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.

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.

Projection of COVID-19 Jakarta using CHIME Technology (Covid-19 Hospital Impact Model for Epidemics) Application

After the coronavirus outbreak, the disease known as COVID-19 has been infecting millions of people, and the number of deaths is pilling up to hundreds of thousands. In Indonesia, especially Jakarta, some of the deaths are caused by pandemic-related surges that strain hospital capacity. Besides, people had many obstacles in this pandemic condition because of the lack of knowledge about COVID-19. On that matter, several models emerged worldwide to help inform public decision making in this pandemic situation. With today's technological advances the CHIME (COVID-19 Hospital Impact Model for Epidemics) application is designed to assist hospitals and public health officials with understanding hospital capacity needs as they relate to the COVID pandemic. This paper aims to help inform public health decision making regarding the transmission of COVID-19 in Jakarta using CHIME. This work uses Jakarta COVID-19 data from November 24th, 2021 and its accumulation from 14 days before (November 10th, 2021) to predict the course of COVID-19 in 30 days. With ArcGIS Pro and ArcGIS Experience, this work successfully made a map that uses CHIME to inform about peak demand of each city in DKI Jakarta and the daily new admissions and hospitalization graph. In addition, a Jakarta COVID-19 dashboard is also made to inform more about the transmission of COVID-19. © 2022 IEEE.

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 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.

A model predictive control approach to optimally devise a two-dose vaccination rollout: A case study on COVID-19 in Italy.

The COVID-19 pandemic has led to the unprecedented challenge of devising massive vaccination rollouts, toward slowing down and eventually extinguishing the diffusion of the virus. The two-dose vaccination procedure, speed requirements, and the scarcity of doses, suitable spaces, and personnel, make the optimal design of such rollouts a complex problem. Mathematical modeling, which has already proved to be determinant in the early phases of the pandemic, can again be a powerful tool to assist public health authorities in optimally planning the vaccination rollout. Here, we propose a novel epidemic model tailored to COVID-19, which includes the effect of nonpharmaceutical interventions and a concurrent two-dose vaccination campaign. Then, we leverage nonlinear model predictive control to devise optimal scheduling of first and second doses, accounting both for the healthcare needs and for the socio-economic costs associated with the epidemics. We calibrate our model to the 2021 COVID-19 vaccination campaign in Italy. Specifically, once identified the epidemic parameters from officially reported data, we numerically assess the effectiveness of the obtained optimal vaccination rollouts for the two most used vaccines. Determining the optimal vaccination strategy is nontrivial, as it depends on the efficacy and duration of the first-dose partial immunization, whereby the prioritization of first doses and the delay of second doses may be effective for vaccines with sufficiently strong first-dose immunization. Our model and optimization approach provide a flexible tool that can be adopted to help devise the current COVID-19 vaccination campaign, and increase preparedness for future epidemics.

Optimizing two-dose vaccine resource allocation to combat a pandemic in the context of limited supply: The case of COVID-19.

The adequate vaccination is a promising solution to mitigate the enormous socio-economic costs of the ongoing COVID-19 pandemic and allow us to return to normal pre-pandemic activity patterns. However, the vaccine supply shortage will be inevitable during the early stage of the vaccine rollout. Public health authorities face a crucial challenge in allocating scarce vaccines to maximize the benefits of vaccination. In this paper, we study a multi-period two-dose vaccine allocation problem when the vaccine supply is highly limited. To address this problem, we constructed a novel age-structured compartmental model to capture COVID-19 transmission and formulated as a nonlinear programming (NLP) model to minimize the total number of deaths in the population. In the NLP model, we explicitly take into account the two-dose vaccination procedure and several important epidemiologic features of COVID-19, such as pre-symptomatic and asymptomatic transmission, as well as group heterogeneity in susceptibility, symptom rates, severity, etc. We validated the applicability of the proposed model using a real case of the 2021 COVID-19 vaccination campaign in the Midlands of England. We conducted comparative studies to demonstrate the superiority of our method. Our numerical results show that prioritizing the allocation of vaccine resources to older age groups is a robust strategy to prevent more subsequent deaths. In addition, we show that releasing more vaccine doses for first-dose recipients could lead to a greater vaccination benefit than holding back second doses. We also find that it is necessary to maintain appropriate non-pharmaceutical interventions (NPIs) during the vaccination rollout, especially in low-resource settings. Furthermore, our analysis indicates that starting vaccination as soon as possible is able to markedly alleviate the epidemic impact when the vaccine resources are limited but are currently available. Our model provides an effective tool to assist policymakers in developing adaptive COVID-19 likewise vaccination strategies for better preparedness against future pandemic threats.

Empirical Analysis of Epidemic Deceases Model using the Effect of Social Distancing

An epidemic model is employed to examine the dynamics of infectious disease transmission. They make predictions about the rate at which an epidemic will spread, how severe the disease will be, and other factors. The Susceptible-Infected-Recovered (is also known as SIR) model, is a straightforward epidemic model [1]. SIR models codify the most straightforward method to conceptualize an epidemic. The Susceptible-Exposed-Infected-Recovered model (known as SEIR) just expands on the Susceptible-Infected-Recovered model by including a further equation of exposed individuals. Persons get contaminated but are not yet contagious throughout a long time of isolation for some serious contaminations. The person is in compartment E (for exposed) at this time[3]. The impact of social estrangement has been examined in the research. © 2022 IEEE.

