic behaviors of the equilibria and their stability analysis are studied. What is more, with the help of least-squares curve fitting technique (LSCFT), the fitting of the parameters is implemented to predict the direction of COVID-19 by using more accurately generated parameters. By trying to minimize the mean absolute relative error between the plotted curve for the infected class solution and the actual data of COVID-19, the optimal values of the parameters used in numerical simulations are acquired successfully. In addition, the numerical solution of the mentioned model is achieved through the Adams-Bashforth-Moulton predictor-corrector method. Meanwhile, the sensitivity analysis of the parameters according to the reproduction number is given. Moreover, numerical simulations of the model are obtained and the biological interpretations explaining the effects of model parameters are performed. Finally, in order to point out the advantages of the fractional order modeling, the memory trace and hereditary traits are taken into consideration. By doing so, the effect of the different fractional order derivatives on the COVID-19 pandemic and diabetes are investigated.

Stability and bifurcation analysis of SIQR for the COVID-19 epidemic model with time delay.

Based on the SIQR model, we consider the influence of time delay from infection to isolation and present a delayed differential equation (DDE) according to the characteristics of the COVID-19 epidemic phenomenon. First, we consider the existence and stability of equilibria in the above delayed SIQR model. Second, we analyze the existence of Hopf bifurcations associated with two equilibria, and we verify that Hopf bifurcations occur as delays crossing some critical values. Then, we derive the normal form for Hopf bifurcation by using the multiple time scales method for determining the stability and direction of bifurcation periodic solutions. Finally, numerical simulations are carried out to verify the analytic results.

Stability analysis of COVID-19 model with fractional-order derivative and a delay in implementing the quarantine strategy.

This study presents methods of hygiene and the use of masks to control the disease. The zero basic reproduction number can be achieved by taking the necessary precautionary measures that prevent the transmission of infection, especially from uninfected virus carriers. The existence of time delay in implementing the quarantine strategy and the threshold values of the time delay that keeping the stability of the system are established. Also, it is found that keeping the infected people quarantined immediately is very important in combating and controlling the spread of the disease. Also, for special cases of the system parameters, the time delay can not affect the asymptotic behavior of the disease. Finally, numerical simulations have been illustrated to validate the theoretical analysis of the proposed model.

Global dynamics of COVID-19 epidemic model with recessive infection and isolation.

In this paper, we present an SEIIaHR epidemic model to study the influence of recessive infection and isolation in the spread of COVID-19. We first prove that the infection-free equilibrium is globally asymptotically stable with condition R0<1 and the positive equilibrium is uniformly persistent when the condition R0>1. By using the COVID-19 data in India, we then give numerical simulations to illustrate our results and carry out some sensitivity analysis. We know that asymptomatic infections will affect the spread of the disease when the quarantine rate is within the range of [0.3519, 0.5411]. Furthermore, isolating people with symptoms is important to control and eliminate the disease.

Dynamics of a stochastic coronavirus (COVID-19) epidemic model with Markovian switching.

In this paper, we analyze a stochastic coronavirus (COVID-19) epidemic model which is perturbed by both white noise and telegraph noise incorporating general incidence rate. Firstly, we investigate the existence and uniqueness of a global positive solution. Then, we establish the stochastic threshold for the extinction and the persistence of the disease. The data from Indian states, are used to confirm the results established along this paper.