Mathematical modeling for estimating influenza vaccine efficacy: A case study of the Valencian Community, Spain

Vaccine efficacy and its quantification is a crucial concept for the proper design of public health vaccination policies. In this work we proposed a mathematical model to estimate the efficacy of the influenza vaccine in a real-word scenario. In particular, our model is a SEIR-type epidemiological model, which distinguishes vaccinated and unvaccinated populations. Mathematically, its dynamics is governed by a nonlinear system of ordinary differential equations, where the non-linearity arises from the effective contacts between susceptible and infected individuals. Two key aspects of this study is that we use a vaccine distribution over time that is based on real data specific to the elderly people in the Valencian Community and the calibration process takes into account that over one influenza season a specific proportion of the population becomes infected with influenza. To consider the effectiveness of the vaccine, the model incorporates a parameter, the vaccine attenuation factor, which is related with the vaccine efficacy against the influenza virus. With this framework, in order to calibrate the model parameters and to obtain an influenza vaccine efficacy estimation, we considered the 2016-2017 influenza season in the Valencian Community, Spain, using the influenza reported cases of vaccinated and unvaccinated. In order to ensure the model identifiability, we choose to deterministically calibrate the parameters for different scenarios and we find the one with the minimum error in order to determine the vaccine efficacy. The calibration results suggest that the influenza vaccine developed for 2016-2017 influenza season has an efficacy of approximately 76.7%, and that the risk of becoming infected is five times higher for an unvaccinated individual in comparison with a vaccinated one. This estimation partially agrees with some previous studies related to the influenza vaccine. This study presents a new integrated mathematical approach to study the influenza vaccine efficacy and gives further insight into this important public health topic.

On a two-strain epidemic mathematical model with vaccination

In this paper, we study mathematically a two strains epidemic model taking into account non-monotonic incidence rates and vaccination strategy. The model contains seven ordinary differential equations that illustrate the interaction between the susceptible, the vaccinated, the exposed, the infected and the removed individuals. The model has four equilibrium points, namely, disease free equilibrium, endemic equilibrium with respect to the first strain, endemic equilibrium with respect to the second strain and the endemic equilibrium with respect to both strains. The global stability of the equilibria has been demonstrated using some suitable Lyapunov functions. The basic reproduction number is found depending on the first strain reproduction number R 0 1 and the second reproduction number R 0 2 . We have shown that the disease dies out when the basic reproduction number is less than unity. It was remarked that the global stability of the endemic equilibria depends, on the strain basic reproduction number and on the strain inhibitory effect reproduction number. We have also observed that the strain with high basic reproduction number will dominate the other strain. Finally, the numerical simulations are presented in the last part of this work to support our theoretical results. We notice that our suggested model has some limitations and does not predicting the long-term dynamics for some reproduction numbers cases.

Bridging the gap - estimation of 2022/2023 SARS-CoV-2 healthcare burden in Germany based on multidimensional data from a rapid epidemic panel

OBJECTIVES

Throughout the SARS-CoV-2 pandemic, Germany like other countries lacked adaptive population-based panels to monitor the spread of epidemic diseases.

METHODS

To fill a gap in population-based estimates needed for winter 2022/23 we resampled in the German SARS-CoV-2 cohort study MuSPAD in mid-2022, including characterization of systemic cellular and humoral immune responses by interferon-γ-release assay (IGRA) and CLIA/IVN assay. We were able to confirm categorization of our study population into four groups with differing protection levels against severe COVID-19 courses based on literature synthesis. Using these estimates, we assessed potential healthcare burden for winter 2022/23 in different scenarios with varying assumptions on transmissibility, pathogenicity, new variants, and vaccine booster campaigns in ordinary differential equation models.

RESULTS

We included 9921 participants from eight German regions. While 85% of individuals were located in one of the two highest protection categories, hospitalization estimates from scenario modeling were highly dependent on viral variant characteristics ranging from 30-300% compared to the 02/2021 peak. Our results were openly communicated and published to an epidemic panel network and a newly established modeling network.

CONCLUSIONS

We demonstrate feasibility of a rapid epidemic panel to provide complex immune protection levels for inclusion in dynamic disease burden modeling scenarios.

Bayesian modeling of dynamic behavioral change during an epidemic

For many infectious disease outbreaks, the at-risk population changes their behavior in response to the outbreak severity, causing the transmission dynamics to change in real-time. Behavioral change is often ignored in epidemic modeling efforts, making these models less useful than they could be. We address this by introducing a novel class of data-driven epidemic models which characterize and accurately estimate behavioral change. Our proposed model allows time-varying transmission to be captured by the level of "alarm" in the population, with alarm specified as a function of the past epidemic trajectory. We investigate the estimability of the population alarm across a wide range of scenarios, applying both parametric functions and non-parametric functions using splines and Gaussian processes. The model is set in the data-augmented Bayesian framework to allow estimation on partially observed epidemic data. The benefit and utility of the proposed approach is illustrated through applications to data from real epidemics.

The impact of non-pharmaceutical interventions on the first COVID-19 epidemic wave in South Africa

OBJECTIVE

In this study, we investigated the impact of COVID-19 NPIs in South Africa to understand their effectiveness in the reduction of transmission of COVID-19 in the South African population. This study also investigated the COVID-19 testing, reporting, hospitalised cases, excess deaths and COVID-19 modelling in the first wave of the COVID-19 epidemic in South Africa.

METHODS

A semi-reactive stochastic COVID-19 model, the ARI COVID-19 SEIR model, was used to investigate the impact of NPIs in South Africa to understand their effectiveness in the reduction of COVID-19 transmission in the South African population. COVID-19 testing, reporting, hospitalised cases and excess deaths in the first COVID-19 epidemic wave in South Africa were investigated using regressional analysis and descriptive statistics.

FINDINGS

The general trend in population movement in South African locations shows that the COVID-19 NPIs (National Lockdown Alert Levels 5,4,3,2) were approximately 30% more effective in reducing population movement concerning each increase by 1 Alert Level. The translated reduction in the effective SARS-CoV-2 daily contact number (β) was 6.12% to 36.1% concerning increasing Alert Levels. Due to the implemented NPIs, the effective SARS-CoV-2 daily contact number in the first COVID-19 epidemic wave in South Africa was reduced by 58.1-71.1% while the peak was delayed by 84 days. The estimated COVID-19 reproductive number was between 1.98 to 0.40. During South Africa's first COVID-19 epidemic wave, the mean COVID-19 admission status in South African hospitals was 58.5%, 95% CI [58.1-59.0] in the general ward, 13.4%, 95% CI [13.1-13.7] in the intensive care unit, 13.3%, 95% CI [12.6-14.0] on oxygen, 6.37%, 95% CI [6.23-6.51] in high care, 6.29%, 95% CI [6.02-6.55] on ventilator and 2.13%, 95% CI [1.87-2.43] in isolation ward respectively. The estimated mean South African COVID-19 patient discharge rate was 11.9 days per patient. While the estimated mean of the South African COVID-19 patient case fatality rate (CFR) in hospital and outside the hospital was 2.06%, 95% CI [1.86-2.25] (deaths per admitted patients) and 2.30%, 95% CI [1.12-3.83](deaths per severe and critical cases) respectively. The relatively high coefficient of variance in COVID-19 model outputs observed in this study shows the uncertainty in the accuracy of the reviewed COVID-19 models in predicting the severity of COVID-19. However, the reviewed COVID-19 models were accurate in predicting the progression of the first COVID-19 epidemic wave in South Africa.

CONCLUSION

The results from this study show that the COVID-19 NPI policies implemented by the Government of South Africa played a significant role in the reduction of COVID-19 active, hospitalised cases and deaths in South Africa's first COVID-19 epidemic wave. The results also show the use of COVID-19 modelling to understand the COVID-19 pandemic and the impact of regressor variables in an epidemic.

