Modeling Provincial Covid-19 Epidemic Data Using an Adjusted Time-Dependent SIRD Model

Fitting Early Phases of the COVID-19 Outbreak: A Comparison of the Performances of Used Models

The COVID-19 outbreak involved a spread of prediction efforts, especially in the early pandemic phase. A better understanding of the epidemiological implications of the different models seems crucial for tailoring prevention policies. This study aims to explore the concordance and discrepancies in outbreak prediction produced by models implemented and used in the first wave of the epidemic. To evaluate the performance of the model, an analysis was carried out on Italian pandemic data from February 24, 2020. The epidemic models were fitted to data collected at 20, 30, 40, 50, 60, 70, 80, 90, and 98 days (the entire time series). At each time step, we made predictions until May 31, 2020. The Mean Absolute Error (MAE) and the Mean Absolute Percentage Error (MAPE) were calculated. The GAM model is the most suitable parameterization for predicting the number of new cases; exponential or Poisson models help predict the cumulative number of cases. When the goal is to predict the epidemic peak, GAM, ARIMA, or Bayesian models are preferable. However, the prediction of the pandemic peak could be made carefully during the early stages of the epidemic because the forecast is affected by high uncertainty and may very likely produce the wrong results.

COVID-19 in Italy: Is the Mortality Analysis a Way to Estimate How the Epidemic Lasts?

When an epidemic breaks out, many health, economic, social, and political problems arise that require a prompt and effective solution. It would be useful to obtain all information about the virus, including epidemiological ones, as soon as possible. In a previous study of our group, the analysis of the positive-alive was proposed to estimate the epidemic duration. It was stated that every epidemic ends when the number of positive-alive (=infected-healed-dead) glides toward zero. In fact, if with the contagion everyone can enter the epidemic phenomenon, only by healing or dying can they get out of it. In this work, a different biomathematical model is proposed. A necessary condition for the epidemic to be resolved is that the mortality reaches the asymptotic value, from there, remains stable. At that time, the number of positive-alive must also be close to zero. This model seems to allow us to interpret the entire development of the epidemic and highlight its phases. It is also more appropriate than the previous one, especially when the spread of the infection is so rapid that the increase in live positives is staggering.

Fuzzy-SIRD model: Forecasting COVID-19 death tolls considering governments intervention

Modeling the trend of contagious diseases has particular importance for managing them and reducing the side effects on society. In this regard, researchers have proposed compartmental models for modeling the spread of diseases. However, these models suffer from a lack of adaptability to variations of parameters over time. This paper introduces a new Fuzzy Susceptible-Infectious-Recovered-Deceased (Fuzzy-SIRD) model for covering the weaknesses of the simple compartmental models. Due to the uncertainty in forecasting diseases, the proposed Fuzzy-SIRD model represents the government intervention as an interval type 2 Mamdani fuzzy logic system. Also, since society's response to government intervention is not a static reaction, the proposed model uses a first-order linear system to model its dynamics. In addition, this paper uses the Particle Swarm Optimization (PSO) algorithm for optimally selecting system parameters. The objective function of this optimization problem is the Root Mean Square Error (RMSE) of the system output for the deceased population in a specific time interval. This paper provides many simulations for modeling and predicting the death tolls caused by COVID-19 disease in seven countries and compares the results with the simple SIRD model. Based on the reported results, the proposed Fuzzy-SIRD model can reduce the root mean square error of predictions by more than 80% in the long-term scenarios, compared with the conventional SIRD model. The average reduction of RMSE for the short-term and long-term predictions are 45.83% and 72.56%, respectively. The results also show that the principle goal of the proposed modeling, i.e., creating a semantic relation between the basic reproduction number, government intervention, and society's response to interventions, has been well achieved. As the results approve, the proposed model is a suitable and adaptable alternative for conventional compartmental models.

