Modeling the second wave of COVID-19 infections in France and Italy via a stochastic SEIR model

Modeling correlated uncertainties in stochastic compartmental models

We consider compartmental models of communicable disease with uncertain contact rates. Stochastic fluctuations are often added to the contact rate to account for uncertainties. White noise, which is the typical choice for the fluctuations, leads to significant underestimation of the disease severity. Here, starting from reasonable assumptions on the social behavior of individuals, we model the contacts as a Markov process which takes into account the temporal correlations present in human social activities. Consequently, we show that the mean-reverting Ornstein-Uhlenbeck (OU) process is the correct model for the stochastic contact rate. We demonstrate the implication of our model on two examples: a Susceptibles-Infected-Susceptibles (SIS) model and a Susceptibles-Exposed-Infected-Removed (SEIR) model of the COVID-19 pandemic and compare the results to the available US data from the Johns Hopkins University database. In particular, we observe that both compartmental models with white noise uncertainties undergo transitions that lead to the systematic underestimation of the spread of the disease. In contrast, modeling the contact rate with the OU process significantly hinders such unrealistic noise-induced transitions. For the SIS model, we derive its stationary probability density analytically, for both white and correlated noise. This allows us to give a complete description of the model's asymptotic behavior as a function of its bifurcation parameters, i.e., the basic reproduction number, noise intensity, and correlation time. For the SEIR model, where the probability density is not available in closed form, we study the transitions using Monte Carlo simulations. Our modeling approach can be used to quantify uncertain parameters in a broad range of biological systems.

Asymptotic analysis on a new stochastic epidemic model involving isolation mechanism

In this paper, a new stochastic epidemic model is established and the dynamical behavior of its solutions is studied for this model. A deterministic epidemic model (ordinary differential equation) is first proposed by considering the isolation mechanism, and the transmission probability function is determined by a Wells-Riley model method to analyze the transmission in the quarantine. For this deterministic model, the basic reproduction number R0 is computed and it is used to determine the existence of disease-free and positive equilibria. The linearized stability of the equilibria is also discussed by analyzing the distribution of eigenvalues of the linear system. Following that, a corresponding stochastic epidemic model is further established by introducing stochastic disturbance. Then, the extinction result of the model is derived also with the help of the basic reproduction number R0s. Furthermore, by applying the theory of Markov semigroups, it is proved that the densities of the distributions of the solutions can converge to an invariant density or sweeping under certain conditions. At last, some numerical simulations are provided and discussed to illustrate the practicability of the model and the obtained theoretical results.

Stochastic transmission in epidemiological models

Recent empirical evidence suggests that the transmission coefficient in susceptible-exposed-infected-removed-like (SEIR-like) models evolves with time, presenting random patterns, and some stylized facts, such as mean-reversion and jumps. To address such observations we propose the use of jump-diffusion stochastic processes to parameterize the transmission coefficient in an SEIR-like model that accounts for death and time-dependent parameters. We provide a detailed theoretical analysis of the proposed model proving the existence and uniqueness of solutions as well as studying its asymptotic behavior. We also compare the proposed model with some variations possibly including jumps. The forecast performance of the considered models, using reported COVID-19 infections from New York City, is then tested in different scenarios. Despite the simplicity of the epidemiological model, by considering stochastic transmission, the forecasted scenarios were fairly accurate.

Exploring the potential of learning methods and recurrent dynamic model with vaccination: A comparative case study of COVID-19 in Austria, Brazil, and China

In order to effectively manage infectious diseases, it is crucial to understand the interplay between disease dynamics and human conduct. Various factors can impact the control of an epidemic, including social interventions, adherence to health protocols, mask-wearing, and vaccination. This article presents the development of an innovative hybrid model, known as the Combined Dynamic-Learning Model, that integrates classical recurrent dynamic models with four different learning methods. The model is composed of two approaches: The first approach introduces a traditional dynamic model that focuses on analyzing the impact of vaccination on the occurrence of an epidemic, and the second approach employs various learning methods to forecast the potential outcomes of an epidemic. Furthermore, our numerical results offer an interesting comparison between the traditional approach and modern learning techniques. Our classic dynamic model is a compartmental model that aims to analyze and forecast the diffusion of epidemics. The model we propose has a recurrent structure with piecewise constant parameters and includes compartments for susceptible, exposed, vaccinated, infected, and recovered individuals. This model can accurately mirror the dynamics of infectious diseases, which enables us to evaluate the impact of restrictive measures on the spread of diseases. We conduct a comprehensive dynamic analysis of our model. Additionally, we suggest an optimal numerical design to determine the parameters of the system. Also, we use regression tree learning, bidirectional long short-term memory, gated recurrent unit, and a combined deep learning method for training and evaluation of an epidemic. In the final section of our paper, we apply these methods to recently published data on COVID-19 in Austria, Brazil, and China from 26 February 2021 to 4 August 2021, which is when vaccination efforts began. To evaluate the numerical results, we utilized various metrics such as RMSE and R-squared. Our findings suggest that the dynamic model is ideal for long-term analysis, data fitting, and identifying parameters that impact epidemics. However, it is not as effective as the supervised learning method for making long-term forecasts. On the other hand, supervised learning techniques, compared to dynamic models, are more effective for predicting the spread of diseases, but not for analyzing the behavior of epidemics.