Anchoring the mean generation time in the SEIR to mitigate biases in ℜ0 estimates due to uncertainty in the distribution of the epidemiological delays

The basic reproduction number, ℜ 0 , is of paramount importance in the study of infectious disease dynamics. Primarily, ℜ 0 serves as an indicator of the transmission potential of an emerging infectious disease and the effort required to control the invading pathogen. However, its estimates from compartmental models are strongly conditioned by assumptions in the model structure, such as the distributions of the latent and infectious periods (epidemiological delays). To further complicate matters, models with dissimilar delay structures produce equivalent incidence dynamics. Following a simulation study, we reveal that the nature of such equivalency stems from a linear relationship between ℜ 0 and the mean generation time, along with adjustments to other parameters in the model. Leveraging this knowledge, we propose and successfully test an alternative parametrization of the SEIR model that produces accurate ℜ 0 estimates regardless of the distribution of the epidemiological delays, at the expense of biases in other quantities deemed of lesser importance. We further explore this approach's robustness by testing various transmissibility levels, generation times and data fidelity (overdispersion). Finally, we apply the proposed approach to data from the 1918 influenza pandemic. We anticipate that this work will mitigate biases in estimating ℜ 0 .

Quantifying the spatial spillover effects of non-pharmaceutical interventions on pandemic risk

BACKGROUND

Non-pharmaceutical interventions (NPIs) implemented in one place can affect neighboring regions by influencing people's behavior. However, existing epidemic models for NPIs evaluation rarely consider such spatial spillover effects, which may lead to a biased assessment of policy effects.

METHODS

Using the US state-level mobility and policy data from January 6 to August 2, 2020, we develop a quantitative framework that includes both a panel spatial econometric model and an S-SEIR (Spillover-Susceptible-Exposed-Infected-Recovered) model to quantify the spatial spillover effects of NPIs on human mobility and COVID-19 transmission.

RESULTS

The spatial spillover effects of NPIs explain [Formula: see text] [[Formula: see text] credible interval: 52.8-[Formula: see text]] of national cumulative confirmed cases, suggesting that the presence of the spillover effect significantly enhances the NPI influence. Simulations based on the S-SEIR model further show that increasing interventions in only a few states with larger intrastate human mobility intensity significantly reduce the cases nationwide. These region-based interventions also can carry over to interstate lockdowns.

CONCLUSIONS

Our study provides a framework for evaluating and comparing the effectiveness of different intervention strategies conditional on NPI spillovers, and calls for collaboration from different regions.

Multi-Criteria Performance Analysis Based on Physics of Decision - Application to COVID-19 and Future Pandemics

The purpose of this study is to present a novel perspective on decision support based on the conventional SEIR pandemic model paradigm considering the risks and opportunities as physical forces deviating the expected performance trajectory of a system. The impact of a pandemic is measured by the deviation of the social system's performance trajectory within the geometrical framework of its Key Performance Indicators (KPIs). According to the overall premise of utilizing Ordinary Differential Equations to simulate epidemics, the deviations are connected to several alternative interventions. The model is essentially built on two sets of parameters: (i) social system parameters and (ii) pandemic parameters. The ultimate objective is to propose a multi-criteria performance framework to control pandemics that includes a combination of timely measures. On the one hand, the current study optimizes prospective strategies to manage the potential future pandemic, while on the other hand, it explores the COVID-19 epidemic in the state of Georgia (USA).

Using compartmental models and Particle Swarm Optimization to assess Dengue basic reproduction number R 0 for the Republic of Panama in the 1999-2022 period

Nowadays, the ability to make data-driven decisions in public health is of utmost importance. To achieve this, it is necessary for modelers to comprehend the impact of models on the future state of healthcare systems. Compartmental models are a valuable tool for making informed epidemiological decisions, and the proper parameterization of these models is crucial for analyzing epidemiological events. This work evaluated the use of compartmental models in conjunction with Particle Swarm Optimization (PSO) to determine optimal solutions and understand the dynamics of Dengue epidemics. The focus was on calculating and evaluating the rate of case reproduction, R 0 , for the Republic of Panama. Three compartmental models were compared: Susceptible-Infected-Recovered (SIR), Susceptible-Exposed-Infected-Recovered (SEIR), and Susceptible-Infected-Recovered Human-Susceptible-Infected Vector (SIR Human-SI Vector, SIR-SI). The models were informed by demographic data and Dengue incidence in the Republic of Panama between 1999 and 2022, and the susceptible population was analyzed. The SIR, SEIR, and SIR-SI models successfully provided R 0 estimates ranging from 1.09 to 1.74. This study provides, to the best of our understanding, the first calculation of R 0 for Dengue outbreaks in the Republic of Panama.

Incorporating infectious duration-dependent transmission into Bayesian epidemic models

Compartmental models are commonly used to describe the spread of infectious diseases by estimating the probabilities of transitions between important disease states. A significant challenge in fitting Bayesian compartmental models lies in the need to estimate the duration of the infectious period, based on limited data providing only symptom onset date or another proxy for the start of infectiousness. Commonly, the exponential distribution is used to describe the infectious duration, an overly simplistic approach, which is not biologically plausible. More flexible distributions can be used, but parameter identifiability and computational cost can worsen for moderately sized or large epidemics. In this article, we present a novel approach, which considers a curve of transmissibility over a fixed infectious duration. The incorporation of infectious duration-dependent (IDD) transmissibility, which decays to zero during the infectious period, is biologically reasonable for many viral infections and fixing the length of the infectious period eases computational complexity in model fitting. Through simulation, we evaluate different functional forms of IDD transmissibility curves and show that the proposed approach offers improved estimation of the time-varying reproductive number. We illustrate the benefit of our approach through a new analysis of the 1995 outbreak of Ebola Virus Disease in the Democratic Republic of the Congo.

Monkeypox outbreaks in the context of the COVID-19 pandemic: Network and clustering analyses of global risks and modified SEIR prediction of epidemic trends

Background

Ninety-eight percent of documented cases of the zoonotic disease human monkeypox (MPX) were reported after 2001, with especially dramatic global spread in 2022. This longitudinal study aimed to assess spatiotemporal risk factors of MPX infection and predict global epidemiological trends.

Method

Twenty-one potential risk factors were evaluated by correlation-based network analysis and multivariate regression. Country-level risk was assessed using a modified Susceptible-Exposed-Infectious-Removed (SEIR) model and a risk-factor-driven k-means clustering analysis.

Results

Between historical cases and the 2022 outbreak, MPX infection risk factors changed from relatively simple [human immunodeficiency virus (HIV) infection and population density] to multiple [human mobility, population of men who have sex with men, coronavirus disease 2019 (COVID-19) infection, and socioeconomic factors], with human mobility in the context of COVID-19 being especially key. The 141 included countries classified into three risk clusters: 24 high-risk countries mainly in West Europe and Northern America, 70 medium-risk countries mainly in Latin America and Asia, and 47 low-risk countries mainly in Africa and South Asia. The modified SEIR model predicted declining transmission rates, with basic reproduction numbers ranging 1.61-7.84 in the early stage and 0.70-4.13 in the current stage. The estimated cumulative cases in Northern and Latin America may overtake the number in Europe in autumn 2022.

Conclusions

In the current outbreak, risk factors for MPX infection have changed and expanded. Forecasts of epidemiological trends from our modified SEIR models suggest that Northern America and Latin America are at greater risk of MPX infection in the future.

[Quantitative evaluation of a SEIR model for forecasting COVID-19 cases]

INTRODUCTION

Epidemiological models have been widely used during the COVID-19 pandemic, although performance evaluation has been limited. The objective of this work was to thoroughly evaluate a SEIR model used for the short-term (1 to 3 weeks) prediction of cases, quantifying its actual past performance, and its potential performance by optimizing the model parameters.

METHODS

Daily case forecasts were obtained for the first wave of cases (July 31, 2020 to March 11, 2021) in the district of General Pueyrredón (Argentina), quantifying the model performance in terms of uncertainty, inaccuracy and imprecision. The evaluation was carried out with the original parameters of the model (used in the forecasts that were published), and also varying different parameters in order to identify optimal values.

RESULTS

The analysis of the model performance showed that alternative values of some parameters, and the correction of the input values using a "moving average" filter to eliminate the weekly variations in the case reports, would have yielded better results. The model with the optimized parameters was able to reduce the uncertainty from almost 40% to less than 15%, with similar values of inaccuracy, and with slightly greater imprecision.

DISCUSSION

Simple epidemiological models, without large requirements for their implementation, can be very useful for making quick decisions in small cities or cities with limited resources, as long as the importance of their evaluation is taken into account and their scope and limitations are considered.

