Nonlinear dynamics modeling and epidemic forecast of COVID-19

To study the spreading trend and risk of COVID-19, according to the characteristics of COVID-19, this paper proposes a new transmission dynamic model named SLIR(susceptible-low-risk-infected-recovered), based on the classic SIR model by considering government control and personal protection measures. The equilibria, stability and bifurcation of the model are analyzed to reveal the propagation mechanism of COVID-19. In order to improve the prediction accuracy of the model, the least square method is employed to estimate the model parameters based on the real data of COVID-19 in the United States. Finally, the model is used to predict and analyze COVID-19 in the United States. The simulation results show that compared with the traditional SIR model, this model can better predict the spreading trend of COVID-19 in the United States, and the actual official data has further verified its effectiveness. The proposed model can effectively simulate the spreading of COVID-19 and help governments choose appropriate prevention and control measures. Copyright ©2023 Control and Decision.

COVID-19: Agent-Based Simulation-Optimization to Vaccine Center Location Vaccine Allocation Problem

This paper presents an agent-based simulation-optimization modeling and algorithmic framework to determine the optimal vaccine center location and vaccine allocation strategies under budget constraints during an epidemic outbreak. Both simulation and optimization models incorporate population health dynamics, such as susceptible (S), vaccinated (V), infected (I) and recovered (R), while their integrated utilization focuses on the COVID-19 vaccine allocation challenges. We first formulate a dynamic location-allocation mixed-integer programming (MIP) model, which determines the optimal vaccination center locations and vaccines allocated to vaccination centers, pharmacies, and health centers in a multi-period setting in each region over a geographical location. We then extend the agent-based epidemiological simulation model of COVID-19 (Covasim) by adding new vaccination compartments representing people who take the first vaccine shot and the first two shots. The Covasim involves complex disease transmission contact networks, including households, schools, and workplaces, and demographics, such as age-based disease transmission parameters. We combine the extended Covasim with the vaccination center location-allocation MIP model into one single simulation-optimization framework, which works iteratively forward and backward in time to determine the optimal vaccine allocation under varying disease dynamics. The agent-based simulation captures the inherent uncertainty in disease progression and forecasts the refined number of susceptible individuals and infections for the current time period to be used as an input into the optimization. We calibrate, validate, and test our simulation-optimization vaccine allocation model using the COVID-19 data and vaccine distribution case study in New Jersey. The resulting insights support ongoing mass vaccination efforts to mitigate the impact of the pandemic on public health, while the simulation-optimization algorithmic framework could be generalized for other epidemics. [ FROM AUTHOR] Copyright of IISE Transactions 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.)

Simulation Analysis of COVID-19 Epidemic Model in Wuhan Based on SIR Model

Based on SIR model, combined with the mode of COVID-19 epidemic spread in Wuhan, the SIR model of COVID-19 epidemic spread is constructed, which mainly includes three aspects: simulation of the average number of infected people in COVID-19, simulation of cross-infection in COVID-19 and simulation of contact infection in COVID-19. Using the results of these three simulations, we can predict the spread of COVID-19 epidemic in the region, and find out the methods to prevent and control the outbreak or spread of the epidemic. © 2023 SPIE.

Study on Infection Probabilities of COVID-19 by SIR Network

Severe Acute Respiratory Syndrome Coronavirus 2 Related Diseases (COVID-19) is now one of the most challenging and concerning epidemics, which has been affecting the world so much. After that, countries around the world have been actively developing vaccines to deal with the sudden disease. How to carry out more efficient epidemic prevention has also become a problem of our concern. Unlike traditional SIR disease transmission models, network percolation has unique advantages in disease immune modelling, which makes it closer to reality in the simulation. This article introduces the study of SIR percolation network on infection probabilities of COVID-19, and proposes a method to preventing the spread of disease. © 2022 IEEE.