Relating quanta conservation and compartmental epidemiological models of airborne disease outbreaks in buildings

We investigate the underlying assumptions and limits of applicability of several documented models for outbreaks of airborne disease inside buildings by showing how they may each be regarded as special cases of a system of equations which combines quanta conservation and compartmental epidemiological modelling. We investigate the behaviour of this system analytically, gaining insight to its behaviour at large time. We then investigate the characteristic timescales of an indoor outbreak, showing how the dilution rate of the space, and the quanta generation rate, incubation rate and removal rate associated with the illness may be used to predict the evolution of an outbreak over time, and may also be used to predict the relative performances of other indoor airborne outbreak models. The model is compared to a more commonly used model, in which it is assumed the environmental concentration of infectious aerosols adheres to a quasi-steady-state, so that the the dimensionless quanta concentration is equal to the the infectious fraction. The model presented here is shown to approach this limit exponentially to within an interval defined by the incubation and removal rates. This may be used to predict the maximum extent to which a case will deviate from the quasi steady state condition.

An updated estimation approach for SEIR models with stochastic perturbations: Application to COVID-19 data in Bogotá

This paper studies the updated estimation method for estimating the transmission rate changes over time. The models for the population dynamics under SEIR epidemic models with stochastic perturbations are analysed the dynamics of the COVID-19 pandemic in Bogotá, Colombia. We performed computational experiments to interpret COVID-19 dynamics using actual data for the proposed models. We estimate the model parameters and updated their estimates for reported infected and recovered data.

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.

Dual ɛ-closed-loop Nash equilibrium method to study pandemic by numerical analysis

In this paper, an approach to the disease transmission dynamic of a coronavirus pandemic is presented. Compared to models commonly known from the literature, new classes that describe this dynamic to our model were added, which are a class representing costs of the pandemic and a class of the individuals being vaccinated but without antibodies. Parameters which at most of them depend on time were used. Sufficient conditions for a dual ɛ-closed-loop Nash equilibrium in the form of the verification theorem are formulated. A numerical algorithm and numerical example are constructed.

Interval type-2 Fuzzy control and stochastic modeling of COVID-19 spread based on vaccination and social distancing rates

BACKGROUND AND OBJECTIVE

Besides efforts on vaccine discovery, robust and intuitive government policies could also significantly influence the pandemic state. However, such policies require realistic virus spread models, and the major works on COVID-19 to date have been only case-specific and use deterministic models. Additionally, when a disease affects large portions of the population, countries develop extensive infrastructures to contain the condition that should adapt continuously and extend the healthcare system's capabilities. An accurate mathematical model that reasonably addresses these complex treatment/population dynamics and their corresponding environmental uncertainties is necessary for making appropriate and robust strategic decisions.

METHODS

Here, we propose an interval type-2 fuzzy stochastic modeling and control strategy to deal with the realistic uncertainties of pandemics and manage the size of the infected population. For this purpose, we first modify a previously established COVID-19 model with definite parameters to a Stochastic SEIAR (S²EIAR) approach with uncertain parameters and variables. Next, we propose to use normalized inputs, rather than the usual parameter settings in the previous case-specific studies, hence offering a more generalized control structure. Furthermore, we examine the proposed genetic algorithm-optimized fuzzy system in two scenarios. The first scenario aims to keep infected cases below a certain threshold, while the second addresses the changing healthcare capacities. Finally, we examine the proposed controller on stochasticity and disturbance in parameters, population sizes, social distance, and vaccination rate.

RESULTS

The results show the robustness and efficiency of the proposed method in the presence of up to 1% noise and 50% disturbance in tracking the desired size of the infected population. The proposed method is compared to Proportional Derivative (PD), Proportional Integral Derivative (PID), and type-1 fuzzy controllers. In the first scenario, both fuzzy controllers perform more smoothly despite PD and PID controllers reaching a lower mean squared error (MSE). Meanwhile, the proposed controller outperforms PD, PID, and the type-1 fuzzy controller for the MSE and decision policies for the second scenario.

CONCLUSIONS

The proposed approach explains how we should decide on social distancing and vaccination rate policies during pandemics against the prevalent uncertainties in disease detection and reporting.

COVID-19 epidemic peaks distribution in the United-States of America, from epidemiological modeling to public health policies

COVID-19 prediction models are characterized by uncertainties due to fluctuating parameters, such as changes in infection or recovery rates. While deterministic models often predict epidemic peaks too early, incorporating these fluctuations into the SIR model can provide a more accurate representation of peak timing. Predicting R0, the basic reproduction number, remains a major challenge with significant implications for government policy and strategy. In this study, we propose a tool for policy makers to show the effects of possible fluctuations in policy strategies on different R0 levels. Results show that epidemic peaks in the United States occur at varying dates, up to 50, 87, and 82 days from the beginning of the second, third, and fourth waves. Our findings suggest that inaccurate predictions and public health policies may result from underestimating fluctuations in infection or recovery rates. Therefore, incorporating fluctuations into SIR models should be considered when predicting epidemic peak times to inform appropriate public health responses.

Modeling the time-dependent transmission rate using gaussian pulses for analyzing the COVID-19 outbreaks in the world

In this work, an SEIR epidemic model with time-dependent transmission rate parameters for the multiple waves of COVID-19 infection was investigated. It is assumed that the transmission rate is determined by the superposition of the Gaussian pulses. The interaction of these dynamics is represented by recursive equations. Analysis of the overall dynamics of disease spread is determined by the effective reproduction number R_e(t) produced throughout the infection period. The study managed to show the evolution of the epidemic over time and provided important information about the occurrence of multiple waves of COVID-19 infection in the world and Indonesia.