Modeling and Global Sensitivity Analysis of Strategies to Mitigate Covid-19 Transmission on a Structured College Campus

In response to the COVID-19 pandemic, many higher educational institutions moved their courses on-line in hopes of slowing disease spread. The advent of multiple highly-effective vaccines offers the promise of a return to "normal" in-person operations, but it is not clear if-or for how long-campuses should employ non-pharmaceutical interventions such as requiring masks or capping the size of in-person courses. In this study, we develop and fine-tune a model of COVID-19 spread to UC Merced's student and faculty population. We perform a global sensitivity analysis to consider how both pharmaceutical and non-pharmaceutical interventions impact disease spread. Our work reveals that vaccines alone may not be sufficient to eradicate disease dynamics and that significant contact with an infectious surrounding community will maintain infections on-campus. Our work provides a foundation for higher-education planning allowing campuses to balance the benefits of in-person instruction with the ability to quarantine/isolate infectious individuals.

SEIR Model to address the impact of face masks amid COVID-19 pandemic

Early in the pandemic of coronavirus disease 2019 (COVID-19), face masks were used extensively by the general public in several Asian countries. The lower transmission rate of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in Asian countries compared with Western countries suggested that the wider community use of face masks has the potential to decrease transmission of SARS-CoV-2. A risk assessment model named Susceptible, Exposed, Infectious, Recovered (SEIR) model is used to quantitatively evaluate the potential impact of community face masks on SARS-CoV-2 reproduction number (R₀ ) and peak number of infectious persons. For a simulated population of one million, the model showed a reduction in R₀ of 49% and 50% when 60% and 80% of the population wore masks, respectively. Moreover, we present a modified model that considers the effect of mask-wearing after community vaccination. Interestingly mask-wearing still provided a considerable benefit in lowering the number of infectious individuals. The results of this research are expected to help public health officials in making prompt decisions involving resource allocation and crafting legislation.

Suit the Remedy to the Case-The Effectiveness of COVID-19 Nonpharmaceutical Prevention and Control Policies Based on Individual Going-Out Behavior

Nonpharmaceutical policies for epidemic prevention and control have been extensively used since the outbreak of COVID-19. Policies ultimately work by limiting individual behavior. The aim of this paper is to evaluate the effectiveness of policies by combining macro nonpharmaceutical policies with micro-individual going-out behavior. For different going out scenarios triggered by individual physiological safety needs, friendship needs, and family needs, this paper categorizes policies with significant differences in intensity, parameterizes the key contents of the policies, and simulates and analyzes the effectiveness of the policies in different going-out scenarios with simulation methods. The empirical results show that enhancing policy intensity can effectively improve policy effectiveness. Among different types of policies, restricting the times of going out is more effective. Further, the effect of controlling going out based on physiological safety needs is better than other needs. We also evaluate the policy effectiveness of 26 global countries or regions. The results show that the policy effectiveness varies among 26 countries or regions. The quantifiable reference provided by this study facilitates decision makers to establish policy and practices for epidemic prevention and control.

Indirect Virus Transmission via Fomites Can Counteract Lock-Down Effectiveness

The spread of severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) has raised major health policy questions. Direct transmission via respiratory droplets seems to be the dominant route of its transmission. However, indirect transmission via shared contact of contaminated objects may also occur. The contribution of each transmission route to epidemic spread might change during lock-down scenarios. Here, we simulate viral spread of an abstract epidemic considering both routes of transmission by use of a stochastic, agent-based SEIR model. We show that efficient contact tracing (CT) at a high level of incidence can stabilize daily cases independently of the transmission route long before effects of herd immunity become relevant. CT efficacy depends on the fraction of cases that do not show symptoms. Combining CT with lock-down scenarios that reduce agent mobility lowers the incidence for exclusive direct transmission scenarios and can even eradicate the epidemic. However, even for small fractions of indirect transmission, such lockdowns can impede CT efficacy and increase case numbers. These counterproductive effects can be reduced by applying measures that favor distancing over reduced mobility. In summary, we show that the efficacy of lock-downs depends on the transmission route. Our results point to the particular importance of hygiene measures during mobility lock-downs.

The role of super-spreaders in modeling of SARS-CoV-2

In stochastic modeling of infectious diseases, it has been established that variations in infectivity affect the probability of a major outbreak, but not the shape of the curves during a major outbreak, which is predicted by deterministic models (Diekmann et al., 2012). However, such conclusions are derived under idealized assumptions such as the population size tending to infinity, and the individual degree of infectivity only depending on variations in the infectiousness period. In this paper we show that the same conclusions hold true in a finite population representing a medium size city, where the degree of infectivity is determined by the offspring distribution, which we try to make as realistic as possible for SARS-CoV-2. In particular, we consider distributions with fat tails, to incorporate the existence of super-spreaders. We also provide new theoretical results on convergence of stochastic models which allows to incorporate any offspring distribution with a finite variance.

COVID-19 Modeling Outcome versus Reality in Sweden

It has been very difficult to predict the development of the COVID-19 pandemic based on mathematical models for the spread of infectious diseases, and due to major non-pharmacological interventions (NPIs), it is still unclear to what extent the models would have fit reality in a “do nothing” scenario. To shed light on this question, the case of Sweden during the time frame from autumn 2020 to spring 2021 is particularly interesting, since the NPIs were relatively minor and only marginally updated. We found that state of the art models are significantly overestimating the spread, unless we assume that social interactions significantly decrease continuously throughout the time frame, in a way that does not correlate well with Google-mobility data nor updates to the NPIs or public holidays. This leads to the question of whether modern SEIR-type mathematical models are unsuitable for modeling the spread of SARS-CoV-2 in the human population, or whether some particular feature of SARS-CoV-2 dampened the spread. We show that, by assuming a certain level of pre-immunity to SARS-CoV-2, we obtain an almost perfect data-fit, and discuss what factors could cause pre-immunity in the mathematical models. In this scenario, a form of herd-immunity under the given restrictions was reached twice (first against the Wuhan-strain and then against the alpha-strain), and the ultimate decline in cases was due to depletion of susceptibles rather than the vaccination campaign.

Uncertainty Modeling of a Modified SEIR Epidemic Model for COVID-19

Based on SEIR (susceptible-exposed-infectious-removed) epidemic model, we propose a modified epidemic mathematical model to describe the spread of the coronavirus disease 2019 (COVID-19) epidemic in Wuhan, China. Using public data, the uncertainty parameters of the proposed model for COVID-19 in Wuhan were calibrated. The uncertainty of the control basic reproduction number was studied with the posterior probability density function of the uncertainty model parameters. The mathematical model was used to inverse deduce the earliest start date of COVID-19 infection in Wuhan with consideration of the lack of information for the initial conditions of the model. The result of the uncertainty analysis of the model is in line with the observed data for COVID-19 in Wuhan, China. The numerical results show that the modified mathematical model could model the spread of COVID-19 epidemics.

Generalized Susceptible-Exposed-Infectious-Recovered model and its contributing factors for analysing the death and recovery rates of the COVID-19 pandemic

COVID-19 is a highly contagious disease that has infected over 136 million people worldwide with over 2.9 million deaths as of 11 April 2021. In March 2020, the WHO declared COVID-19 as a pandemic and countries began to implement measures to control the spread of the virus. The spread and the death rates of the virus displayed dramatic differences among countries globally, showing that there are several factors affecting its spread and mortality. By utilizing the cumulative number of cases from John Hopkins University, the recovery rate, death rate, and the number of active, recovered, and death cases were simulated to analyse the trends and patterns within the chosen countries. 10 countries from 3 different case severity categories (high cases, medium cases, and low cases) and 5 continents (Asia, North America, South America, Europe, and Oceania) were studied. A generalized SEIR model which considers control measures such as isolation, and preventive measures such as vaccination is applied in this study. This model is able to capture not only the dynamics between the states, but also the time evolution of the states by using the fourth-order-Runge-Kutta process. This study found no significant patterns in the countries under the same case severity category, suggesting that there are other factors contributing to the pattern in these countries. One of the factors influencing the pattern in each country is the population's age. COVID-19 related deaths were found to be notably higher among older people, indicating that countries comprising of a larger proportion of older age groups have an increased risk of experiencing higher death rates. Tighter governmental control measures led to fewer infections and eventually reduced the number of death cases, while increasing the recovery rate, and early implementations were found to be far more effective in controlling the spread of the virus and produced better outcomes.

