Systematic review of predictive mathematical models of COVID-19 epidemic

Leveraging advances in data-driven deep learning methods for hybrid epidemic modeling

Mathematical modeling of epidemic dynamics is crucial to understand its underlying mechanisms, quantify important parameters, and make predictions that facilitate more informed decision-making. There are three major types of models: mechanistic models including the SEIR-type paradigm, alternative data-driven (DD) approaches, and hybrid models that combine mechanistic models with DD approaches. In this paper, we summarize our work in the COVID-19 Scenario Modeling Hub (SMH) for more than 12 rounds since early 2021 for informed decision support. We emphasize the importance of deep learning techniques for epidemic modeling via a flexible DD framework that substantially complements the mechanistic paradigm to evaluate various future epidemic scenarios. We start with a traditional curve-fitting approach to model cumulative COVID-19 based on the underlying SEIR-type mechanisms. Hospitalizations and deaths are modeled as binomial processes of cases and hospitalization, respectively. We further formulate two types of deep learning models based on multivariate long short term memory (LSTM) to address the challenges of more traditional DD models. The first LSTM is structurally similar to the curve fitting approach and assumes that hospitalizations and deaths are binomial processes of cases. Instead of using a predefined exponential curve, LSTM relies on the underlying data to identify the most appropriate functions, and is capable of capturing both long-term and short-term epidemic behaviors. We then relax the assumption of dependent inputs among cases, hospitalizations, and death. Another type of LSTM that handles all input time series as parallel signals, the independent multivariate LSTM, is developed. Independent multivariate LSTM can incorporate a wide range of data sources beyond traditional case-based epidemiological surveillance. The DD framework unleashes its potential in big data era with previously neglected heterogeneous surveillance data sources, such as syndromic, environment, genomic, serologic, infoveillance, and mobility data. DD approaches, especially LSTM, complement and integrate with the mechanistic modeling paradigm, provide a feasible alternative approach to model today's complex socio-epidemiological systems, and further leverage our ability to explore different scenarios for more informed decision-making during health emergencies.

Impact assessment of self-medication on COVID-19 prevalence in Gauteng, South Africa, using an age-structured disease transmission modelling framework

OBJECTIVE

To assess the impact of self-medication on the transmission dynamics of COVID-19 across different age groups, examine the interplay of vaccination and self-medication in disease spread, and identify the age group most prone to self-medication.

METHODS

We developed an age-structured compartmentalized epidemiological model to track the early dynamics of COVID-19. Age-structured data from the Government of Gauteng, encompassing the reported cumulative number of cases and daily confirmed cases, were used to calibrate the model through a Markov Chain Monte Carlo (MCMC) framework. Subsequently, uncertainty and sensitivity analyses were conducted on the model parameters.

RESULTS

We found that self-medication is predominant among the age group 15-64 (74.52%), followed by the age group 0-14 (34.02%), and then the age group 65+ (11.41%). The mean values of the basic reproduction number, the size of the first epidemic peak (the highest magnitude of the disease), and the time of the first epidemic peak (when the first highest magnitude occurs) are 4.16499, 241,715 cases, and 190.376 days, respectively. Moreover, we observed that self-medication among individuals aged 15-64 results in the highest spreading rate of COVID-19 at the onset of the outbreak and has the greatest impact on the first epidemic peak and its timing.

CONCLUSION

Studies aiming to understand the dynamics of diseases in areas prone to self-medication should account for this practice. There is a need for a campaign against COVID-19-related self-medication, specifically targeting the active population (ages 15-64).

Changing risk factors for developing SARS-CoV-2 infection from Delta to Omicron

BACKGROUND

One of the few studies to estimate infection risk with SARS-CoV-2 in the general population was the UK Office of National Statistics Infection Survey. This survey provided data that allowed us to describe and interpret apparent risk factors for testing positive for SARS-CoV-2 in a period when variants and COVID-19 controls experienced large changes.

METHOD

The ONS published estimates of likelihood of individuals testing positive in two week monitoring periods between 21st November 2021 and 7th May 2022, relating this positivity to social and behavioural factors. We applied meta-regression to these estimates of likelihood of testing positive to determine whether the monitored potential risk factors remained constant during the pandemic.