Using the SIR Model to Analyze the Epidemiological Situation in Kazakhstan and Neighboring Countries

In this paper, we study the epidemic situation in Kazakhstan and neighboring countries, taking into account territorial features in emergency situations. As you know, the excessive concentration of the population in large cities and the transition to a world without borders created ideal conditions for a global pandemic. The article also provides the results of a detailed analysis of the solution approaches to modeling the development of epidemics by types of models (basic SIR model, modified SEIR models) and the practical application of the SIR model using an example (Kazakhstan, Russia, Kyrgyzstan, Uzbekistan and other neighboring countries). The obtained processing results are based on statistical data from open sources on the development of the COVID-19 epidemic. The result obtained is a general solution of the SIR-model of the spread of the epidemic according to the fourth-order Runge-Kutta method. The parameters β, γ, which are indicators of infection, recovery, respectively, were calculated using data at the initial phase of the Covid 2019 epidemic. An analysis of anti-epidemic measures in neighboring countries is given. © 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).

Intelligent Approach to Combat COVID-19: An Insight Analysis

COVID-19 – the utmost global crisis and the major global pandemic is literally changing our life. Every person is observing at the everyday rise of the death toll and the fast, exponential growth of this novel and dynamic strain of the virus. To find the effective treatment, the virus source prediction, infection classifications are important issues to be addressed. As we are waiting to get rid of this situation and waiting to know the peak and down fall timing of this pandemic, forecasting of epidemic development is also important issue to be addressed. In this present chapter we have used some mathematical modeling and Artificial Intelligence based or more specifically Machine learning based approaches to combat this pandemic. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022.

Long-term prediction of the COVID-19 epidemics induced by Omicron-virus in China based on a novel non-autonomous delayed SIR model

Since the outbreak of COVID-19, the severe acute respiratory syndrome coronavirus 2 genome is still mutating. Omicron, a recently emerging virus with a shorter incubation period, faster transmission speed, and stronger immune escape ability, is soaring worldwide and becoming the mainstream virus in the COVID-19 pandemic. It is especially critical for the governments, healthcare systems, and economic sectors to have an accurate estimate of the trend of this disaster. By using different mathematical approaches, including the classical susceptible-infected-recovered (SIR) model and its extensions, many investigators have tried to predict the outbreaks of COVID-19. In this study, we employed a novel model which is based upon the well-known susceptible-infected-removed (SIR) model with the time-delay and time-varying coefficients in our previous works. We aim to predict the evolution of the epidemics effectively in nine cities and provinces of China, including A City, B City, C City, D City, E City, F City, G City, H City and I Province. The results show it is effective to model the spread of the large-scale and sporadic COVID-19 induced by Omicron virus by the novel non-autonomous delayed SIR compartment model. The significance of this study is that it can provide the management department of epidemic control with theoretical references and subsequent evaluation of the prevention, control measures, and effects.

Differential and Time-Discrete SEIRS Models with Vaccination: Local Stability, Validation and Sensitivity Analysis Using Bulgarian COVID-19 Data

Bulgaria has the lowest COVID-19 vaccination rate in the European Union and the second-highest COVID-19 mortality rate in the world. That is why we think it is important better to understand the reason for this situation and to analyse the development of the disease over time. In this paper, an extended time-dependent SEIRS model SEIRS-VB is used to investigate the long-term behaviour of the COVID-19 epidemic. This model includes vaccination and vital dynamics. To apply the SEIRS-VB model some numerical simulation tools have been developed and for this reason a family of time-discrete variants are introduced. Suitable inverse problems for the identification of parameters in discrete models are solved. A methodology is proposed for selecting a discrete model from the constructed family, which has the closest parameter values to these in the differential SEIRS-VB model. To validate the studied models, Bulgarian COVID-19 data are used. To obtain all these results for the discrete models a mathematical analysis is carried out to illustrate some biological properties of the differential model SEIRS-VB, such as the non-negativity, boundedness, existence, and uniqueness. Using the next-generation method, the basic reproduction number associated with the model in the autonomous case is defined. The local stability of the disease-free equilibrium point is studied. Finally, a sensitivity analysis of the basic reproduction number is performed.