Stochastic compartmental models of the COVID-19 pandemic must have temporally correlated uncertainties

Compartmental models are an important quantitative tool in epidemiology, enabling us to forecast the course of a communicable disease. However, the model parameters, such as the infectivity rate of the disease, are riddled with uncertainties, which has motivated the development and use of stochastic compartmental models. Here, we first show that a common stochastic model, which treats the uncertainties as white noise, is fundamentally flawed since it erroneously implies that greater parameter uncertainties will lead to the eradication of the disease. Then, we present a principled modelling of the uncertainties based on reasonable assumptions on the contacts of each individual. Using the central limit theorem and Doob’s theorem on Gaussian Markov processes, we prove that the correlated Ornstein–Uhlenbeck (OU) process is the appropriate tool for modelling uncertainties in the infectivity rate. We demonstrate our results using a compartmental model of the COVID-19 pandemic and the available US data from the Johns Hopkins University COVID-19 database. In particular, we show that the white noise stochastic model systematically underestimates the severity of the Omicron variant of COVID-19, whereas the OU model correctly forecasts the course of this variant. Moreover, using an SIS model of sexually transmitted disease, we derive an exact closed-form solution for the final distribution of infected individuals. This analytical result shows that the white noise model underestimates the severity of the pandemic because of unrealistic noise-induced transitions. Our results strongly support the need for temporal correlations in modelling of uncertainties in compartmental models of infectious disease.

Periodic epidemic outbursts explained by local saturation of clusters

Adding the notion of spatial locality to the susceptible-infected-recovered (or SIR) model, allows to capture local saturation of an epidemic. The resulting minimum model of an epidemic, consisting of five ordinary differential equations with constant model coefficients, reproduces slowly decaying periodic outbursts, as observed in the COVID-19 or Spanish flu epidemic. It is shown that if immunity decays, even slowly, the model yields a fully periodic dynamics.

Dynamics Analysis of a Class of Stochastic SEIR Models with Saturation Incidence Rate

In this article, a class of stochastic SEIR models with saturation incidence is studied. The model is a symmetric and compatible distribution family. This paper studies various properties of the system by constructing Lyapunov functions. First, the gradual properties of the systematic solution near the disease-free equilibrium of the deterministic model is studied, followed by the final behavior of the model, including stochastic persistence and final extinction. Finally, the existence conditions of the stationary distribution of the model are given, and then it is proved that it is traversed, and the corresponding conclusions are verified through numerical simulation.

How do the smart travel ban policy and intercity travel pattern affect COVID-19 trends? Lessons learned from Iran

COVID-19, as the most significant epidemic of the century, infected 467 million people and took the lives of more than 6 million individuals as of March 19, 2022. Due to the rapid transmission of the disease and the lack of definitive treatment, countries have employed nonpharmaceutical interventions. This study aimed to investigate the effectiveness of the smart travel ban policy, which has been implemented for non-commercial vehicles in the intercity highways of Iran since November 21, 2020. The other goal was to suggest efficient COVID-19 forecasting tools and to examine the association of intercity travel patterns and COVID-19 trends in Iran. To this end, weekly confirmed cases and deaths due to COVID-19 and the intercity traffic flow reported by loop detectors were aggregated at the country's level. The Box-Jenkins methodology was employed to evaluate the policy's effectiveness, using the interrupted time series analysis. The results indicated that the autoregressive integrated moving average with explanatory variable (ARIMAX) model outperformed the univariate ARIMA model in predicting the disease trends based on the MAPE criterion. The weekly intercity traffic and its lagged variables were entered as covariates in both models of the disease cases and deaths. The results indicated that the weekly intercity traffic increases the new weekly COVID-19 cases and deaths with a time lag of two and five weeks, respectively. Besides, the interrupted time series analysis indicated that the smart travel ban policy had decreased intercity travel by around 29%. Nonetheless, it had no significant direct effect on COVID-19 trends. This study suggests that the travel ban policy would not be efficient lonely unless it is coupled with active measures and adherence to health protocols by the people.

Modelling of spatial infection spread through heterogeneous population: from lattice to partial differential equation models

We present a simple model for the spread of an infection that incorporates spatial variability in population density. Starting from first-principle considerations, we explore how a novel partial differential equation with state-dependent diffusion can be obtained. This model exhibits higher infection rates in the areas of higher population density-a feature that we argue to be consistent with epidemiological observations. The model also exhibits an infection wave, the speed of which varies with population density. In addition, we demonstrate the possibility that an infection can 'jump' (i.e. tunnel) across areas of low population density towards areas of high population density. We briefly touch upon the data reported for coronavirus spread in the Canadian province of Nova Scotia as a case example with a number of qualitatively similar features as our model. Lastly, we propose a number of generalizations of the model towards future studies.

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.

Preventive control strategy on second wave of Covid-19 pandemic model incorporating lock-down effect

This study presents an optimal control strategy through a mathematical model of the Covid-19 outbreak without lock-down. The pandemic model analyses the lock-down effect without control strategy based on the current scenario of second wave data to control the rapid spread of the virus. The pandemic model has been discussed with respect to the basic reproduction number and stability analysis of disease-free and endemic equilibrium. A new optimal control problem with treatment is framed to minimize the vulnerable situation of the second wave. This system is applied to study the effects of vaccines and treatment controls. Numerical solutions and the graphical presentation of the results predict the fate of India’s second wave situation on account of the control strategy. Lastly, a comparative study with control and without control has been analysed for the exposed phase, infective phase, and recovery phase to understand the effectiveness of the controls. This model is used to estimate the total number of infected and active cases, deaths, and recoveries in order to control the disease using this system and studying the effects of vaccines and treatment controls.