RESULTS

Some risk factors had consistent relationship with risk of infection (always protective or always linked to higher risk, throughout monitoring period). Other risk factors had variable relationship with risk of infection, with changes seeming to especially correlate with the emergence of Omicron BA.2 dominance. These variable factors were mask-wearing habits, history of foreign travel, household size, working status (retired or not) and contact with children or persons age over 70.

CONCLUSION

Relevance of some risk factors to likelihood of testing positive for SARS-CoV-2 may relate to reinfection risk, variant infectiousness and status of social distancing regulations.

A computational approach to identifiability analysis for a model of the propagation and control of COVID-19 in Chile

A computational approach is adapted to analyze the parameter identifiability of a compartmental model. The model is intended to describe the progression of the COVID-19 pandemic in Chile during the initial phase in early 2020 when government declared quarantine measures. The computational approach to analyze the structural and practical identifiability is applied in two parts, one for synthetic data and another for some Chilean regional data. The first part defines the identifiable parameter sets when these recover the true parameters used to create the synthetic data. The second part compares the results derived from synthetic data, estimating the identifiable parameter sets from regional Chilean epidemic data. Experiments provide evidence of the loss of identifiability if some initial conditions are estimated, the period of time used to fit is before the peak, and if a significant proportion of the population is involved in quarantine periods.

Pharmaceutical and non-pharmaceutical interventions for controlling the COVID-19 pandemic

Disease spread can be affected by pharmaceutical interventions (such as vaccination) and non-pharmaceutical interventions (such as physical distancing, mask-wearing and contact tracing). Understanding the relationship between disease dynamics and human behaviour is a significant factor to controlling infections. In this work, we propose a compartmental epidemiological model for studying how the infection dynamics of COVID-19 evolves for people with different levels of social distancing, natural immunity and vaccine-induced immunity. Our model recreates the transmission dynamics of COVID-19 in Ontario up to December 2021. Our results indicate that people change their behaviour based on the disease dynamics and mitigation measures. Specifically, they adopt more protective behaviour when mandated social distancing measures are in effect, typically concurrent with a high number of infections. They reduce protective behaviour when vaccination coverage is high or when mandated contact reduction measures are relaxed, typically concurrent with a reduction of infections. We demonstrate that waning of infection and vaccine-induced immunity are important for reproducing disease transmission in autumn 2021.

An analysis of the waning effect of COVID-19 vaccinations

Vaccine development is one of the key efforts to control the spread of coronavirus disease 2019 (COVID-19). However, it has become apparent that the immunity acquired through vaccination is not permanent, known as the waning effect. Therefore, monitoring the proportion of the population with immunity is essential to improve the forecasting of future waves of the pandemic. Despite this, the impact of the waning effect on forecasting accuracies has not been extensively studied. We proposed a method for the estimation of the effective immunity (EI) rate which represents the waning effect by integrating the second and booster doses of COVID-19 vaccines. The EI rate, with different periods to the onset of the waning effect, was incorporated into three statistical models and two machine learning models. Stringency Index, omicron variant BA.5 rate (BA.5 rate), booster shot rate (BSR), and the EI rate were used as covariates and the best covariate combination was selected using prediction error. Among the prediction results, Generalized Additive Model showed the best improvement (decreasing 86% test error) with the EI rate. Furthermore, we confirmed that South Korea's decision to recommend booster shots after 90 days is reasonable since the waning effect onsets 90 days after the last dose of vaccine which improves the prediction of confirmed cases and deaths. Substituting BSR with EI rate in statistical models not only results in better predictions but also makes it possible to forecast a potential wave and help the local community react proactively to a rapid increase in confirmed cases.

A Model for Predicting the Duration of Viral Shedding in Patients Who Had Been Hospitalized with Mild COVID-19: A Single-Center Retrospective Study

Background

Clinical decision-making is enhanced by the development of a mathematical model for prognosis prediction. Screening criteria associated with viral shedding time and developing a prediction model facilitate clinical decision-making and are, thus, of great medical value.

Methods

This study comprised 631 patients who were hospitalized with mild COVID-19 from a single center and 30 independent variables included. The data set was randomly divided into the training set (80%) and the validation set (20%). The outcome variable included viral shedding time and whether the viral shedding time >14 days, LASSO was used to screen the influencing factors.