Complex model calibration through emulation, a worked example for a stochastic epidemic model

Uncertainty quantification is a formal paradigm of statistical estimation that aims to account for all uncertainties inherent in the modelling process of real-world complex systems. The methods are directly applicable to stochastic models in epidemiology, however they have thus far not been widely used in this context. In this paper, we provide a tutorial on uncertainty quantification of stochastic epidemic models, aiming to facilitate the use of the uncertainty quantification paradigm for practitioners with other complex stochastic simulators of applied systems. We provide a formal workflow including the important decisions and considerations that need to be taken, and illustrate the methods over a simple stochastic epidemic model of UK SARS-CoV-2 transmission and patient outcome. We also present new approaches to visualisation of outputs from sensitivity analyses and uncertainty quantification more generally in high input and/or output dimensions.

Water Transmission Increases the Intensity of COVID-19 Outbreaks

India suffered from a devastating 2021 spring outbreak of coronavirus disease 2019 (COVID-19), surpassing any other outbreaks before. However, the reason for the acceleration of the outbreak in India is still unknown. We describe the statistical characteristics of infected patients from the first case in India to June 2021, and trace the causes of the two outbreaks in a complete way, combined with data on natural disasters, environmental pollution and population movements etc. We found that water-to-human transmission accelerates COVID-19 spreading. The transmission rate is 382% higher than the human-to-human transmission rate during the 2020 summer outbreak in India. When syndrome coronavirus 2 (SARS-CoV-2) enters the human body directly through the water-oral transmission pathway, virus particles and nitrogen salt in the water accelerate viral infection and mutation rates in the gastrointestinal tract. Based on the results of the attribution analysis, without the current effective interventions, India could have experienced a third outbreak during the monsoon season this year, which would have increased the severity of the disaster and led to a South Asian economic crisis.

Inferring the effective start dates of non-pharmaceutical interventions during COVID-19 outbreaks

BACKGROUND

During Feb-Apr. 2020, many countries implemented non-pharmaceutical interventions (NPIs), such as school closures and lockdowns, to control the COVID-19 pandemic caused by the SARS-CoV-2 virus. Overall, these interventions seem to have reduced the spread of the pandemic. We hypothesized that the official and effective start dates of NPIs can be noticeably different, for example, due to slow adoption by the population, and that these differences can lead to errors in the estimation of the impact of NPIs.

METHODS

SEIR models were fitted to case data from 12 regions to infer the effective start dates of interventions and compare these with the official dates. The impact of NPIs was estimated from the inferred model parameters.

RESULTS

We infer mostly late effective start dates of interventions. For example, Italy implemented a lockdown on Mar 11, but we infer the effective start date on Mar 17 (+3.05-2.01 days 95% CI). Moreover, we find that the impact of NPIs can be underestimated if it is assumed they start on their official date.

CONCLUSIONS

Differences between the official and effective start of NPIs are likely. Neglecting such differences can lead to underestimation of the impact of NPIs, which could cause decision-makers to escalate interventions and guidelines.

Empirical Model of Spring 2020 Decrease in Daily Confirmed COVID-19 Cases in King County, Washington

Projections of the near future of daily case incidence of COVID-19 are valuable for informing public policy. Near-future estimates are also useful for outbreaks of other diseases. Short-term predictions are unlikely to be affected by changes in herd immunity. In the absence of major net changes in factors that affect reproduction number (R), the two-parameter exponential model should be a standard model - indeed, it has been standard for epidemiological analysis of pandemics for a century but in recent decades has lost popularity to more complex compartmental models. Exponential models should be routinely included in reports describing epidemiological models as a reference, or null hypothesis. Exponential models should be fitted separately for each epidemiologically distinct jurisdiction. They should also be fitted separately to time intervals that differ by any major changes in factors that affect R. Using an exponential model, incidence-count half-life (t1/2) is a better statistic than R. Here an example of the exponential model is applied to King County, Washington during Spring 2020. During the pandemic, the parameters and predictions of this model have remained stable for intervals of one to four months, and the accuracy of model predictions has outperformed models with more parameters. The COVID pandemic can be modeled as a series of exponential curves, each spanning an interval ranging from one to four months. The length of these intervals is hard to predict, other than to extrapolate that future intervals will last about as long as past intervals.

Transmission dynamics model and the coronavirus disease 2019 epidemic: applications and challenges

Since late 2019, the beginning of coronavirus disease 2019 (COVID-19) pandemic, transmission dynamics models have achieved great development and were widely used in predicting and policy making. Here, we provided an introduction to the history of disease transmission, summarized transmission dynamics models into three main types: compartment extension, parameter extension and population-stratified extension models, highlight the key contribution of transmission dynamics models in COVID-19 pandemic: estimating epidemiological parameters, predicting the future trend, evaluating the effectiveness of control measures and exploring different possibilities/scenarios. Finally, we pointed out the limitations and challenges lie ahead of transmission dynamics models.

Brazil's COVID-19 Epicenter in Manaus: How Much of the Population Has Already Been Exposed and Are Vulnerable to SARS-CoV-2?

Is Brazil's COVID-19 epicenter really approaching herd immunity? A recent study estimated that in October 2020 three-quarters of the population of Manaus (the capital of the largest state in the Brazilian Amazon) had contact with SARS-CoV-2. We show that 46% of the Manaus population having had contact with SARS-CoV-2 at that time is a more plausible estimate, and that Amazonia is still far from herd immunity. The second wave of COVID-19 is now evident in Manaus. We predict that the pandemic of COVID-19 will continue throughout 2021, given the duration of naturally acquired immunity of only 240 days and the slow pace of vaccination. Manaus has a large percentage of the population that is susceptible (35 to 45% as of May 17, 2021). Against this backdrop, measures to restrict urban mobility and social isolation are still necessary, such as the closure of schools and universities, since the resumption of these activities in 2020 due to the low attack rates of SARS-CoV-2 was the main trigger for the second wave in Manaus.

COVID-19 pandemic, predictions and control in Saudi Arabia using SIR-F and age-structured SEIR model

COVID-19 has affected every individual physically or physiologically, leading to substantial impacts on how they perceive and respond to the pandemic's danger. Due to the lack of vaccines or effective medicines to cure the infection, an urgent control measure is required to prevent the continued spread of COVID-19. This can be achieved using advanced computing, such as artificial intelligence (AI), machine learning (ML), deep learning (DL), cloud computing, and edge computing. To control the exponential spread of the novel virus, it is crucial for countries to contain and mitigate interventions. To prevent exponential growth, several control measures have been applied in the Kingdom of Saudi Arabia to mitigate the COVID-19 epidemic. As the pandemic has been spreading globally for more than a year, an ample amount of data is available for researchers to predict and forecast the effect of the pandemic in the near future. This article interprets the effects of COVID-19 using the Susceptible-Infected-Recovered (SIR-F) while F-stands for 'Fatal with confirmation,' age-structured SEIR (Susceptible Exposed Infectious Removed) and machine learning for smart health care and the well-being of citizens of Saudi Arabia. Additionally, it examines the different control measure scenarios produced by the modified SEIR model. The evolution of the simulation results shows that the interventions are vital to flatten the virus spread curve, which can delay the peak and decrease the fatality rate.

A dynamic microsimulation model for epidemics

A large evidence base demonstrates that the outcomes of COVID-19 and national and local interventions are not distributed equally across different communities. The need to inform policies and mitigation measures aimed at reducing the spread of COVID-19 highlights the need to understand the complex links between our daily activities and COVID-19 transmission that reflect the characteristics of British society. As a result of a partnership between academic and private sector researchers, we introduce a novel data driven modelling framework together with a computationally efficient approach to running complex simulation models of this type. We demonstrate the power and spatial flexibility of the framework to assess the effects of different interventions in a case study where the effects of the first UK national lockdown are estimated for the county of Devon. Here we find that an earlier lockdown is estimated to result in a lower peak in COVID-19 cases and 47% fewer infections overall during the initial COVID-19 outbreak. The framework we outline here will be crucial in gaining a greater understanding of the effects of policy interventions in different areas and within different populations.