Combining and comparing regional SARS-CoV-2 epidemic dynamics in Italy: Bayesian meta-analysis of compartmental models and global sensitivity analysis

During autumn 2020, Italy faced a second important SARS-CoV-2 epidemic wave. We explored the time pattern of the instantaneous reproductive number, R ₀(t), and estimated the prevalence of infections by region from August to December calibrating SIRD models on COVID-19-related deaths, fixing at values from literature Infection Fatality Rate (IFR) and average infection duration. A Global Sensitivity Analysis (GSA) was performed on the regional SIRD models. Then, we used Bayesian meta-analysis and meta-regression to combine and compare the regional results and investigate their heterogeneity. The meta-analytic R ₀(t) curves were similar in the Northern and Central regions, while a less peaked curve was estimated for the South. The maximum R ₀(t) ranged from 2.15 (South) to 2.61 (North) with an increase following school reopening and a decline at the end of October. The predictive performance of the regional models, assessed through cross validation, was good, with a Mean Absolute Percentage Error of 7.2% and 10.9% when considering prediction horizons of 7 and 14 days, respectively. Average temperature, urbanization, characteristics of family medicine and healthcare system, economic dynamism, and use of public transport could partly explain the regional heterogeneity. The GSA indicated the robustness of the regional R ₀(t) curves to different assumptions on IFR. The infectious period turned out to have a key role in determining the model results, but without compromising between-region comparisons.

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

With the outbreaks of the COVID-19 epidemics in several provinces of China, government takes prevention and control measures to contain the epidemics. It is more difficult to make the long-term prediction of the sporadic COVID-19 epidemics than widespread ones in that the former cannot obey the laws of the infectious disease well like the latter. In this paper, we make long-term predictions including end time and final size, peak and peak time of current confirmed cases and the number of accumulative removed cases of the sporadic COVID-19 epidemics in different regions of China by a novel non-autonomous delayed SIR compartment model (S-susceptible, I-infected, R-removed). The key contribution of this paper is that under the rigorous containments, we find transmission rate β ( t ) is approximately an exponential decreasing function with respect to time t, rather than a fixed constant. In addition, the removed rate γ ( t ) is approximately a piecewise linear increasing function instead of a linear increasing function which is (at + b)heaviside (t-14). First, according to the few data in the early stage, i.e., roughly the first 7 days, issued by the National Health Commission of China and local Health Commissions, we can accurately estimate these parameters, i.e., transmission and removed rates of the model. Then, by them, we accurately predict the evolution of the COVID-19 there. On the basis of them to predict Category A of the sporadic COVID-19 epidemics since July 20th, 2021 in this summer. The results agree very well to the actual ones. It is also adopted to predict Category B - - - the tour group epidemics since October 17th, 2021 and Category C - - - other sporadic epidemics since October 27th, 2021. The results show that although our method is simple and the needed data are very few, the long-term prediction of the sporadic COVID-19 epidemics in China is quite effective. We can use this novel non-autonomous delayed SIR model to accurately predict its end time and final size, peak and peak time of current confirmed cases and the number of accumulative removed cases in China. This work can help governments and policy-makers make optimal prevention and control policies for all cities and provinces to contain the COVID-19 epidemics, and prepare well for the resumption of work, production and classes in advance to reduce the economic and social losses.

Change-Point Detection in Homogeneous Segments of COVID-19 Daily Infection

Modeling the number of individuals in different states is a principal tool in the event of an epidemic. The natural transition of individuals between possible states often includes deliberate interference such as isolation or vaccination. Thus, the mathematical model may need to be re-calibrated due to various factors. The model considered in this paper is the SIRD epidemic model. An additional parameter is the moment of changing the description of the phenomenon when the parameters of the model change and the change is not pre-specified. Detecting and estimating the moment of change in real time is the subject of statistical research. A sequential (online) approach was applied using the Bayesian shift point detection algorithm and trimmed exact linear time. We show how methods of analysis behave in different instances. These methods are verified on simulated data and applied to pandemic data of a selected European country. The simulation is performed with a social network graph to obtain a practical representation ability. The epidemiological data used come from the territory of Poland and concern the COVID-19 epidemic in Poland. The results show satisfactory detection of the moments where the applied model needs to be verified and re-calibrated. These show the effectiveness of the proposed combination of methods.