Does Social Distancing Matter for Infectious Disease Propagation? An SEIR Model and Gompertz Law Based Cellular Automaton

In this paper, we present stochastic synchronous cellular automaton defined on a square lattice. The automaton rules are based on the SEIR (susceptible → exposed → infected → recovered) model with probabilistic parameters gathered from real-world data on human mortality and the characteristics of the SARS-CoV-2 disease. With computer simulations, we show the influence of the radius of the neighborhood on the number of infected and deceased agents in the artificial population. The increase in the radius of the neighborhood favors the spread of the pandemic. However, for a large range of interactions of exposed agents (who neither have symptoms of the disease nor have been diagnosed by appropriate tests), even isolation of infected agents cannot prevent successful disease propagation. This supports aggressive testing against disease as one of the useful strategies to prevent large peaks of infection in the spread of SARS-CoV-2-like diseases.

A multi-strain epidemic model for COVID-19 with infected and asymptomatic cases: application to French data

Many SARS-CoV-2 variants have appeared over the last months, and many more will continue to appear. Understanding the competition between these different variants could help make future predictions on the evolution of epidemics. In this study we use a mathematical model to investigate the impact of three different SARS-CoV-2 variants on the spread of COVID-19 across France, between January-May 2021 (before vaccination was extended to the full population). To this end, we use the data from Geodes (produced by Public Health France) and a particle swarm optimisation algorithm, to estimate the model parameters and further calculate a value for the basic reproduction number R₀. Sensitivity and uncertainty analysis is then used to better understand the impact of estimated parameter values on the number of infections leading to both symptomatic and asymptomatic individuals. The results confirmed that, as expected, the alpha, beta and gamma variants are more transmissible than the original viral strain. In addition, the sensitivity results showed that the beta/gamma variants could have lead to a larger number of infections in France (of both symptomatic and asymptomatic people).

A Time-Delayed Deterministic Model for the Spread of COVID-19 with Calibration on a Real Dataset

During the evolution of the COVID-19 pandemic, each country has adopted different control measures to contrast the epidemic’s diffusion. Restrictions to mobility, public transport, and social life in general have been actuated to contain the spread of the pandemic. In this paper, we consider the deterministic SIRD model with delays proposed by (Calleri et al., 2021), which is improved by adding the vaccinated compartment V (SIRDV model) and considering a time-dependent contact frequency. The three delays take into account the incubation time of the disease, the healing time, and the death time. The aim of this work is to study the effect of the vaccination campaigns in Great Britain (GBR) and Israel (ISR) during the pandemic period. The different restriction periods are included by fitting the contact frequency on real datasets as a piecewise constant function. As expected, the vaccination campaign reduces the amount of deaths and infected people. Furthermore, for the different levels of restriction policy, we find specific values of the contact frequency that can be used to predict the trend of the pandemic.

Heterogeneity of the COVID-19 Pandemic in the United States of America: A Geo-Epidemiological Perspective

The spread of the COVID-19 pandemic has shown great heterogeneity between regions of countries, e. g., in the United States of America (USA). With the growing of the worldwide COVID-19 pandemic, there is a need to better highlight the variability in the trajectory of this disease in different worldwide geographic areas. Indeed, the epidemic trends across areas can display completely different evolution at a given time. Geo-epidemiological analyses using data, that are publicly available, could be a major topic to help governments and public administrations to implement health policies. Geo-epidemiological analyses could provide a basis for the implementation of relevant public health policies. With the COVID-19 pandemic, geo-epidemiological analyses can be readily utilized by policy interventions and USA public health authorities to highlight geographic areas of particular concern and enhance the allocation of resources.

Effect of 2021 assembly election in India on COVID-19 transmission

India is one of the countries in the world which is badly affected by the COVID-19 second wave. Assembly election in four states and a union territory of India was taken place during March-May 2021 when the COVID-19 second wave was close to its peak and affected a huge number of people. We studied the impact of assembly election on the effective contact rate and the effective reproduction number of COVID-19 using different epidemiological models like SIR, SIRD, and SEIR. We also modeled the effective reproduction number for all election-bound states using different mathematical functions. We separately studied the case of all election-bound states and found all the states showed a distinct increase in the effective contact rate and the effective reproduction number during the election-bound time and just after that compared to pre-election time. States, where elections were conducted in single-phase, showed less increase in the effective contact rate and the reproduction number. The election commission imposed extra measures from the first week of April 2021 to restrict big campaign rallies, meetings, and different political activities. The effective contact rate and the reproduction number showed a trend to decrease for few states due to the imposition of the restrictions. We also compared the effective contact rate, and the effective reproduction number of all election-bound states and the rest of India and found all the parameters related to the spread of virus for election-bound states are distinctly high compared to the rest of India.