A simulated measurement for COVID-19 pandemic using the effective reproductive number on an empirical portion of population: epidemiological models

COVID-19 as a global pandemic has had an unprecedented impact on the entire world. Projecting the future spread of the virus in relation to its characteristics for a specific suite of countries against a temporal trend can provide public health guidance to governments and organizations. Therefore, this paper presented an epidemiological comparison of the traditional SEIR model with an extended and modified version of the same model by splitting the infected compartment into asymptomatic mild and symptomatic severe. We then exposed our derived layered model into two distinct case studies with variations in mitigation strategies and non-pharmaceutical interventions (NPIs) as a matter of benchmarking and comparison. We focused on exploring the United Arab Emirates (a small yet urban centre (where clear sequential stages NPIs were implemented). Further, we concentrated on extending the models by utilizing the effective reproductive number (R t) estimated against time, a more realistic than the static R 0, to assess the potential impact of NPIs within each case study. Compared to the traditional SEIR model, the results supported the modified model as being more sensitive in terms of peaks of simulated cases and flattening determinations.

Age-stratified transmission model of COVID-19 in Ontario with human mobility during pandemic's first wave

In this work, we employ a data-fitted compartmental model to visualize the progression and behavioral response to COVID-19 that match provincial case data in Ontario, Canada from February to June of 2020. This is a "rear-view mirror" glance at how this region has responded to the 1st wave of the pandemic, when testing was sparse and NPI measures were the only remedy to stave off the pandemic. We use an SEIR-type model with age-stratified subpopulations and their corresponding contact rates and asymptomatic rates in order to incorporate heterogeneity in our population and to calibrate the time-dependent reduction of Ontario-specific contact rates to reflect intervention measures in the province throughout lockdown and various stages of social-distancing measures. Cellphone mobility data taken from Google, combining several mobility categories, allows us to investigate the effects of mobility reduction and other NPI measures on the evolution of the pandemic. Of interest here is our quantification of the effectiveness of Ontario's response to COVID-19 before and after provincial measures and our conclusion that the sharp decrease in mobility has had a pronounced effect in the first few weeks of the lockdown, while its effect is harder to infer once other NPI measures took hold.

Understanding COVID-19 dynamics and the effects of interventions in the Philippines: A mathematical modelling study

BACKGROUND

COVID-19 initially caused less severe outbreaks in many low- and middle-income countries (LMIC) compared with many high-income countries, possibly because of differing demographics, socioeconomics, surveillance, and policy responses. Here, we investigate the role of multiple factors on COVID-19 dynamics in the Philippines, a LMIC that has had a relatively severe COVID-19 outbreak.

METHODS

We applied an age-structured compartmental model that incorporated time-varying mobility, testing, and personal protective behaviors (through a "Minimum Health Standards" policy, MHS) to represent the first wave of the Philippines COVID-19 epidemic nationally and for three highly affected regions (Calabarzon, Central Visayas, and the National Capital Region). We estimated effects of control measures, key epidemiological parameters, and interventions.

FINDINGS

Population age structure, contact rates, mobility, testing, and MHS were sufficient to explain the Philippines epidemic based on the good fit between modelled and reported cases, hospitalisations, and deaths. The model indicated that MHS reduced the probability of transmission per contact by 13-27%. The February 2021 case detection rate was estimated at ~8%, population recovered at ~9%, and scenario projections indicated high sensitivity to MHS adherence.

INTERPRETATION

COVID-19 dynamics in the Philippines are driven by age, contact structure, mobility, and MHS adherence. Continued compliance with low-cost MHS should help the Philippines control the epidemic until vaccines are widely distributed, but disease resurgence may be occurring due to a combination of low population immunity and detection rates and new variants of concern.

Impact of age-selective vs non-selective physical-distancing measures against coronavirus disease 2019: a mathematical modelling study

BACKGROUND

There is a real possibility of successive COVID-19-epidemic waves with devastating consequences. In this context, it has become mandatory to design age-selective measures aimed at achieving an optimal balance between protecting public health and maintaining a viable economic activity.

METHODS

We programmed a Susceptible, Exposed, Infected, Removed (SEIR) model in order to introduce epidemiologically relevant age classes into the outbreak-dynamics analysis. The model was fitted to the official death toll and calculated age distribution of deaths in Wuhan using a constrained linear least-squares algorithm. Subsequently, we used synthetic location-specific and age-structured contact matrices to quantify the effect of age-selective interventions both on mortality and on economic activity in Wuhan. For this purpose, we simulated four different scenarios ranging from an absence of measures to age-selective interventions with stronger physical-distancing measures for older individuals.

RESULTS

An age-selective strategy could reduce the death toll by >30% compared with the non-selective measures applied during Wuhan's lockdown for the same workforce. Moreover, an alternative age-selective strategy could allow a 5-fold increase in the population working on site without a detrimental impact on the death toll compared with the Wuhan scenario.

CONCLUSION

Our results suggest that age-selective-distancing measures focused on the older population could have achieved a better balance between COVID-19 mortality and economic activity during the first COVID-19 outbreak in Wuhan. However, the implications of this need to be interpreted along with considerations of the practical feasibility and potential wider benefits and drawbacks of such a strategy.

Mathematical modelling of the spread of COVID-19 on a university campus

In this paper we present a deterministic transmission dynamic compartmental model for the spread of the novel coronavirus on a college campus for the purpose of analyzing strategies to mitigate an outbreak. The goal of this project is to determine and compare the utility of certain containment strategies including gateway testing, surveillance testing, and contact tracing as well as individual level control measures such as mask wearing and social distancing. We modify a standard SEIR-type model to reflect what is currently known about COVID-19. We also modify the model to reflect the population present on a college campus, separating it into students and faculty. This is done in order to capture the expected different contact rates between groups as well as the expected difference in outcomes based on age known for COVID-19. We aim to provide insight into which strategies are most effective, rather than predict exact numbers of infections. We analyze effectiveness by looking at relative changes in the total number of cases as well as the effect a measure has on the estimated basic reproductive number. We find that the total number of infections is most sensitive to parameters relating to student behaviors. We also find that contact tracing can be an effective control strategy when surveillance testing is unavailable. Lastly, we validate the model using data from Villanova University's online COVID-19 Dashboard from Fall 2020 and find good agreement between model and data when superspreader events are incorporated in the model as shocks to the number of infected individuals approximately two weeks after each superspreader event.

[Evaluation of interventions during the COVID-19 pandemic: development of a model based on subpopulations with different contact rates]

Si bien se han realizado múltiples intentos de modelar matemáticamente la pandemia de la enfermedad por coronavirus 2019 (COVID-19), causada por SARS-CoV-2, pocos modelos han sido pensados como herramientas interactivas accesibles para usuarios de distintos ámbitos. El objetivo de este trabajo fue desarrollar un modelo que tuviera en cuenta la heterogeneidad de las tasas de contacto de la población e implementarlo en una aplicación accesible, que permitiera estimar el impacto de posibles intervenciones a partir de información disponible. Se desarrolló una versión ampliada del modelo susceptible-expuesto-infectado-resistente (SEIR), denominada SEIR-HL, que asume una población dividida en dos subpoblaciones, con tasas de contacto diferentes. Asimismo, se desarrolló una fórmula para calcular el número básico de reproducción (R₀) para una población dividida en n subpoblaciones, discriminando las tasas de contacto de cada subpoblación según el tipo o contexto de contacto. Se compararon las predicciones del SEIR-HL con las del SEIR y se demostró que la heterogeneidad en las tasas de contacto puede afectar drásticamente la dinámica de las simulaciones, aun partiendo de las mismas condiciones iniciales y los mismos parámetros. Se empleó el SEIR-HL para mostrar el efecto sobre la evolución de la pandemia del desplazamiento de individuos desde posiciones de alto contacto hacia posiciones de bajo contacto. Finalmente, a modo de ejemplo, se aplicó el SEIR-HL al análisis de la pandemia de COVID-19 en Argentina; también se desarrolló un ejemplo de uso de la fórmula del R₀. Tanto el SEIR-HL como una calculadora del R₀ fueron implementados informáticamente y puestos a disposición de la comunidad.

How much leeway is there to relax COVID-19 control measures?