Forecasting of COVID-19 Dynamics by Agent-Based Model

The novel coronavirus pandemic has continued to spread worldwide for more than two years. The development of automated solutions to support decision-making in pandemic control is still an ongoing challenge. This study aims to develop an agent-based model of the COVID-19 epidemic process to predict its dynamics in a specific area. The model shows sufficient accuracy for decision-making by public health authorities. At the same time, the advantage of the model is that it allows taking into account the stochastic nature of the epidemic process and the heterogeneity of the studied population. At the same time, the adequacy of the model can be improved with a more detailed description of the population and external factors that can affect the dynamics of the epidemic process. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

An Optimal Vaccine Allocation Model Considering Vaccine Hesitancy and Efficacy Rates Among Populations

Vaccines need to be urgently allocated in pandemics like the ongoing COVID-19 pandemic. In the literature, vaccines are optimally allocated using various mathematical models, including the extensively used Susceptible-Infected-Recovered epidemic model. However, these models do not account for the time duration concerning multi-dose vaccines, time duration from infection to recovery or death, the vaccine hesitancy (i.e., delay in acceptance or refusal of vaccination), and vaccine efficacy (i.e., the time-varying protection capability of the vaccine). To make the vaccine allocation model more applicable to reality, this paper presents an optimal model considering the above mentioned time duration concerning multi-dose vaccination, time duration from infection to recovery or death, hesitancy rates, efficacy levels, and also breakthrough rates - the rates at which individuals get infected after vaccination. This vaccine allocation model is constructed using a revised Susceptible-Infected-Recovered model. The concept of people∗week infections is introduced to measure the number of infected people within a certain time duration, and in this paper, the amount of people∗week infections is minimized by the proposed vaccine allocation model. Our case study of the New York State 2021 population of 19,840,000 shows that this optimal allocation method can avoid 0.05%2.75% people∗week infections than the baseline allocation method when 2 to 11 million vaccines are optimally allocated. In conclusion, the obtained optimal allocation method can effectively reduce people∗week infections and avoid vaccine waste when more vaccines are available. © 2013 IEEE.

Dynamics and application of a generalized SIQR epidemic model with vaccination and treatment

In this paper, we propose and investigate the SIQR epidemic model with a generalized incidence rate function, a general treatment function and vaccination term. We firstly consider the existence and uniqueness of the global nonnegative solution to the deterministic model. Further, we show the locally asymptotic stability of the disease-free equilibrium and endemic equilibrium of the deterministic model, and obtain the basic reproduction number R0. Then we study the existence and uniqueness of the global positive solution to the stochastic model with any positive initial value. Meanwhile, we obtain sufficient conditions for the extinction of the disease in the stochastic epidemic model, and find that the large noise can make the disease die out exponentially. Finally, we make an empirical analysis by the COVID-19 data of Russia and Serbia. By the performance comparison of different models, it shows that the model with vaccination and treatment we proposed is better for the real situation, which is also verified by different estimation methods. Especially, that shows the recovery rate of the infected increases by 0.042 and the death rate of the recovered is 1.525 times that of normal human in Russia. Through statistical analysis, the short-term trend of epidemic transmission is predicted: under the condition of unchanged prevention and control policies, it may reach a stable endemic equilibrium state in Russia and the epidemic will eventually extinct in Serbia. © 2023 Elsevier Inc.

Forecasting the Temporal Evolution of COVID-19

COVID-19 epidemic has resulted in severe chaos across the globe. Complex frameworks can be investigated and studied using mathematical models, which are reliable and efficient. The objective of this research is to scrutinize the progression and prediction of parameters that evaluate the emergence and transmission of COVID-19 in the two most affected nations, i.e., the USA and India. Five models including the standard and hybrid epidemic models, viz, SIR (Susceptible-Infectious-Removed), SIRD (Susceptible-Infectious-Recovered-Death), SIRD with vaccination, SIRD with vital dynamics (i.e., including birth rate and death rate) and, SIRD with vital dynamics and vaccination have been developed. Worldwide statistics have been observed utilizing graphical layouts. Model evaluation measures such as Mean Absolute error (MAE), Mean-square error (MSE), and Root Mean Square Error (RMSE) for different parameters namely infection rate, recovery rate, and death rate have been estimated. © 2022 IEEE.

Effect of Transmission and Vaccination on Time to Dominance of Emerging Viral Strains: A Simulation-Based Study.