Research on the spread of infectious diseases based on computer simulation

The virus has a big impact on the whole world. The new Coronavirus has a great impact on everyone's life and will even lead to changes in the world pattern. Because of the virus, society is not functioning properly, the recession, people's expectations of economic development are falling. Trains and planes were suspended in some areas. In this paper, computer is used to simulate SIR model, based on system dynamics, to study the spread of infectious diseases. The SIR model passes reality and limit tests. On the basis of the original model, supplementing the original model, isolation and vaccination can effectively stop the spread of the virus. It can slow the outbreak of the virus and reduce the number of infected people. Panic comes from the unknown, and our confidence in defeating the 2019-nCoV virus comes from our scientific base. © 2022 IEEE.

A systematic approach for COVID-19 predictions and parameter estimation.

The world is currently facing a pandemic called COVID-19 which has drastically changed our human lifestyle, affecting it badly. The lifestyle and the thought processes of every individual have changed with the current situation. This situation was unpredictable, and it contains a lot of uncertainties. In this paper, the authors have attempted to predict and analyze the disease along with its related issues to determine the maximum number of infected people, the speed of spread, and most importantly, its evaluation using a model-based parameter estimation method. In this research the Susceptible-Infectious-Recovered model with different conditions has been used for the analysis of COVID-19. The effects of lockdown, the light switch method, and parameter variations like contact ratio and reproduction number are also analyzed. The authors have attempted to study and predict the lockdown effect, particularly in India in terms of infected and recovered numbers, which show substantial improvement. A disease-free endemic stability analysis using Lyapunov and LaSalle's method is presented, and novel methods such as the convalescent plasma method and the Who Acquires Infection From Whom method are also discussed, as they are considered to be useful in flattening the curve of COVID-19.

CDC (Cindy and David's Conversations) Game: Advising President to Survive Pandemic.

Ongoing debates on anti-COVID19 policies have been focused on coexistence-with vs. zero-out (virus) strategies, which can be simplified as "always open (AO)" vs. "always closed (AC)." We postulate that a middle ground, dubbed LOHC (low-risk-open and high-risk-closed), is likely favorable, precluding obviously irrational HOLC (high-risk-open and low-risk-closed). From a meta-strategy perspective, these four policies cover the full spectrum of anti-pandemic policies. By emulating the reality of anti-pandemic policies today, the study aims to identify possible cognitive gaps and traps by harnessing the power of evolutionary game-theoretic analysis and simulations, which suggest that (i) AO and AC seems to be "high-probability" events (0.412-0.533); (ii) counter-intuitively, the middle ground-LOHC-seems to be small-probability event (0.053), possibly mirroring its wide adoptions but broad failures. Besides devising specific policies, an equally important challenge seems to deal with often hardly avoidable policy transitions along the process from emergence, epidemic, through pandemic, to endemic state.

A KdV-SIR equation and its analytical solutions: An application for COVID-19 data analysis.

To describe the time evolution of infected persons associated with an epidemic wave, we recently derived the KdV-SIR equation that is mathematically identical to the Kortewegde Vries (KdV) equation in the traveling wave coordinate and that represents the classical SIR model under a weakly nonlinear assumption. This study further discusses the feasibility of applying the KdV-SIR equation and its analytical solutions together with COVID-19 data in order to estimate a peak time for a maximum number of infected persons. To propose a prediction method and to verify its performance, three types of data were generated based on COVID-19 raw data, using the following procedures: (1) a curve fitting package, (2) the empirical mode decomposition (EMD) method, and (3) the 28-day running mean method. Using the produced data and our derived formulas for ensemble forecasts, we determined various estimates for growth rates, providing outcomes for possible peak times. Compared to other methods, our method mainly relies on one parameter, σo (i.e., a time independent growth rate), which represents the collective impact of a transmission rate (ß) and a recovery rate (ν). Utilizing an energy equation that describes the relationship between the time dependent and independent growth rates, our method offers a straightforward alternative for estimating peak times in ensemble predictions.