Following successful non-pharmaceutical interventions (NPI) aiming to control COVID-19, many jurisdictions reopened their economies and borders. As little immunity had developed in most populations, re-establishing higher contact carried substantial risks, and therefore many locations began to see resurgence in COVID-19 cases. We present a Bayesian method to estimate the leeway to reopen, or alternatively the strength of change required to re-establish COVID-19 control, in a range of jurisdictions experiencing different COVID-19 epidemics. We estimated the timing and strength of initial control measures such as widespread distancing and compared the leeway jurisdictions had to reopen immediately after NPI measures to later estimates of leeway. Finally, we quantified risks associated with reopening and the likely burden of new cases due to introductions from other jurisdictions. We found widely varying leeway to reopen. After initial NPI measures took effect, some jurisdictions had substantial leeway (e.g., Japan, New Zealand, Germany) with > 0.99 probability that contact rates were below 80% of the threshold for epidemic growth. Others had little leeway (e.g., the United Kingdom, Washington State) and some had none (e.g., Sweden, California). For most such regions, increases in contact rate of 1.5-2 fold would have had high (> 0.7) probability of exceeding past peak sizes. Most jurisdictions experienced June-August trajectories consistent with our projections of contact rate increases of 1-2-fold. Under such relaxation scenarios for some regions, we projected up to ∼100 additional cases if just one case were imported per week over six weeks, even between jurisdictions with comparable COVID-19 risk. We provide an R package covidseir to enable jurisdictions to estimate leeway and forecast cases under different future contact patterns. Estimates of leeway can establish a quantitative basis for decisions about reopening. We recommend a cautious approach to reopening economies and borders, coupled with strong monitoring for changes in transmission.

RLIM: a recursive and latent infection model for the prediction of US COVID-19 infections and turning points

Initially found in Hubei, Wuhan, and identified as a novel virus of the coronavirus family by the WHO, COVID-19 has spread worldwide at exponential speed, causing millions of deaths and public fear. Currently, the USA, India, Brazil, and other parts of the world are experiencing a secondary wave of COVID-19. However, the medical, mathematical, and pharmaceutical aspects of its transmission, incubation, and recovery processes are still unclear. The classical susceptible-infected-recovered model has limitations in describing the dynamic behavior of COVID-19. Hence, it is necessary to introduce a recursive, latent model to predict the number of future COVID-19 infection cases in the USA. In this article, a dynamic recursive and latent infection model (RLIM) based on the classical SEIR model is proposed to predict the number of COVID-19 infections. Given COVID-19 infection and recovery data for a certain period, the RLIM is able to fit current values and produce an optimal set of parameters with a minimum error rate according to actual reported numbers. With these optimal parameters assigned, the RLIM model then becomes able to produce predictions of infection numbers within a certain period. To locate the turning point of COVID-19 transmission, an initial value for the secondary infection rate is given to the RLIM algorithm for calculation. RLIM will then calculate the secondary infection rates of a continuous time series with an iterative search strategy to speed up the convergence of the prediction outcomes and minimize the maximum square errors. Compared with other forecast algorithms, RLIM is able to adapt the COVID-19 infection curve faster and more accurately and, more importantly, provides a way to identify the turning point in virus transmission by searching for the equilibrium between recoveries and new infections. Simulations of four US states show that with the secondary infection rate ω initially set to 0.5 within the selected latent period of 14 days, RLIM is able to minimize this value at 0.07 and reach an equilibrium condition. A successful forecast is generated using New York state's COVID-19 transmission, in which a turning point is predicted to emerge on January 31, 2021.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s11071-021-06520-1.

Age-Stratified Infection Probabilities Combined With a Quarantine-Modified Model for COVID-19 Needs Assessments: Model Development Study

BACKGROUND

Classic compartmental models such as the susceptible-exposed-infectious-removed (SEIR) model all have the weakness of assuming a homogenous population, where everyone has an equal chance of getting infected and dying. Since it was identified in Hubei, China, in December 2019, COVID-19 has rapidly spread around the world and been declared a pandemic. Based on data from Hubei, infection and death distributions vary with age. To control the spread of the disease, various preventive and control measures such as community quarantine and social distancing have been widely used.

OBJECTIVE

Our aim is to develop a model where age is a factor, considering the study area's age stratification. Additionally, we want to account for the effects of quarantine on the SEIR model.

METHODS

We use the age-stratified COVID-19 infection and death distributions from Hubei, China (more than 44,672 infections as of February 11, 2020) as an estimate or proxy for a study area's infection and mortality probabilities for each age group. We then apply these probabilities to the actual age-stratified population of Quezon City, Philippines, to predict infectious individuals and deaths at peak. Testing with different countries shows the predicted number of infectious individuals skewing with the country's median age and age stratification, as expected. We added a Q parameter to the SEIR model to include the effects of quarantine (Q-SEIR).

RESULTS

The projections from the age-stratified probabilities give much lower predicted incidences of infection than the Q-SEIR model. As expected, quarantine tends to delay the peaks for both the exposed and infectious groups, and to "flatten" the curve or lower the predicted values for each compartment. These two estimates were used as a range to inform the local government's planning and response to the COVID-19 threat.

CONCLUSIONS

Age stratification combined with a quarantine-modified model has good qualitative agreement with observations on infections and death rates. That younger populations will have lower death rates due to COVID-19 is a fair expectation for a disease where most fatalities are among older adults.

Social Restrictions versus Testing Campaigns in the COVID-19 Crisis: A Predictive Model Based on the Spanish Case

The global COVID-19 spread has forced countries to implement non-pharmacological interventions (NPI) (i.e., mobility restrictions and testing campaigns) to preserve health systems. Spain is one of the most severely impacted countries, both clinically and economically. In an effort to support policy decision-making, we aimed to assess the impacts of different NPI on COVID-19 epidemiology, healthcare costs and Gross Domestic Product (GDP). A modified Susceptible-Exposed-Infectious-Removed epidemiological model was created to simulate the pandemic evolution. Its output was used to populate an economic model to quantify healthcare costs and GDP variation through a regression model which correlates NPI and GDP change from 42 countries. Thirteen scenarios combining different NPI were consecutively simulated in the epidemiological and economic models. Both increased testing and stringency could reduce cases, hospitalizations and deaths. While policies based on increased testing rates lead to higher healthcare costs, increased stringency is correlated with greater GDP declines, with differences of up to 4.4% points. Increased test sensitivity may lead to a reduction of cases, hospitalizations and deaths and to the implementation of pooling techniques that can increase throughput testing capacity. Alternative strategies to control COVID-19 spread entail differing economic outcomes. Decision-makers may utilize this tool to identify the most suitable strategy considering epidemiological and economic outcomes.

Effectiveness of isolation policies in schools: evidence from a mathematical model of influenza and COVID-19

Background

Non-pharmaceutical interventions such as social distancing, school closures and travel restrictions are often implemented to control outbreaks of infectious diseases. For influenza in schools, the Center of Disease Control (CDC) recommends that febrile students remain isolated at home until they have been fever-free for at least one day and a related policy is recommended for SARS-CoV-2 (COVID-19). Other authors proposed using a school week of four or fewer days of in-person instruction for all students to reduce transmission. However, there is limited evidence supporting the effectiveness of these interventions.

Methods

We introduced a mathematical model of school outbreaks that considers both intervention methods. Our model accounts for the school structure and schedule, as well as the time-progression of fever symptoms and viral shedding. The model was validated on outbreaks of seasonal and pandemic influenza and COVID-19 in schools. It was then used to estimate the outbreak curves and the proportion of the population infected (attack rate) under the proposed interventions.

Results

For influenza, the CDC-recommended one day of post-fever isolation can reduce the attack rate by a median (interquartile range) of 29 (13–59)%. With 2 days of post-fever isolation the attack rate could be reduced by 70 (55–85)%. Alternatively, shortening the school week to 4 and 3 days reduces the attack rate by 73 (64–88)% and 93 (91–97)%, respectively. For COVID-19, application of post-fever isolation policy was found to be less effective and reduced the attack rate by 10 (5–17)% for a 2-day isolation policy and by 14 (5–26)% for 14 days. A 4-day school week would reduce the median attack rate in a COVID-19 outbreak by 57 (52–64)%, while a 3-day school week would reduce it by 81 (79–83)%. In both infections, shortening the school week significantly reduced the duration of outbreaks.

Conclusions

Shortening the school week could be an important tool for controlling influenza and COVID-19 in schools and similar settings. Additionally, the CDC-recommended post-fever isolation policy for influenza could be enhanced by requiring two days of isolation instead of one.