Results

There were 321 males and 310 females among the 631 cases, with an average age of 62.1 years; the median viral shedding time was 12 days, and 68.8% of patients experienced viral shedding within 14 days, with fever (50.9%) and cough (44.2%) being the most common clinical manifestations. Using LASSO with viral shedding time as the outcome variable, the model with lambda as 0.1592 (λ = 0.1592) and 13 variables (eg the time from diagnosis to admission, constipation, cough, hs-CRP, IL-8, IL-1β, etc.) was more accurate. Factors were screened by LASSO and multivariable logistic regression with whether the viral shedding time >14 days as the outcome variable, five variables, including the time from diagnosis to admission, CD4 cell count, Ct value of ORF1ab, constipation, and IL-8, were included, and a nomogram was drawn; after model validation, the consistency index was 0.888, the AUC was 0.847, the sensitivity was 0.744, and the specificity was 0.830.

Conclusion

A clinical model developed after LASSO regression was used to identify the factors that influence the viral shedding time. The predicted performance of the model was good, and it was useful for the allocation of medical resources.

Exposure notification system activity as a leading indicator for SARS-COV-2 caseload forecasting

PURPOSE

Digital methods to augment traditional contact tracing approaches were developed and deployed globally during the COVID-19 pandemic. These "Exposure Notification (EN)" systems present new opportunities to support public health interventions. To date, there have been attempts to model the impact of such systems, yet no reports have explored the value of real-time system data for predictive epidemiological modeling.

METHODS

We investigated the potential to short-term forecast COVID-19 caseloads using data from California's implementation of the Google Apple Exposure Notification (GAEN) platform, branded as CA Notify. CA Notify is a digital public health intervention leveraging resident's smartphones for anonymous EN. We extended a published statistical model that uses prior case counts to investigate the possibility of predicting short-term future case counts and then added EN activity to test for improved forecast performance. Additional predictive value was assessed by comparing the pandemic forecasting models with and without EN activity to the actual reported caseloads from 1-7 days in the future.

RESULTS

Observation of time series presents noticeable evidence for temporal association of system activity and caseloads. Incorporating earlier ENs in our model improved prediction of the caseload counts. Using Bayesian inference, we found nonzero influence of EN terms with probability one. Furthermore, we found a reduction in both the mean absolute percentage error and the mean squared prediction error, the latter of at least 5% and up to 32% when using ENs over the model without.

CONCLUSIONS

This preliminary investigation suggests smartphone based ENs can significantly improve the accuracy of short-term forecasting. These predictive models can be readily deployed as local early warning systems to triage resources and interventions.

Leveraging an epidemic-economic mathematical model to assess human responses to COVID-19 policies and disease progression

It is imperative that resources are channelled towards programs that are efficient and cost effective in combating the spread of COVID-19, the disease caused by the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2). This study proposed and analyzed control strategies for that purpose. We developed a mathematical disease model within an optimal control framework that allows us to investigate the best approach for curbing COVID-19 epidemic. We address the following research question: what is the role of community compliance as a measure for COVID-19 control? Analyzing the impact of community compliance of recommended guidelines by health authorities-examples, social distancing, face mask use, and sanitizing-coupled with efforts by health authorities in areas of vaccine provision and effective quarantine-showed that the best intervention in addition to implementing vaccination programs and effective quarantine measures, is the active incorporation of individuals' collective behaviours, and that resources should also be directed towards community campaigns on the importance of face mask use, social distancing, and frequent sanitizing, and any other collective activities. We also demonstrated that collective behavioral response of individuals influences the disease dynamics; implying that recommended health policy should be contextualized.

A Multi-SCALE Community Network-Based SEIQR Model to Evaluate the Dynamic NPIs of COVID-19

Regarding the problem of epidemic outbreak prevention and control, infectious disease dynamics models cannot support urban managers in reducing urban-scale healthcare costs through community-scale control measures, as they usually have difficulty meeting the requirements for simulation at different scales. In this paper, we propose combining contact networks at different spatial scales to study the COVID-19 outbreak in Shanghai from March to July 2022, calculate the initial Rt through the number of cases at the beginning of the outbreak, and evaluate the effectiveness of dynamic non-pharmaceutical interventions (NPIs) adopted at different time periods in Shanghai using our proposed approach. In particular, our proposed contact network is a three-layer multi-scale network that is used to distinguish social interactions occurring in areas of different sizes, as well as to distinguish between intensive and non-intensive population contacts. This susceptible-exposure-infection-quarantine-recovery (SEIQR) epidemic model constructed based on a multi-scale network can more effectively assess the feasibility of small-scale control measures, such as assessing community quarantine measures and mobility restrictions at different moments and phases of an epidemic. Our experimental results show that this model can meet the simulation needs at different scales, and our further discussion and analysis show that the spread of the epidemic in Shanghai from March to July 2022 can be successfully controlled by implementing a strict long-term dynamic NPI strategy.

