Mathematical modeling of COVID-19 and Omicron outbreak spread: Optimal control approach for intervention strategies

In Morocco, 966,777 confirmed cases and 14,851 confirmed deaths because of COVID-19 were recorded as of January 1, 2022. Recently, a new strain of COVID-19, the so-called Omicron variant, was reported in Morocco, which is considered to be more dangerous than the existing COVID-19 virus. To end this ongoing global COVID-19 pandemic and Omicron variant, there is an urgent need to implement multiple population-wide policies like vaccination, testing more people, and contact tracing. To forecast the pandemic's progress and put together a strategy to effectively contain it, we propose a new hybrid mathematical model that predicts the dynamics of COVID-19 in Morocco, considering the difference between COVID-19 and the Omicron variant, and investigate the impact of some control strategies on their spread. The proposed model monitors the dynamics of eight compartments, namely susceptible (S)$$ (S) $$, exposed (E)$$ (E) $$, infected with COVID-19 (I)$$ (I) $$, infected with Omicron (IO)$$ \left({I}_O\right) $$, hospitalized (H)$$ (H) $$, people in intensive care units (U)$$ (U) $$, quarantined (Q)$$ (Q) $$, and recovered (R)$$ (R) $$, collectively expressed as SEIIOHUQR$$ SEI{I}_O HUQR $$. We calculate the basic reproduction number Script capital R0$$ {\mathcal{R}}_0 $$, studying the local and global infection-free equilibrium stability, a sensitivity analysis is conducted to determine the robustness of model predictions to parameter values, and the sensitive parameters are estimated from the real data on the COVID-19 pandemic in Morocco. We incorporate two control variables that represent vaccination and diagnosis of infected individuals and we propose an optimal strategy for an awareness program that will help to decrease the rate of the virus' spread. Pontryagin's maximum principle is used to characterize the optimal controls, and the optimality system is solved by an iterative method. Finally, extensive numerical simulations are employed with and without controls to illustrate our results using MATLAB software. Our results reveal that achieving a reduction in the contact rate between uninfected and infected individuals by vaccinating and diagnosing the susceptible individuals, can effectively reduce the basic reproduction number and tends to decrease the intensity of epidemic peaks, spreading the maximal impact of an epidemic over an extended period of time. The model simulations demonstrate that the elimination of the ongoing SARS-COV-2 pandemic and its variant Omicron in Morocco is possible by implementing, at the start of the pandemic, a strategy that combines the two variables of control mentioned above. Our predictions are based on real data with reasonable assumptions.

Modeling COVID-19 with big mobility data: Surveillance and reaffirming the people in the data

To better understand the COVID-19 pandemic, public health researchers turned to "big mobility data”—location data collected from mobile devices by companies engaged in surveillance capitalism. Publishing formerly private big mobility datasets, firms trumpeted their efforts to "fight” COVID-19 and researchers highlighted the potential of big mobility data to improve infectious disease models tracking the pandemic. However, these collaborations are defined by asymmetries in information, access, and power. The release of data is characterized by a lack of obligation on the part of the data provider towards public health goals, particularly those committed to a community-based, participatory model. There is a lack of appropriate reciprocities between data company, data subject, researcher, and community. People are de-centered, surveillance is de-linked from action while the agendas of public health and surveillance capitalism grow closer. This article argues that the current use of big mobility data in the COVID-19 pandemic represents a poor approach with respect to community and person-centered frameworks. © The Author(s) 2023.

LSTM-based Forecasting using Policy Stringency and Time-varying Parameters of the SIR Model for COVID-19

Accurate forecasting of the number of infections is an important task that can allow health care decision makers to allocate medical resources efficiently during a pandemic. Two approaches have been combined, a stochastic model by Vega et al. for modelling infectious disease and Long Short-Term Memory using COVID-19 data and government's policies. In the proposed model, LSTM functions as a nonlinear adaptive filter to modify the outputs of the SIR model for more accurate forecasts one to four weeks in the future. Our model outperforms most models among the CDC models using the United States data. We also applied the model on the Canadian data from two provinces, Saskatchewan and Ontario where it performs with a low mean absolute percentage error. © 2023 IEEE.