A spread model of COVID-19 with some strict anti-epidemic measures

In the absence of specific drugs and vaccines, the best way to control the spread of COVID-19 is to adopt and diligently implement effective and strict anti-epidemic measures. In this paper, a mathematical spread model is proposed based on strict epidemic prevention measures and the known spreading characteristics of COVID-19. The equilibria (disease-free equilibrium and endemic equilibrium) and the basic regenerative number of the model are analyzed. In particular, we prove the asymptotic stability of the equilibria, including locally and globally asymptotic stability. In order to validate the effectiveness of this model, it is used to simulate the spread of COVID-19 in Hubei Province of China for a period of time. The model parameters are estimated by the real data related to COVID-19 in Hubei. To further verify the model effectiveness, it is employed to simulate the spread of COVID-19 in Hunan Province of China. The mean relative error serves to measure the effect of fitting and simulations. Simulation results show that the model can accurately describe the spread dynamics of COVID-19. Sensitivity analysis of the parameters is also done to provide the basis for formulating prevention and control measures. According to the sensitivity analysis and corresponding simulations, it is found that the most effective non-pharmaceutical intervention measures for controlling COVID-19 are to reduce the contact rate of the population and increase the quarantine rate of infected individuals.

Comparing community mobility reduction between first and second COVID-19 waves

Background

In this paper, we conduct a mobility reduction rate comparison between the first and second COVID-19 waves in several localities from America and Europe using Google community mobility reports (CMR) data. Through multi-dimensional visualization, we are able to compare the reduction in mobility from the different lockdown periods for each locality selected, simultaneously considering multiple place categories provided in CMR. In addition, our analysis comprises a 56-day lockdown period for each locality and COVID-19 wave, which we analyze both as 56-day periods and as 14-day consecutive windows.

Methods

We use locality-wise calibrated CMR data, which we process through seasonal-trend decomposition by LOESS (STL) to isolate trend from seasonal and noise effects. We scale trend data to draw Pareto-compliant conclusions using radar charts. For each temporal granularity considered, data for a given place category is aggregated using the area under the curve (AUC) approach.

Results

In general, reduction rates observed during the first wave were much higher than during the second. Alarmingly, December holiday season mobility in some of the localities reached pre-pandemic levels for some of the place categories reported. Manaus was the only locality where second wave mobility was nearly as reduced as during the first wave, likely due to the P1 variant outbreak and oxygen supply crisis.

Delayed epidemic peak caused by infection and recovery rate fluctuations

Forecasting epidemic scenarios has been critical to many decision-makers in imposing various public health interventions. Despite progresses in determining the magnitude and timing of epidemics, epidemic peak time predictions for H1N1 and COVID-19 were inaccurate, with the peaks delayed with respect to predictions. Here, we show that infection and recovery rate fluctuations play a critical role in peak timing. Using a susceptible-infected-recovered model with daily fluctuations on control parameters, we show that infection counts follow a lognormal distribution at the beginning of an epidemic wave, similar to price distributions for financial assets. The epidemic peak time of the stochastic solution exhibits an inverse Gaussian probability distribution, fitting the spread of the epidemic peak times observed across Italian regions. We also show that, for a given basic reproduction number R₀, the deterministic model anticipates the peak with respect to the most probable and average peak time of the stochastic model. The epidemic peak time distribution allows one for a robust estimation of the epidemic evolution. Considering these results, we believe that the parameters' dynamical fluctuations are paramount to accurately predict the epidemic peak time and should be introduced in epidemiological models.

Continuous-time stochastic processes for the spread of COVID-19 disease simulated via a Monte Carlo approach and comparison with deterministic models

Two stochastic models are proposed to describe the evolution of the COVID-19 pandemic. In the first model the population is partitioned into four compartments: susceptible S, infected I, removed R and dead people D. In order to have a cross validation, a deterministic version of such a model is also devised which is represented by a system of ordinary differential equations with delays. In the second stochastic model two further compartments are added: the class A of asymptomatic individuals and the class L of isolated infected people. Effects such as social distancing measures are easily included and the consequences are analyzed. Numerical solutions are obtained with Monte Carlo simulations. Quantitative predictions are provided which can be useful for the evaluation of political measures, e.g. the obtained results suggest that strategies based on herd immunity are too risky. Finally, the models are calibrated on data referring to the second wave of infection in Italy.

The effect of population size for pathogen transmission on prediction of COVID-19 spread

Extreme public health interventions play a critical role in mitigating the local and global prevalence and pandemic potential. Here, we use population size for pathogen transmission to measure the intensity of public health interventions, which is a key characteristic variable for nowcasting and forecasting of COVID-19. By formulating a hidden Markov dynamic system and using nonlinear filtering theory, we have developed a stochastic epidemic dynamic model under public health interventions. The model parameters and states are estimated in time from internationally available public data by combining an unscented filter and an interacting multiple model filter. Moreover, we consider the computability of the population size and provide its selection criterion. With applications to COVID-19, we estimate the mean of the effective reproductive number of China and the rest of the globe except China (GEC) to be 2.4626 (95% CI: 2.4142-2.5111) and 3.0979 (95% CI: 3.0968-3.0990), respectively. The prediction results show the effectiveness of the stochastic epidemic dynamic model with nonlinear filtering. The hidden Markov dynamic system with nonlinear filtering can be used to make analysis, nowcasting and forecasting for other contagious diseases in the future since it helps to understand the mechanism of disease transmission and to estimate the population size for pathogen transmission and the number of hidden infections, which is a valid tool for decision-making by policy makers for epidemic control.

Is Curfew Effective in Limiting SARS-CoV-2 Progression? An Evaluation in France Based on Epidemiokinetic Analyses

BACKGROUND

Since late summer 2020, the French authorities implemented a curfew/lightened lockdown-alternating strategy instead of strict lockdown, to improve acceptability and limit socioeconomic consequences. However, data on curfew-related efficacy to control the epidemic are scarce.