Hybrid discrete-time-continuous-time models and a SARS CoV-2 mystery: Sub-Saharan Africa's low SARS CoV-2 disease burden

Worldwide, the recent SARS-CoV-2 virus has infected more than 670 million people and killed nearly 67.0 million. In Africa, the number of confirmed COVID-19 cases was approximately 12.7 million as of January 11, 2023, that is about 2% of the infections around the world. Many theories and modeling techniques have been used to explain this lower-than-expected number of reported COVID-19 cases in Africa relative to the high disease burden in most developed countries. We noted that most epidemiological mathematical models are formulated in continuous-time interval, and taking Cameroon in Sub-Saharan Africa, and New York State in the USA as case studies, in this paper we developed parameterized hybrid discrete-time-continuous-time models of COVID-19 in Cameroon and New York State. We used these hybrid models to study the lower-than-expected COVID-19 infections in developing countries. We then used error analysis to show that a time scale for a data-driven mathematical model should match that of the actual data reporting.

The role of machine learning in health policies during the COVID-19 pandemic and in long COVID management

The ongoing COVID-19 pandemic is arguably one of the most challenging health crises in modern times. The development of effective strategies to control the spread of SARS-CoV-2 were major goals for governments and policy makers. Mathematical modeling and machine learning emerged as potent tools to guide and optimize the different control measures. This review briefly summarizes the SARS-CoV-2 pandemic evolution during the first 3 years. It details the main public health challenges focusing on the contribution of mathematical modeling to design and guide government action plans and spread mitigation interventions of SARS-CoV-2. Next describes the application of machine learning methods in a series of study cases, including COVID-19 clinical diagnosis, the analysis of epidemiological variables, and drug discovery by protein engineering techniques. Lastly, it explores the use of machine learning tools for investigating long COVID, by identifying patterns and relationships of symptoms, predicting risk indicators, and enabling early evaluation of COVID-19 sequelae.

Modeling COVID-19 hospital admissions and occupancy in the Netherlands

We describe the models we built for predicting hospital admissions and bed occupancy of COVID-19 patients in the Netherlands. These models were used to make short-term decisions about transfers of patients between regions and for long-term policy making. For forecasting admissions we developed a new technique using linear programming. To predict occupancy we fitted residual lengths of stay and used results from queueing theory. Our models increased the accuracy of and trust in the predictions and helped manage the pandemic, minimizing the impact in terms of beds and maximizing remaining capacity for other types of care.

Insight into Delta variant dominated second wave of COVID-19 in Nepal

OBJECTIVE

To study the spreading nature of Delta variant (B.1.617.2) dominated COVID-19 in Nepal to help the policymakers assess and manage health care facilities and vaccination programs.

METHODS

Deterministic mathematical models in the form of systems of ordinary differential equations were developed to describe the COVID-19 transmission in the high- and the low-risk regions of Nepal. The models were validated using the multiple data sets containing daily new cases in the whole country, the high-risk region, the low-risk region, and cases needing medical care, ICU, and ventilator.

RESULTS

We found the reproduction number of R_t=4.2 at the beginning of the second wave, larger than the first wave (∼1.8 estimated previously), indicating that the transmissibility of Delta variant is higher than the wild-type circulated during the first wave. Model predicts that ∼5% of the COVID-19 cases were reported in Nepal, estimating the seroprevalence of ∼63.9% as of July 2021, consistent with the survey conducted by the Government of Nepal. The seroprevalence was expected to reach 94.46% by April 2022, among which ∼46% would have both infection and vaccination. The expected cases from September 2021 to April 2022 is 111,300, among which 11,890 people might need medical care, 3590 need ICU, and 953 need ventilators. The COVID-19 cases and medical care needs could be significantly reduced with proper implementation of vaccination and social distancing.