SEAHIR: A Specialized Compartmental Model for COVID-19

The SEIR (Susceptible-Exposed-Infected-Removed) model is widely used in epidemiology to mathematically model the spread of infectious diseases with incubation periods. However, the SEIR model prototype is generic and not able to capture the unique nature of a novel viral pandemic such as SARS-CoV-2. We have developed and tested a specialized version of the SEIR model, called SEAHIR (Susceptible-Exposed-Asymptomatic-Hospitalized-Isolated-Removed) model. This proposed model is able to capture the unique dynamics of the COVID-19 outbreak including further dividing the Infected compartment into: (1) “Asymptomatic”, (2) “Isolated” and (3) “Hospitalized” to delineate the transmission specifics of each compartment and forecast healthcare requirements. The model also takes into consideration the impact of non-pharmaceutical interventions such as physical distancing and different testing strategies on the number of confirmed cases. We used a publicly available dataset from the United Arab Emirates (UAE) as a case study to optimize the main parameters of the model and benchmarked it against the historical number of cases. The SEAHIR model was used by decision-makers in Dubai’s COVID-19 Command and Control Center to make timely decisions on developing testing strategies, increasing healthcare capacity, and implementing interventions to contain the spread of the virus. The novel six-compartment SEAHIR model could be utilized by decision-makers and researchers in other countries for current or future pandemics.

COVID-19: Analytic results for a modified SEIR model and comparison of different intervention strategies

The Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model is one of the standard models of disease spreading. Here we analyse an extended SEIR model that accounts for asymptomatic carriers, believed to play an important role in COVID-19 transmission. For this model we derive a number of analytic results for important quantities such as the peak number of infections, the time taken to reach the peak and the size of the final affected population. We also propose an accurate way of specifying initial conditions for the numerics (from insufficient data) using the fact that the early time exponential growth is well-described by the dominant eigenvector of the linearized equations. Secondly we explore the effect of different intervention strategies such as social distancing (SD) and testing-quarantining (TQ). The two intervention strategies (SD and TQ) try to reduce the disease reproductive number, R 0 , to a target value R 0 target < 1 , but in distinct ways, which we implement in our model equations. We find that for the same R 0 target < 1 , TQ is more efficient in controlling the pandemic than SD. However, for TQ to be effective, it has to be based on contact tracing and our study quantifies the required ratio of tests-per-day to the number of new cases-per-day. Our analysis shows that the largest eigenvalue of the linearised dynamics provides a simple understanding of the disease progression, both pre- and post- intervention, and explains observed data for many countries. We apply our results to the COVID data for India to obtain heuristic projections for the course of the pandemic, and note that the predictions strongly depend on the assumed fraction of asymptomatic carriers.

The analysis of isolation measures for epidemic control of COVID-19

This paper proposes a susceptible exposed infectious recovered model (SEIR) with isolation measures to evaluate the COVID-19 epidemic based on the prevention and control policy implemented by the Chinese government on February 23, 2020. According to the Chinese government's immediate isolation and centralized diagnosis of confirmed cases, and the adoption of epidemic tracking measures on patients to prevent further spread of the epidemic, we divide the population into susceptible, exposed, infectious, quarantine, confirmed and recovered. This paper proposes an SEIR model with isolation measures that simultaneously investigates the infectivity of the incubation period, reflects prevention and control measures and calculates the basic reproduction number of the model. According to the data released by the National Health Commission of the People's Republic of China, we estimated the parameters of the model and compared the simulation results of the model with actual data. We have considered the trend of the epidemic under different incubation periods of infectious capacity. When the incubation period is not contagious, the peak number of confirmed in the model is 33,870; and when the infectious capacity is 0.1 times the infectious capacity in the infectious period, the peak number of confirmed in the model is 57,950; when the infectious capacity is doubled, the peak number of confirmed will reach 109,300. Moreover, by changing the contact rate in the model, we found that as the intensity of prevention and control measures increase, the peak of the epidemic will come earlier, and the peak number of confirmed will also be significantly reduced. Under extremely strict prevention and control measures, the peak number of confirmed cases has dropped by nearly 50%. In addition, we use the EEMD method to decompose the time series data of the epidemic, and then combine the LSTM model to predict the trend of the epidemic. Compared with the method of directly using LSTM for prediction, more detailed information can be obtained.

A review on COVID-19 forecasting models

The novel coronavirus (COVID-19) has spread to more than 200 countries worldwide, leading to more than 36 million confirmed cases as of October 10, 2020. As such, several machine learning models that can forecast the outbreak globally have been released. This work presents a review and brief analysis of the most important machine learning forecasting models against COVID-19. The work presented in this study possesses two parts. In the first section, a detailed scientometric analysis presents an influential tool for bibliometric analyses, which were performed on COVID-19 data from the Scopus and Web of Science databases. For the above-mentioned analysis, keywords and subject areas are addressed, while the classification of machine learning forecasting models, criteria evaluation, and comparison of solution approaches are discussed in the second section of the work. The conclusion and discussion are provided as the final sections of this study.

A model for COVID-19 with isolation, quarantine and testing as control measures

In this article we propose a compartmental model for the dynamics of Coronavirus Disease 2019 (COVID-19). We take into account the presence of asymptomatic infections and the main policies that have been adopted so far to contain the epidemic: social distancing, isolation of a portion of the population, quarantine for confirmed cases and testing. We refer to quarantine as strict isolation, and it is applied to confirmed infected cases.

In the proposed model, the proportion of people in isolation, the level of contact reduction and the testing rate are control parameters that can vary in time, representing policies that evolve in different stages. We obtain an explicit expression for the basic reproduction number R0 in terms of the parameters of the disease and of the control policies. In this way we can quantify the effect that isolation and testing have in the evolution of the epidemic. We present a series of simulations to illustrate different realistic scenarios. From the expression of R0 and the simulations we conclude that isolation (social distancing) and testing among asymptomatic cases are fundamental actions to control the epidemic, and the stricter these measures are and the sooner they are implemented, the more effective they are in flattening the curve of infections. Additionally, we show that people that remain in isolation significantly reduce their probability of contagion, so risk groups should be recommended to maintain a low contact rate during the course of the epidemic.

Systems dynamics approach for modelling South Africa's response to COVID-19: A "what if" scenario

Background: Many countries in the world are still struggling to control COVID-19 pandemic. As of April 28, 2020, South Africa reported the highest number of COVID-19 cases in Sub- Sahara Africa. The country took aggressive steps to control the spread of the virus including setting a national command team for COVID-19 and putting the country on a complete lockdown for more than 100 days. Evidence across most countries has shown that, it is vital to monitor the progression of pandemics and assess the effects of various public health measures, such as lockdowns. Countries need to have scientific tools to assist in monitoring and assessing the effectiveness of mitigation interventions. The objective of this study was thus to assess the extent to which a systems dynamics model can forecast COVID-19 infections in South Africa and be a useful tool in evaluating government interventions to manage the epidemic through 'what if' simulations. Design and Methods: This study presents a systems dynamics model (SD) of the COVID-19 infection in South Africa, as one of such tools. The development of the SD model in this study is grounded in design science research which fundamentally builds on prior research of modelling complex systems. Results: The SD model satisfactorily replicates the general trend of COVID-19 infections and recovery for South Africa within the first 100 days of the pandemic. The model further confirms that the decision to lockdown the country was a right one, otherwise the country's health capacity would have been overwhelmed. Going forward, the model predicts that the level of infection in the country will peak towards the last quarter of 2020, and thereafter start to decline. Conclusions: Ultimately, the model structure and simulations suggest that a systems dynamics model can be a useful tool in monitoring, predicting and testing interventions to manage COVID-19 with an acceptable margin of error. Moreover, the model can be developed further to include more variables as more facts on the COVID-19 emerge.

COVID-19 pandemic: a mobility-dependent SEIR model with undetected cases in Italy, Europe, and US

OBJECTIVES

to describe the first wave of the COVID-19 pandemic with a focus on undetected cases and to evaluate different post-lockdown scenarios.

DESIGN

the study introduces a SEIR compartmental model, taking into account the region-specific fraction of undetected cases, the effects of mobility restrictions, and the personal protective measures adopted, such as wearing a mask and washing hands frequently.