OBJECTIVE

To investigate the effects on COVID-19 spread in France of curfew combined to local and/or nationwide restrictions from late summer 2020 to mid-February 2021.

DESIGN

We conducted a comparative evaluation using a susceptible-infected-recovered (SIR)-based model completed with epidemiokinetic tools.

MAIN MEASURES

We analyzed the time-course of epidemic progression rate under curfew in French Guyana and five metropolitan regions where additional restrictions were implemented at different times. Using linear regressions of the decay/increase rates in daily contaminations, we calculated the epidemic regression half-lives (t_1/2β) for each identified period.

KEY RESULTS

In French Guyana, two decay periods with rapid regression (t_1/2β of ~10 days) were observed under curfew, with slowing (t_1/2β of ~43 days) when curfew was lightened. During the 2-week pre-lockdown curfew (2020/10/17-2020/11/02) in Provence-Alpes-Côte-d'Azur, Auvergne-Rhône-Alpes, and Ile-de-France, the epidemic progression was unchanged. During the post-lockdown curfew (2020/12/15-2020/02/14), the epidemic slowly regressed in Grand-Est (t_1/2β of ~37 days), whereas its progression rate plateaued in Auvergne-Rhône-Alpes and increased immediately in Provence-Alpes-Côte-d'Azur, Ile-de-France, and Nouvelle-Aquitaine, whatever the curfew starting time was (06:00 or 08:00 pm). Interestingly, a delayed slow decay (17 days < t_1/2β < 64 days) occurred under curfew in all regions except Ile-de-France.

CONCLUSIONS

Curfew allowed the temporary control of SARS-CoV-2 epidemic, however variably in the French regions, without preventing lockdown necessity. To accelerate the epidemic regression such as observed in French Guyana, curfew should be implemented timely with additional restrictions.

Determination of critical decision points for COVID-19 measures in Japan

Coronavirus disease 2019 (COVID-19) has spread throughout the world. The prediction of the number of cases has become essential to governments' ability to define policies and take countermeasures in advance. The numbers of cases have been estimated using compartment models of infectious diseases such as the susceptible-infected-removed (SIR) model and its derived models. However, the required use of hypothetical future values for parameters, such as the effective reproduction number or infection rate, increases the uncertainty of the prediction results. Here, we describe our model for forecasting future COVID-19 cases based on observed data by considering the time delay (tdelay). We used machine learning to estimate the future infection rate based on real-time mobility, temperature, and relative humidity. We then used this calculation with the susceptible-exposed-infectious-removed (SEIR) model to forecast future cases with less uncertainty. The results suggest that changes in mobility affect observed infection rates with 5-10 days of time delay. This window should be accounted for in the decision-making phase especially during periods with predicted infection surges. Our prediction model helps governments and medical institutions to take targeted early countermeasures at critical decision points regarding mobility to avoid significant levels of infection rise.

Assessing the impact of data-driven limitations on tracing and forecasting the outbreak dynamics of COVID-19

The availability of the epidemiological data strongly affects the reliability of several mathematical models in tracing and forecasting COVID-19 pandemic, hampering a fair assessment of their relative performance. The marked difference between the lethality of the virus when comparing the first and second waves is an evident sign of the poor reliability of the data, also related to the variability over time in the number of performed swabs. During the early epidemic stage, swabs were made only to patients with severe symptoms taken to hospital or intensive care unit. Thus, asymptomatic people, not seeking medical assistance, remained undetected. Conversely, during the second wave of infection, total infectives included also a percentage of detected asymptomatic infectives, being tested due to close contacts with swab positives and thus registered by the health system. Here, we compared the outcomes of two SIR-type models (the standard SIR model and the A-SIR model that explicitly considers asymptomatic infectives) in reproducing the COVID-19 epidemic dynamic in Italy, Spain, Germany, and France during the first two infection waves, simulated separately. We found that the A-SIR model overcame the SIR model in simulating the first wave, whereas these discrepancies are reduced in simulating the second wave, when the accuracy of the epidemiological data is considerably higher. These results indicate that increasing the complexity of the model is useless and unnecessarily wasteful if not supported by an increased quality of the available data.

Learning from the past: Taiwan's responses to COVID-19 versus SARS

OBJECTIVES

To evaluate the prevalence of infection prevention behaviors in Taiwan-wearing facemasks and alcohol-based hand hygiene (AHH)-and compare their practice rates during SARS and COVID-19.

METHODS

We surveyed 2328 Taiwanese from July 29 to August 6, 2020, assessing demographics, information sources, and preventive behaviors during the 2003 SARS outbreaks, 2009 pandemic influenza H1N1, COVID-19, and with post-survey intentions. Characteristics associated with the practice of preventive behaviors in 2020 were identified through logistic regression.

RESULTS

Preventive behaviors were conscientiously practiced by 70.2% of participants. Compared with 2003 SARS/2009 H1N1, the percentages of facemask use (66.6% vs 99.2% [indoors], P < 0.001) and on-person AHH (44.2% vs 65.4% [hand sanitizers], P < 0.001) significantly increasedduring 2020 COVID-19. Highest adherence to preventive behaviors in 2020 was among females (adjusted odds ratio [aOR], 1.72), those receiving government COVID-19 information (aOR, 1.52), participants recruited from primary-care clinics (aOR, 1.43), and those who practiced AHH during 2003 SARS/2009 H1N1 (aOR, 1.37).