CONCLUSIONS

The data-driven mathematical models are useful to assess control programs in resource-limited countries. The appropriate combination of vaccination and social distancing are necessary to keep the pandemic under-control and manage the medical care facilities in Nepal.

Simulating and Forecasting the COVID-19 Spread in a U.S. Metropolitan Region with a Spatial SEIR Model

The global COVID-19 pandemic has taken a heavy toll on health, social, and economic costs since the end of 2019. Predicting the spread of a pandemic is essential to developing effective intervention policies. Since the beginning of this pandemic, many models have been developed to predict its pathways. However, the majority of these models assume homogeneous dynamics over the geographic space, while the pandemic exhibits substantial spatial heterogeneity. In addition, spatial interaction among territorial entities and variations in their magnitude impact the pandemic dynamics. In this study, we used a spatial extension of the SEIR-type epidemiological model to simulate and predict the 4-week number of COVID-19 cases in the Charlotte-Concord-Gastonia Metropolitan Statistical Area (MSA), USA. We incorporated a variety of covariates, including mobility, pharmaceutical, and non-pharmaceutical interventions, demographics, and weather data to improve the model's predictive performance. We predicted the number of COVID-19 cases for up to four weeks in the 10 counties of the studied MSA simultaneously over the time period 29 March 2020 to 13 March 2021, and compared the results with the reported number of cases using the root-mean-squared error (RMSE) metric. Our results highlight the importance of spatial heterogeneity and spatial interactions among locations in COVID-19 pandemic modeling.

Modeling approaches for early warning and monitoring of pandemic situations as well as decision support

The COVID-19 pandemic has highlighted the lack of preparedness of many healthcare systems against pandemic situations. In response, many population-level computational modeling approaches have been proposed for predicting outbreaks, spatiotemporally forecasting disease spread, and assessing as well as predicting the effectiveness of (non-) pharmaceutical interventions. However, in several countries, these modeling efforts have only limited impact on governmental decision-making so far. In light of this situation, the review aims to provide a critical review of existing modeling approaches and to discuss the potential for future developments.

Control in Probability for SDE Models of Growth Population

In this paper, we consider a (control) optimization problem, which involves a stochastic dynamic. The model proposes selecting the best control function that keeps bounded a stochastic process over an interval of time with a high probability level. Here, the stochastic process is governed by a stochastic differential equation affected by a stochastic process. This setting becomes a chance-constrained control optimization problem, where the constraint is given by the probability level of infinitely many random inequalities. Since such a model is challenging, we discretize the dynamic and restrict the space of control functions to piecewise mappings. On the one hand, it transforms the infinite-dimensional optimization problem into a finite-dimensional one. On the other hand, it allows us to provide the well-posedness of the problem and approximation. Finally, the results are illustrated with numerical results, where classical model for the growth of a population are considered.

An evaluation of prospective COVID-19 modelling studies in the USA: from data to science translation

Infectious disease modelling can serve as a powerful tool for situational awareness and decision support for policy makers. However, COVID-19 modelling efforts faced many challenges, from poor data quality to changing policy and human behaviour. To extract practical insight from the large body of COVID-19 modelling literature available, we provide a narrative review with a systematic approach that quantitatively assessed prospective, data-driven modelling studies of COVID-19 in the USA. We analysed 136 papers, and focused on the aspects of models that are essential for decision makers. We have documented the forecasting window, methodology, prediction target, datasets used, and geographical resolution for each study. We also found that a large fraction of papers did not evaluate performance (25%), express uncertainty (50%), or state limitations (36%). To remedy some of these identified gaps, we recommend the adoption of the EPIFORGE 2020 model reporting guidelines and creating an information-sharing system that is suitable for fast-paced infectious disease outbreak science.

Stochastic epidemiological model: Simulations of the SARS-CoV-2 spreading in Mexico

In this paper we model the spreading of the SARS-CoV-2 in Mexico by introducing a new stochastic approximation constructed from first principles, where the number of new infected individuals caused by a single infectious individual per unit time (a day), is a random variable of a time-dependent Poisson distribution. The model, structured on the basis of a Latent-Infectious-(Recovered or Deceased) (LI(RD)) compartmental approximation together with a modulation of the mean number of new infections (the Poisson parameters), provides a good tool to study theoretical and real scenarios.