Evaluation of the main parameters of the compartmental model of the epidemic development based on the example of the spread of the COVID-19 pandemic in Chernivtsi region

The paper considers the application of the theoretical model of epidemiological development of COVID-19 disease among the regional population based on the statistical data in Chernivtsi region of Ukraine for the period from March 2020 to June 2021. Using these data, a mathematical assessment of the values of the main parameters of the compartmental model (SIR) beta and gamma was performed and the analysis of the relationship between the values of beta and gamma and antiepidemiological measures was carried out for the region. Determining the parameters beta and gamma based on available statistics allows us to predict the duration of precautionary measures such as quarantine, lockdown, border closure and predict the effectiveness of their implementation as well. The analysis of statistical data showed the moderate effectiveness of quarantine and lockdown in changing the daily rates of infected and recovered people, while the dynamics of the epidemic development during these periods changed from negative to positive. The introduction of vaccination has shown the significant reduction in the daily rate of infected people and the substantial increase in the daily rate of the recovered people.

The Transmissibility of Covid-19: A Modelling Study in China

Covid-19 is a serious disease for human. It can be easily spread between human. In order to model the spread of Covid-19 and determinate the appropriate policy by government, I use the SEIRD model, which is extended from SIR model. In this paper, the SEIRD model studies the transmissibility of Covid-19 in China. This work first gives out the flowchart of the SEIRD model and then I derive the differential equation and find out the disease-free equilibrium based on the flowchart. Then I calculate the generation matrix and basic reproduction number which is directly related to the transmissibility of the virus. At last, the sensitivity analysis analyzes the different impact from different parameter. From that, we can find out the best way to control the transmission. The result is that the parameter that refer to strictness has a great impact on the spread of Covid-19. However, it doesn't have to be as large as possible since the covid can be well controlled with an appropriate value of strictness and smallest negative effect for people. This paper tries to find out the best extent of strictness of policy that is able to control the transmission. © 2023 SPIE.

The logistic growth regression model with the genetic algorithm for predicting the third wave of the COVID-19 epidemic in Thailand

The world is currently facing the novel coronavirus 2019 (COVID-19). Thailand, with a high basic reproduction number (2.27), the situation remains serious as the disease spreads throughout the country. Applying various control measures to contain the outbreak has increased the need for policymakers to assess the scale of the epidemic. In this study, a logistic growth regression (LGR) model is implemented to characterize the trends and estimate the final size of the third wave of the epidemic in Thailand at both the provincial and national levels. The parameters of the LGR are fine-tuned through the genetic algorithm assisted by the Gauss-Newton algorithm (GA/GNA). The outbreak data from the previous two waves of infection is used to validate the model performance. As a result, the LGR-GA/GNA model provides goodness-of-fit with a low RMSE, high R2, and highly significant parameters. Furthermore, when compared to the LGR model parameterized by particle swarm optimization and ant colony optimization, the proposed model outperforms the rest. In addition, to verify the prediction performance by comparing with the Susceptible-Infectious-Recovered (SIR) model, the proposed model improves the prediction accuracy better than the other. As the work was completed on May 6, 2021, the study found a possible increasing trend of COVID-19 for some vulnerable provinces and the whole country and an estimated final and peak size of the epidemic and their occurrences. The study concluded that the epidemic size of the third wave of COVID-19 in Thailand was about 190,000 by mid-July 2021. © 2023, Khon Kaen University,Research and Technology Transfer Affairs Division. All rights reserved.

Vaccination strategies in structured populations under partial immunity and reinfection