CONCLUSIONS

Government leadership, healthcare providers risk communication, and public cooperation rapidly mitigated the spread of COVID-19 in Taiwan even before vaccination. Future global efforts must implement such population-based preventive behaviors at a level above the viral-transmission-threshold, particularly in areas with fast-spreading SARS-CoV-2 variants.

Convolutional neural networks and temporal CNNs for COVID-19 forecasting in France

This paper focus on multiple CNN-based (Convolutional Neural Network) models for COVID-19 forecast developed by our research team during the first French lockdown. In an effort to understand and predict both the epidemic evolution and the impacts of this disease, we conceived models for multiple indicators: daily or cumulative confirmed cases, hospitalizations, hospitalizations with artificial ventilation, recoveries, and deaths. In spite of the limited data available when the lockdown was declared, we achieved good short-term performances at the national level with a classical CNN for hospitalizations, leading to its integration into a hospitalizations surveillance tool after the lockdown ended. Also, A Temporal Convolutional Network with quantile regression successfully predicted multiple COVID-19 indicators at the national level by using data available at different scales (worldwide, national, regional). The accuracy of the regional predictions was improved by using a hierarchical pre-training scheme, and an efficient parallel implementation allows for quick training of multiple regional models. The resulting set of models represent a powerful tool for short-term COVID-19 forecasting at different geographical scales, complementing the toolboxes used by health organizations in France.

Interrupting vaccination policies can greatly spread SARS-CoV-2 and enhance mortality from COVID-19 disease: The AstraZeneca case for France and Italy

Several European countries have suspended the inoculation of the AstraZeneca vaccine out of suspicion that it causes deep vein thrombosis. In this letter, we report some Fermi estimates performed using a stochastic model aimed at making a risk-benefit analysis of the interruption of the delivery of the AstraZeneca vaccine in France and Italy. Our results clearly show that excess deaths due to the interruption of the vaccination campaign injections largely overrun those due to thrombosis even in worst case scenarios of frequency and gravity of the vaccine side effects.

Suppressing the impact of the COVID-19 pandemic using controlled testing and isolation

The Corona virus disease has significantly affected lives of people around the world. Existing quarantine policies led to large-scale lock-downs because of the slow tracking of the infection paths, and indeed we see new waves of the disease. This can be solved by contact tracing combined with efficient testing policies. Since the number of daily tests is limited, it is crucial to exploit them efficiently to improve the outcome of contact tracing (technological or human-based epidemiological investigations). We develop a controlled testing framework to achieve this goal. The key is to test individuals with high probability of being infected to identify them before symptoms appear. These probabilities are updated based on contact tracing and test results. We demonstrate that the proposed method could reduce the quarantine and morbidity rates compared to existing methods by up to a 50%. The results clearly demonstrate the necessity of accelerating the epidemiological investigations by using technological contact tracing. Furthermore, proper use of the testing capacity using the proposed controlled testing methodology leads to significantly improved results under both small and large testing capacities. We also show that for small new outbreaks controlled testing can prevent the large spread of new waves. Author contributions statement: The authors contributed equally to this work, including conceptualization, analysis, methodology, software, and drafting the work.

A new approximation of mean-time trends for the second wave of COVID-19 pandemic evolving in key six countries

We have presented in the current analytic research the generating formulae and results of direct mathematical modelling of non-classical trends for COVID-19's evolution in world which, nevertheless, can be divided into two types: (1) the general trends for European countries such as Germany presented by the curve of modified sigmoid-type with up-inclination of the upper limit of saturation (at the end of first wave of pandemic) as well as for other cases of key countries that suffered from pandemic such as USA, India, Brazil, Russia (we conclude that the same type of coronavirus pandemic is valid for most of the countries in world with similar scenarios of the same type for general trends); (2) non-classical general trends for Middle East countries (such as Iran), with the appropriate bulge on graphical plots at the beginning of first wave of pandemic. We expect that the second wave of pandemic will pass its peak at the end of December 2020 for various countries. Moreover, the second wave of pandemic will have come to end at first decade of January 2021 in Germany and Iran (but at the end of January 2021 in India as well), so we should restrict ourselves in modelling the first and second waves of pandemic within this time period for these countries. Thus, the model of first approximation is considered here which allows to understand the mean-time trends of COVID-19 evolution for the first + second waves of pandemic for USA, Brazil and Russia, or predict the approximated time period of the upcoming third wave of pandemic in cases of India, Germany and Iran.

COVID-19: A Boon or a Bane for Creativity?

In many countries, the COVID-19 pandemic led to a period of lockdown that impacted individuals' lifestyles, in both professional and personal spheres. New problems and challenges arose, as well as opportunities. Numerous studies have examined the negative effects of lockdown measures, but few have attempted to shine light on the potential positive effects that may come out of these measures. We focused on one particular positive outcome that might have emerged from lockdown: creativity. To this end, this paper compared self-reported professional creativity (Pro-C) and everyday creativity (little-c) before and during lockdown, using a questionnaire-based study conducted on a French sample (N = 1266). We expected participants to be more creative during than prior to lockdown, in both professional and everyday spheres. Regarding Pro-C, we did not see any significant differences between the two comparison points, before and during lockdown. Regarding everyday creativity, we observed a significant increase during lockdown. Furthermore, our results suggest that participants with a lower baseline creativity (before lockdown) benefited more from the situation than those with a higher initial baseline creativity. Our results provide new insights on the impact of lockdown and its positive outcomes. These measures may have inarguably negative consequences on the physical and mental health of many, but their positive impact exists as well.