Forecasting of a complex phenomenon using stochastic data-based techniques under non-conventional schemes: The SARS-CoV-2 virus spread case

Epidemics are complex dynamical processes that are difficult to model. As revealed by the SARS-CoV-2 pandemic, the social behavior and policy decisions contribute to the rapidly changing behavior of the virus' spread during outbreaks and recessions. In practice, reliable forecasting estimations are needed, especially during early contagion stages when knowledge and data are insipient. When stochastic models are used to address the problem, it is necessary to consider new modeling strategies. Such strategies should aim to predict the different contagious phases and fast changes between recessions and outbreaks. At the same time, it is desirable to take advantage of existing modeling frameworks, knowledge and tools. In that line, we take Autoregressive models with exogenous variables (ARX) and Vector autoregressive (VAR) techniques as a basis. We then consider analogies with epidemic's differential equations to define the structure of the models. To predict recessions and outbreaks, the possibility of updating the model's parameters and stochastic structures is considered, providing non-stationarity properties and flexibility for accommodating the incoming data to the models. The Generalized-Random-Walk (GRW) and the State-Dependent-Parameter (SDP) techniques shape the parameters' variability. The stochastic structures are identified following the Akaike (AIC) criterion. The models use the daily rates of infected, death, and healed individuals, which are the most common and accurate data retrieved in the early stages. Additionally, different experiments aim to explore the individual and complementary role of these variables. The results show that although both the ARX-based and VAR-based techniques have good statistical accuracy for seven-day ahead predictions, some ARX models can anticipate outbreaks and recessions. We argue that short-time predictions for complex problems could be attained through stochastic models that mimic the fundamentals of dynamic equations, updating their parameters and structures according to incoming data.

Uncertainty quantification in Covid-19 spread: Lockdown effects

We develop a Bayesian inference framework to quantify uncertainties in epidemiological models. We use SEIJR and SIJR models involving populations of susceptible, exposed, infective, diagnosed, dead and recovered individuals to infer from Covid-19 data rate constants, as well as their variations in response to lockdown measures. To account for confinement, we distinguish two susceptible populations at different risk: confined and unconfined. We show that transmission and recovery rates within them vary in response to facts, and that the diagnose rate is quite low, which leads to large amounts of undiagnosed infective individuals. A key unknown to predict the evolution of the epidemic is the fraction of the population affected by the virus, including asymptomatic subjects. Our study tracks its time evolution with quantified uncertainty from available official data, limited, however, by the data quality. We exemplify the technique with data from Spain, country in which late drastic lockdowns were enforced for months during the first wave of the current pandemic. In late actions and in the absence of other measures, spread is delayed but not stopped unless a large enough fraction of the population is confined until the asymptomatic population is depleted. To some extent, confinement can be replaced by strong distancing through masks in adequate circumstances.

Policy responses to COVID-19 pandemic waves: Cross-region and cross-sector economic impact

This paper proposes a modelling approach to assess the cross-region and cross-sector economic impacts of the restrictions imposed by governments to contain the COVID-19 pandemic. The nationwide lockdown imposed in Italy during the first wave of the pandemic is used as a benchmark. However, the adopted approach allows an ex-ante assessment of alternative policy responses, in the event of successive pandemic waves, in order to rationalise the policy intervention and reach the best possible compromise between containing the risk of contagion and reducing economic losses. The used approach consists of a non-linear programming model based on a multiregional Input-Output (I-O) table, which guarantees greater flexibility than traditional I-O analysis. It is applied to estimate both direct and indirect losses of GDP and employment produced by alternative policy responses represented by general and differentiated lockdowns. The evidence deriving from the Italian experience shows a sort of learning process through successive waves based on the introduction of increasingly flexible and tailored policy responses to the pandemic.