SETTING AND PARTICIPANTS

the model is experimentally validated with data of all the Italian regions, some European countries, and the US.

MAIN OUTCOME MEASURES

the accuracy of the model results is measured through the mean absolute percentage error (MAPE) and Lewis criteria; fitting parameters are in good agreement with previous literature.

RESULTS

the epidemic curves for different countries and the amount of undetected and asymptomatic cases are estimated, which are likely to represent the main source of infections in the near future. The model is applied to the Hubei case study, which is the first place to relax mobility restrictions. Results show different possible scenarios. Mobility and the adoption of personal protective measures greatly influence the dynamics of the infection, determining either a huge and rapid secondary epidemic peak or a more delayed and manageable one.

CONCLUSIONS

mathematical models can provide useful insights for healthcare decision makers to determine the best strategy in case of future outbreaks.

A new SEAIRD pandemic prediction model with clinical and epidemiological data analysis on COVID-19 outbreak

Measuring the spread of disease during a pandemic is critically important for accurately and promptly applying various lockdown strategies, so to prevent the collapse of the medical system. The latest pandemic of COVID-19 that hits the world death tolls and economy loss very hard, is more complex and contagious than its precedent diseases. The complexity comes mostly from the emergence of asymptomatic patients and relapse of the recovered patients which were not commonly seen during SARS outbreaks. These new characteristics pertaining to COVID-19 were only discovered lately, adding a level of uncertainty to the traditional SEIR models. The contribution of this paper is that for the COVID-19 epidemic, which is infectious in both the incubation period and the onset period, we use neural networks to learn from the actual data of the epidemic to obtain optimal parameters, thereby establishing a nonlinear, self-adaptive dynamic coefficient infectious disease prediction model. On the basis of prediction, we considered control measures and simulated the effects of different control measures and different strengths of the control measures. The epidemic control is predicted as a continuous change process, and the epidemic development and control are integrated to simulate and forecast. Decision-making departments make optimal choices. The improved model is applied to simulate the COVID-19 epidemic in the United States, and by comparing the prediction results with the traditional SEIR model, SEAIRD model and adaptive SEAIRD model, it is found that the adaptive SEAIRD model's prediction results of the U.S. COVID-19 epidemic data are in good agreement with the actual epidemic curve. For example, from the prediction effect of these 3 different models on accumulative confirmed cases, in terms of goodness of fit, adaptive SEAIRD model (0.99997) ≈ SEAIRD model (0.98548) > Classical SEIR model (0.66837); in terms of error value: adaptive SEAIRD model (198.6563) < < SEAIRD model(4739.8577) < < Classical SEIR model (22,652.796); The objective of this contribution is mainly on extending the current spread prediction model. It incorporates extra compartments accounting for the new features of COVID-19, and fine-tunes the new model with neural network, in a bid of achieving a higher level of prediction accuracy. Based on the SEIR model of disease transmission, an adaptive model called SEAIRD with internal source and isolation intervention is proposed. It simulates the effects of the changing behaviour of the SARS-CoV-2 in U.S. Neural network is applied to achieve a better fit in SEAIRD. Unlike the SEIR model, the adaptive SEAIRD model embraces multi-group dynamics which lead to different evolutionary trends during the epidemic. Through the risk assessment indicators of the adaptive SEAIRD model, it is convenient to measure the severity of the epidemic situation for consideration of different preventive measures. Future scenarios are projected from the trends of various indicators by running the adaptive SEAIRD model.

Comparing COVID-19 vaccine allocation strategies in India: A mathematical modelling study

Background

The development and widespread use of an effective SARS-CoV-2 vaccine could prevent substantial morbidity and mortality associated with COVID-19 and mitigate the secondary effects associated with non-pharmaceutical interventions.

Methods

We used an age-structured, expanded SEIR model with social contact matrices to assess age-specific vaccine allocation strategies in India. We used state-specific age structures and disease transmission coefficients estimated from confirmed incident cases of COVID-19 between 1 July and 31 August 2020. Simulations were used to investigate the relative reduction in mortality and morbidity of vaccine allocation strategies based on prioritizing different age groups, and the interactions of these strategies with concurrent non-pharmaceutical interventions. Given the uncertainty associated with COVID-19 vaccine development, we varied vaccine characteristics in the modelling simulations.

Results

Prioritizing COVID-19 vaccine allocation for older populations (i.e., >60 years) led to the greatest relative reduction in deaths, regardless of vaccine efficacy, control measures, rollout speed, or immunity dynamics. Preferential vaccination of this group often produced relatively higher total symptomatic infections and more pronounced estimates of peak incidence than other assessed strategies. Vaccine efficacy, immunity type, target coverage, and rollout speed significantly influenced overall strategy effectiveness, with the time taken to reach target coverage significantly affecting the relative mortality benefit comparative to no vaccination.

Conclusions

Our findings support global recommendations to prioritize COVID-19 vaccine allocation for older age groups. Relative differences between allocation strategies were reduced as the speed of vaccine rollout was increased. Optimal vaccine allocation strategies will depend on vaccine characteristics, strength of concurrent non-pharmaceutical interventions, and region-specific goals.

It Takes More than Two to Tango with COVID-19: Analyzing Argentina's Early Pandemic Response (Jan 2020-April 2020)

In November 2019, the world was introduced to a new coronavirus that has since ravaged it. Argentina began to see an increase of COVID-19 quickly in the new year and as of April 2020 the country was still being burdened by the transmission of the virus. With the progression of the epidemic turning into a pandemic, health authorities constantly updated health prevention strategies and responses to the novel coronavirus in its first wave. The Center for Disease Control and Prevention (CDC) issued a level three warning for international travel to/from Argentina because of COVID-19's rapid transmission. With Argentina's already fragile economy, health systems had to meet the challenge of being able to treat the infected. This case presentation aims to provide an overview of Argentina's earliest epidemiological situation of the COVID-19 pandemic. The data provided in this study concern Argentina's COVID-19 situation during the period of January 2020-April 2020. Mathematical modeling was used to forecast COVID-19 transmission after the first wave, specifically focusing on Buenos Aires. The country's demographics and an impression of its health systems will be analyzed in this case presentation for preparedness. The case study concludes in depicting Argentina's current and anticipated economic, social, and political disruptions because of the first wave of the pandemic.

Comparative infection modeling and control of COVID-19 transmission patterns in China, South Korea, Italy and Iran

The COVID-19 has become a pandemic. The timing and nature of the COVID-19 pandemic response and control varied among the regions and from one country to the other, and their role in affecting the spread of the disease has been debated. The focus of this work is on the early phase of the disease when control measures can be most effective. We proposed a modified susceptible-exposed-infected-removed model (SEIR) model based on temporal moving windows to quantify COVID-19 transmission patterns and compare the temporal progress of disease spread in six representative regions worldwide: three Chinese regions (Zhejiang, Guangdong and Xinjiang) vs. three countries (South Korea, Italy and Iran). It was found that in the early phase of COVID-19 spread the disease follows a certain empirical law that is common in all regions considered. Simulations of the imposition of strong social distancing measures were used to evaluate the impact that these measures might have had on the duration and severity of COVID-19 outbreaks in the three countries. Measure-dependent transmission rates followed a modified normal distribution (empirical law) in the three Chinese regions. These rates responded quickly to the launch of the 1st-level Response to Major Public Health Emergency in each region, peaking after 1-2 days, reaching their inflection points after 10-19 days, and dropping to zero after 11-18 days since the 1st-level response was launched. By March 29th, the mortality rates were 0.08% (Zhejiang), 0.54% (Guangdong) and 3.95% (Xinjiang). Subsequent modeling simulations were based on the working assumption that similar infection transmission control measures were taken in South Korea as in Zhejiang on February 25th, in Italy as in Guangdong on February 25th, and in Iran as in Xinjiang on March 8th. The results showed that by June 15th the accumulated infection cases could have been reduced by 32.49% (South Korea), 98.16% (Italy) and 85.73% (Iran). The surface air temperature showed stronger association with transmission rate of COVID-19 than surface relative humidity. On the basis of these findings, disease control measures were shown to be particularly effective in flattening and shrinking the COVID-10 case curve, which could effectively reduce the severity of the disease and mitigate medical burden. The proposed empirical law and the SEIR-temporal moving window model can also be used to study infectious disease outbreaks worldwide.