Towards Providing Effective Data-Driven Responses to Predict the Covid-19 in São Paulo and Brazil

São Paulo is the most populous state in Brazil, home to around 22% of the country's population. The total number of Covid-19-infected people in São Paulo has reached more than 1 million, while its total death toll stands at 25% of all the country's fatalities. Joining the Brazilian academia efforts in the fight against Covid-19, in this paper we describe a unified framework for monitoring and forecasting the Covid-19 progress in the state of São Paulo. More specifically, a freely available, online platform to collect and exploit Covid-19 time-series data is presented, supporting decision-makers while still allowing the general public to interact with data from different regions of the state. Moreover, a novel forecasting data-driven method has also been proposed, by combining the so-called Susceptible-Infectious-Recovered-Deceased model with machine learning strategies to better fit the mathematical model's coefficients for predicting Infections, Recoveries, Deaths, and Viral Reproduction Numbers. We show that the obtained predictor is capable of dealing with badly conditioned data samples while still delivering accurate 10-day predictions. Our integrated computational system can be used for guiding government actions mainly in two basic aspects: real-time data assessment and dynamic predictions of Covid-19 curves for different regions of the state. We extend our analysis and investigation to inspect the virus spreading in Brazil in its regions. Finally, experiments involving the Covid-19 advance in other countries are also given.

Standard and Anomalous Waves of COVID-19: A Multiple-Wave Growth Model for Epidemics

We apply a generalized logistic growth model, with time-dependent parameters, to describe the fatality curves of the COVID-19 disease for several countries that exhibit multiple waves of infections. In the case of two waves only, the model parameters vary as a function of time according to a logistic function, whose two extreme values, i.e., for early and late times, characterize the first and second waves, respectively. For the multiple-wave model, the time-dependency of the parameters is likewise described by a multi-step logistic function with N intermediate plateaus, representing the N waves of the epidemic. We show that the theoretical curves are in excellent agreement with the empirical data for all countries considered here, namely: Brazil, Canada, Germany, Iran, Italy, Japan, Mexico, South Africa, Sweden, and the USA. The model also allows for predictions about the time of occurrence and severity of the subsequent waves. It is shown furthermore that the subsequent waves of COVID-19 can be generically classified into two main types, namely, standard and anomalous waves, according as to whether a given wave starts well after or well before the preceding one has subsided, respectively.

Mathematical modelling of the second wave of COVID-19 infections using deterministic and stochastic SIDR models

Recently, various countries from across the globe have been facing the second wave of COVID-19 infections. In order to understand the dynamics of the spread of the disease, much effort has been made in terms of mathematical modeling. In this scenario, compartmental models are widely used to simulate epidemics under various conditions. In general, there are uncertainties associated with the reported data, which must be considered when estimating the parameters of the model. In this work, we propose an effective methodology for estimating parameters of compartmental models in multiple wave scenarios by means of a dynamic data segmentation approach. This robust technique allows the description of the dynamics of the disease without arbitrary choices for the end of the first wave and the start of the second. Furthermore, we adopt a time-dependent function to describe the probability of transmission by contact for each wave. We also assess the uncertainties of the parameters and their influence on the simulations using a stochastic strategy. In order to obtain realistic results in terms of the basic reproduction number, a constraint is incorporated into the problem. We adopt data from Germany and Italy, two of the first countries to experience the second wave of infections. Using the proposed methodology, the end of the first wave (and also the start of the second wave) occurred on 166 and 187 days from the beginning of the epidemic, for Germany and Italy, respectively. The estimated effective reproduction number for the first wave is close to that obtained by other approaches, for both countries. The results demonstrate that the proposed methodology is able to find good estimates for all parameters. In relation to uncertainties, we show that slight variations in the design variables can give rise to significant changes in the value of the effective reproduction number. The results provide information on the characteristics of the epidemic for each country, as well as elements for decision-making in the economic and governmental spheres.

Generalized Richards model for predicting COVID-19 dynamics in Saudi Arabia based on particle swarm optimization Algorithm

COVID-19 pandemic is spreading around the world becoming thus a serious concern for health, economic and social systems worldwide. In such situation, predicting as accurately as possible the future dynamics of the virus is a challenging problem for scientists and decision-makers. In this paper, four phenomenological epidemic models as well as Suspected-Infected-Recovered (SIR) model are investigated for predicting the cumulative number of infected cases in Saudi Arabia in addition to the probable end-date of the outbreak. The prediction problem is formulated as an optimization framework and solved using a Particle Swarm Optimization (PSO) algorithm. The Generalized Richards Model (GRM) has been found to be the best one in achieving two objectives: first, fitting the collected data (covering 223 days between March 2^nd and October 10, 2020) with the lowest mean absolute percentage error (MAPE = 3.2889%), the highest coefficient of determination (R² = 0.9953) and the lowest root mean squared error (RMSE = 8827); and second, predicting a probable end date found to be around the end of December 2020 with a projected number of 378,299 at the end of the outbreak. The obtained results may help the decision-makers to take suitable decisions related to the pandemic mitigation and containment and provide clear understanding of the virus dynamics in Saudi Arabia.

Analytical solution of SEIR model describing the free spread of the COVID-19 pandemic

We analytically study the SEIR (Susceptible Exposed Infectious Removed) epidemic model. The aim is to provide simple analytical expressions for the peak and asymptotic values and their characteristic times of the populations affected by the COVID-19 pandemic.