Data-Driven Analytics Leveraging Artificial Intelligence in the Era of COVID-19: An Insightful Review of Recent Developments

This paper presents the role of artificial intelligence (AI) and other latest technologies that were employed to fight the recent pandemic (i.e., novel coronavirus disease-2019 (COVID-19)). These technologies assisted the early detection/diagnosis, trends analysis, intervention planning, healthcare burden forecasting, comorbidity analysis, and mitigation and control, to name a few. The key-enablers of these technologies was data that was obtained from heterogeneous sources (i.e., social networks (SN), internet of (medical) things (IoT/IoMT), cellular networks, transport usage, epidemiological investigations, and other digital/sensing platforms). To this end, we provide an insightful overview of the role of data-driven analytics leveraging AI in the era of COVID-19. Specifically, we discuss major services that AI can provide in the context of COVID-19 pandemic based on six grounds, (i) AI role in seven different epidemic containment strategies (a.k.a non-pharmaceutical interventions (NPIs)), (ii) AI role in data life cycle phases employed to control pandemic via digital solutions, (iii) AI role in performing analytics on heterogeneous types of data stemming from the COVID-19 pandemic, (iv) AI role in the healthcare sector in the context of COVID-19 pandemic, (v) general-purpose applications of AI in COVID-19 era, and (vi) AI role in drug design and repurposing (e.g., iteratively aligning protein spikes and applying three/four-fold symmetry to yield a low-resolution candidate template) against COVID-19. Further, we discuss the challenges involved in applying AI to the available data and privacy issues that can arise from personal data transitioning into cyberspace. We also provide a concise overview of other latest technologies that were increasingly applied to limit the spread of the ongoing pandemic. Finally, we discuss the avenues of future research in the respective area. This insightful review aims to highlight existing AI-based technological developments and future research dynamics in this area.

Hybrid Model-Based Simulation Analysis on the Effects of Social Distancing Policy of the COVID-19 Epidemic

This study utilizes modeling and simulation to analyze coronavirus (COVID-19) infection trends depending on government policies. Two modeling requirements are considered for infection simulation: (1) the implementation of social distancing policies and (2) the representation of population movements. To this end, we propose an extended infection model to combine analytical models with discrete event-based simulation models in a hybrid form. Simulation parameters for social distancing policies are identified and embedded in the analytical models. Administrative districts are modeled as a fundamental simulation agent, which facilitates representing the population movements between the cities. The proposed infection model utilizes real-world data regarding suspected, infected, recovered, and deceased people in South Korea. As an application, we simulate the COVID-19 epidemic in South Korea. We use real-world data for 160 days, containing meaningful days that begin the distancing policy and adjust the distancing policy to the next stage. We expect that the proposed work plays a principal role in analyzing how social distancing effectively affects virus prevention and provides a simulation environment for the biochemical field.

Inversion of a SIR-based model: A critical analysis about the application to COVID-19 epidemic

Calibration of a SIR (Susceptibles-Infected-Recovered) model with official international data for the COVID-19 pandemics provides a good example of the difficulties inherent in the solution of inverse problems. Inverse modeling is set up in a framework of discrete inverse problems, which explicitly considers the role and the relevance of data. Together with a physical vision of the model, the present work addresses numerically the issue of parameters calibration in SIR models, it discusses the uncertainties in the data provided by international authorities, how they influence the reliability of calibrated model parameters and, ultimately, of model predictions.

Network-based prediction of COVID-19 epidemic spreading in Italy

Initially emerged in the Chinese city Wuhan and subsequently spread almost worldwide causing a pandemic, the SARS-CoV-2 virus follows reasonably well the Susceptible-Infectious-Recovered (SIR) epidemic model on contact networks in the Chinese case. In this paper, we investigate the prediction accuracy of the SIR model on networks also for Italy. Specifically, the Italian regions are a metapopulation represented by network nodes and the network links are the interactions between those regions. Then, we modify the network-based SIR model in order to take into account the different lockdown measures adopted by the Italian Government in the various phases of the spreading of the COVID-19. Our results indicate that the network-based model better predicts the daily cumulative infected individuals when time-varying lockdown protocols are incorporated in the classical SIR model.