Optimal protocols of vaccine administration to minimize the effects of infectious diseases depend on a number of variables that admit different degrees of control. Examples include the characteristics of the disease and how it impacts on different groups of individuals as a function of sex, age or socioeconomic status, its transmission mode, or the demographic structure of the affected population. Here we introduce a compartmental model of infection propagation with vaccination and reinfection and analyze the effect that variations on the rates of these two processes have on the progression of the disease and on the number of fatalities. The population is split into two groups to highlight the overall effects on disease caused by different relationships between vaccine administration and various demographic structures. As a practical example, we study COVID-19 dynamics in various countries using real demographic data. The model can be easily applied to any other disease transmitted through direct interaction between infected and susceptible individuals, and any demographic structure, through a suitable estimation of parameter values. Two main conclusions stand out. First, the higher the fraction of reinfected individuals, the higher the likelihood that the disease becomes quasi-endemic. Second, optimal vaccine roll-out depends on demographic structure and disease fatality, so there is no unique vaccination protocol, valid for all countries, that minimizes the effects of a specific disease. Simulations of the general model can be carried out at this interactive webpage Atienza (2021 S2iyrd model simulator). © 2023 The Author(s). Published by IOP Publishing Ltd.

A highly accurate peak time formula of epidemic outbreak from the SIR model

Forecasting the epidemic peak time right from the origination of a disease is vital to take over dynamical behaviour of its spread over time. The decision of isolation, social distance and lock down strategic progresses does all rely on an accurate prediction of the peak time so that reduction of the time of peak or of the infected size of population will be made possible. Therefore, recent efforts concentrated on deriving elaborative and analytically accessible expressions representing the peak time of the infected compartment from the classical SIR epidemic mathematical model. In this research paper, two closed-form formulae are introduced to yield a straightforward computation of peak time of an infectious disease with no restrictions on the SIR quantities. In addition to this, the calculations can be implemented on a usual calculator, without requiring the use of advanced mathematical functions, having provided the initial fractions of infected and susceptible populations as well as the recovery to infectious ratio. A comparison including the COVID-19 data is fulfilled with the very recent formulas available in the open literature. With the proposed new scalings, evaluation of the peak time is reduced only to two parameter space and the accuracy of the present formulas in reduced form is ultimately confirmed yielding an error of order of magnitude 10−4 valid for the complete regime of the set of SIR model parameters. Even in the case of an endemic, the past peak time of the illness can also be captured accurately by the given formulae. Two simple approximations in terms of usual geometric series are also provided. These can be safely used with a pocket calculator without sophisticated laboratory equipments.

An explicit formula for minimizing the infected peak in an SIR epidemic model when using a fixed number of complete lockdowns

Careful timing of nonpharmaceutical interventions such as social distancing may avoid high "second waves" of infections of COVID‐19. This article asks what should be the timing of a set of K complete‐lockdowns of prespecified lengths (such as two weeks) so as to minimize the peak of the infective compartment. Perhaps surprisingly, it is possible to give an explicit and easily computable rule for when each lockdown should commence. Simulations are used to show that the rule remains fairly accurate even if lockdowns are not perfect. [ FROM AUTHOR] Copyright of International Journal of Robust & Nonlinear Control is the property of John Wiley & Sons, Inc. 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.)

A country-specific COVID-19 model

To dynamically measure COVID-19 transmissibility consistently normalized by population size in each country.A reduced-form model enhanced from the classical SIR is proposed to stochastically represent the Reproduction Number and Mortality Rate, directly measuring the combined effects of viral evolution and population behavioral response functions.Evidences are shown that this e(hanced)-SIR model has the power to fit country-specific empirical data, produce interpretable model parameters to be used for generating probabilistic scenarios adapted to the still unfolding pandemic.Stochastic processes embedded within compartmental epidemiological models can produce measurables and actionable information for surveillance and planning purposes.

LSTM-based Forecasting using Policy Stringency and Time-varying Parameters of the SIR Model for COVID-19

Accurate forecasting of the number of infections is an important task that can allow health care decision makers to allocate medical resources efficiently during a pandemic. Two approaches have been combined, a stochastic model by Vega et al. for modelling infectious disease and Long Short-Term Memory using COVID-19 data and government's policies. In the proposed model, LSTM functions as a nonlinear adaptive filter to modify the outputs of the SIR model for more accurate forecasts one to four weeks in the future. Our model outperforms most models among the CDC models using the United States data. We also applied the model on the Canadian data from two provinces, Saskatchewan and Ontario where it performs with a low mean absolute percentage error. © 2023 IEEE.