We studied the effect of transmissibility and vaccination on the time required for an emerging strain of an existing virus to dominate in the infected population using a simulation-based experiment. The emergent strain is assumed to be completely resistant to the available vaccine. A stochastic version of a modified SIR model for emerging viral strains was developed to simulate surveillance data for infections. The proportion of emergent viral strain infections among the infected was modeled using a logistic curve and the time to dominance (TTD) was recorded for each simulation. A factorial experiment was implemented to compare the TTD values for different transmissibility coefficients, vaccination rates, and initial vaccination coverage. We discovered a non-linear relationship between TTD and the relative transmissibility of the emergent strain for populations with low vaccination coverage. Furthermore, higher vaccination coverage and high vaccination rates in the population yielded significantly lower TTD values. Vaccinating susceptible individuals against the current strain increases the susceptible pool of the emergent virus, which leads to the emergent strain spreading faster and requiring less time to dominate the infected population.

A differential epidemic Model for Information, Misinformation, and disinformation in online Social Networks: CoVId-19 Vaccination

These days the online social network has become a huge source of data. People are actively sharing information on these platforms. The data on online social networks can be misinformation, information, and disinformation. Because online social networks have become an important part of our lives, the information on online social networks makes a great impact on us. Here a differential epidemic model for information, misinformation, and disinformation on online social networks is proposed. The expression for basic reproduction number has been developed. Again, the stability condition for the system at both infection-free and endemic equilibriums points has been discussed. The numerical simulation has been performed to validate the theoretical results. Data available on Twitter related to COVID-19 vaccination is used to perform the experiment. Finally, the authors discuss the control strategy to minimize the misinformation and disinformation related to vaccination. © 2022 Authors. All rights reserved.

Forecasting the Temporal Evolution of COVID-19

COVID-19 epidemic has resulted in severe chaos across the globe. Complex frameworks can be investigated and studied using mathematical models, which are reliable and efficient. The objective of this research is to scrutinize the progression and prediction of parameters that evaluate the emergence and transmission of COVID-19 in the two most affected nations, i.e., the USA and India. Five models including the standard and hybrid epidemic models, viz, SIR (Susceptible-Infectious-Removed), SIRD (Susceptible-Infectious-Recovered-Death), SIRD with vaccination, SIRD with vital dynamics (i.e., including birth rate and death rate) and, SIRD with vital dynamics and vaccination have been developed. Worldwide statistics have been observed utilizing graphical layouts. Model evaluation measures such as Mean Absolute error (MAE), Mean-square error (MSE), and Root Mean Square Error (RMSE) for different parameters namely infection rate, recovery rate, and death rate have been estimated. © 2022 IEEE.

Model-Based Optimization of Vaccination Strategies in Different Phases of Pandemic Virus Spread

This paper aims at applying optimal control principles to investigate optimal vaccination strategies in different phases of a pandemic. Background of the study is that many countries have started their vaccination procedures against the COVID-19 disease in the beginning of 2021, but supply shortages for the vaccines prevented that everyone could be vaccinated immediately. At the beginning of 2022, in contrast, the vaccine supply was ample, but the effectiveness of different existing vaccines to avoid infection by new virus variants was in doubt, as well as the acceptance of booster doses decreased over time. To account for these effects, two formulations of optimization tasks based on different epidemic models are proposed in this paper. The solution of these tasks determines optimal distribution strategies for available vaccines, and optimized vaccination schemes to reduce the need of booster doses for later phase. Effectiveness of these strategies compared with other popular strategies (as applied in practice) is demonstrated through a series of simulations © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

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.

Modelling presymptomatic infectiousness in COVID-19

This paper considers SEPIR, an extension of the well-known SEIR continuous simulation compartment model. Both models can be fitted to real data as they include parameters that can be estimated from the data. SEPIR deploys an additional presymptomatic infectious compartment, not modelled in SEIR but known to exist in COVID-19. This stage can also be fitted to data. We focus on how to fit SEPIR to a first wave of COVID. Both SEIR and SEPIR and the existing SEIR models assume a homogeneous mixing population with parameters fixed. Moreover, neither includes dynamically varying control strategies deployed against the virus. If either model is to represent more than just a single wave of the epidemic, then the parameters of the model would have to be time dependent. In view of this, we also show how reproduction numbers can be calculated to investigate the long-term overall outcome of an epidemic. © 2023 The Operational Research Society.

MepoGNN: Metapopulation Epidemic Forecasting with Graph Neural Networks

Epidemic prediction is a fundamental task for epidemic control and prevention. Many mechanistic models and deep learning models are built for this task. However, most mechanistic models have difficulty estimating the time/region-varying epidemiological parameters, while most deep learning models lack the guidance of epidemiological domain knowledge and interpretability of prediction results. In this study, we propose a novel hybrid model called MepoGNN for multi-step multi-region epidemic forecasting by incorporating Graph Neural Networks (GNNs) and graph learning mechanisms into Metapopulation SIR model. Our model can not only predict the number of confirmed cases but also explicitly learn the epidemiological parameters and the underlying epidemic propagation graph from heterogeneous data in an end-to-end manner. Experiment results demonstrate our model outperforms the existing mechanistic models and deep learning models by a large margin. Furthermore, the analysis on the learned parameters demonstrates the high reliability and interpretability of our model and helps better understanding of epidemic spread. Our model and data have already been public on GitHub https://github.com/deepkashiwa20/MepoGNN.git. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

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.