Mathematical modeling of the impact of Omicron variant on the COVID-19 situation in South Korea

The rise of newer coronavirus disease 2019 (COVID-19) variants has brought a challenge to ending the spread of COVID-19. The variants have a different fatality, morbidity, and transmission rates and affect vaccine efficacy differently. Therefore, the impact of each new variant on the spread of COVID-19 is of interest to governments and scientists. Here, we proposed mathematical SEIQRDVP and SEIQRDV3P models to predict the impact of the Omicron variant on the spread of the COVID-19 situation in South Korea. SEIQEDVP considers one vaccine level at a time while SEIQRDV3P considers three vaccination levels (only one dose received, full doses received, and full doses + booster shots received) simultaneously. The omicron variant's effect was contemplated as a weighted sum of the delta and omicron variants' transmission rate and tuned using a hyperparameter k. Our models' performances were compared with common models like SEIR, SEIQR, and SEIQRDVUP using the root mean square error (RMSE). SEIQRDV3P performed better than the SEIQRDVP model. Without consideration of the variant effect, we don't see a rapid rise in COVID-19 cases and high RMSE values. But, with consideration of the omicron variant, we predicted a continuous rapid rise in COVID-19 cases until maybe herd immunity is developed in the population. Also, the RMSE value for the SEIQRDV3P model decreased by 27.4%. Therefore, modeling the impact of any new risen variant is crucial in determining the trajectory of the spread of COVID-19 and determining policies to be implemented.

Predictive Models for Forecasting Public Health Scenarios: Practical Experiences Applied during the First Wave of the COVID-19 Pandemic

Background: Forecasting the behavior of epidemic outbreaks is vital in public health. This makes it possible to anticipate the planning and organization of the health system, as well as possible restrictive or preventive measures. During the COVID-19 pandemic, this need for prediction has been crucial. This paper attempts to characterize the alternative models that were applied in the first wave of this pandemic context, trying to shed light that could help to understand them for future practical applications. Methods: A systematic literature search was performed in standardized bibliographic repertoires, using keywords and Boolean operators to refine the findings, and selecting articles according to the main PRISMA 2020 statement recommendations. Results: After identifying models used throughout the first wave of this pandemic (between March and June 2020), we begin by examining standard data-driven epidemiological models, including studies applying models such as SIR (Susceptible-Infected-Recovered), SQUIDER, SEIR, time-dependent SIR, and other alternatives. For data-driven methods, we identify experiences using autoregressive integrated moving average (ARIMA), evolutionary genetic programming machine learning, short-term memory (LSTM), and global epidemic and mobility models. Conclusions: The COVID-19 pandemic has led to intensive and evolving use of alternative infectious disease prediction models. At this point it is not easy to decide which prediction method is the best in a generic way. Moreover, although models such as the LSTM emerge as remarkably versatile and useful, the practical applicability of the alternatives depends on the specific context of the underlying variable and on the information of the target to be prioritized. In addition, the robustness of the assessment is conditioned by heterogeneity in the quality of information sources and differences in the characteristics of disease control interventions. Further comprehensive comparison of the performance of models in comparable situations, assessing their predictive validity, is needed. This will help determine the most reliable and practical methods for application in future outbreaks and eventual pandemics.

The Multi-Compartment SI(RD) Model with Regime Switching: An Application to COVID-19 Pandemic

We study—with existence and unicity results—a variant of the SIR model for an infectious disease incorporating both the possibility of a death outcome—in a short period of time—and a regime switch that can account for the mitigation measures used to control the spreading of the infections, such as a total lockdown. This model is parametrised by three parameters: the basic reproduction number, the mortality rate of the infected, and the duration of the disease. We discuss a particular example of application to Portuguese COVID-19 data in two short periods just after the start of the epidemic in 4 March 2020, with the first two cases dated that day. We propose a simple and effective method for the estimation of the main parameters of the disease, namely, the basic reproduction number and the mortality rate of the infected. We correct these estimated values to take into account the asymptomatic non-diagnosed members of the population. We compare the outcome of the model in the cases of the existence, or not, of a regime switch, and under three different scenarios, with a remarkable agreement between model and data deaths in the case of our basis scenario. In a final short remark, we deal with the existence of symmetries for the proposed model.