Measuring the Interference Effect of Bots in Disseminating Opposing Viewpoints Related to COVID-19 on Twitter Using Epidemiological Modeling

The activity of bots can influence the opinions and behavior of people, especially within the political landscape where hot-button issues are debated. To evaluate the bot presence among the propagation trends of opposing politically-charged viewpoints on Twitter, we collected a comprehensive set of hashtags related to COVID-19. We then applied both the SIR (Susceptible, Infected, Recovered) and the SEIZ (Susceptible, Exposed, Infected, Skeptics) epidemiological models to three different dataset states including, total tweets in a dataset, tweets by bots, and tweets by humans. Our results show the ability of both models to model the diffusion of opposing viewpoints on Twitter, with the SEIZ model outperforming the SIR. Additionally, although our results show that both models can model the diffusion of information spread by bots with some difficulty, the SEIZ model outperforms. Our analysis also reveals that the magnitude of the bot-induced diffusion of this type of information varies by subject. © 2023 IEEE Computer Society. All rights reserved.

Applying an Epidemiological Model to Evaluate the Propagation of Toxicity related to COVID-19 on Twitter

The prevalence of social media has increased the propagation of toxic behavior among users. Toxicity can have detrimental effects on users' emotion and insight and disrupt beneficial discourse. Evaluating the propagation of toxic content on social networks such as Twitter can provide the opportunity to understand the characteristics of this harmful phenomena. Identifying a mathematical model that can describe the propagation of toxic content on social networks is a valuable approach to this evaluation. In this paper, we utilized the SEIZ (Susceptible, Exposed, Infected, Skeptic) epidemiological model to find a mathematical model for the propagation of toxic content related to COVID-19 topics on Twitter. We collected Twitter data based on specific hashtags related to different COVID-19 topics such as covid, mask, vaccine, and lockdown. The findings demonstrate that the SEIZ model can properly model the propagation of toxicity on a social network with relatively low error. Determining an efficient mathematical model can increase the understanding of the dynamics of the propagation of toxicity on a social network such as Twitter. This understanding can help researchers and policymakers to develop methods to limit the propagation of toxic content on social networks. © 2022 IEEE Computer Society. All rights reserved.

Effect of sojourn time distributions on the early dynamics of COVID-19 outbreak.

Compartmental models are commonly used in practice to investigate the dynamical response of infectious diseases such as the COVID-19 outbreak. Such models generally assume exponentially distributed latency and infectiousness periods. However, the exponential distribution assumption fails when the sojourn times are expected to distribute around their means. This study aims to derive a novel S (Susceptible)-E (Exposed)-P (Presymptomatic)-A (Asymptomatic)-D (Symptomatic)-C (Reported) model with arbitrarily distributed latency, presymptomatic infectiousness, asymptomatic infectiousness, and symptomatic infectiousness periods. The SEPADC model is represented by nonlinear Volterra integral equations that generalize ordinary differential equation-based models. Our primary aim is the derivation of a general relation between intrinsic growth rate r and basic reproduction number R0 with the help of the well-known Lotka-Euler equation. The resulting r-R0 equation includes separate roles of various stages of the infection and their sojourn time distributions. We show that R0 estimates are considerably affected by the choice of the sojourn time distributions for relatively higher values of r. The well-known exponential distribution assumption has led to the underestimation of R0 values for most of the countries. Exponential and delta-distributed sojourn times have been shown to yield lower and upper bounds of the R0 values depending on the r values. In quantitative experiments, R0 values of 152 countries around the world were estimated through our novel formulae utilizing the parameter values and sojourn time distributions of the COVID-19 pandemic. The global convergence, R0=4.58, has been estimated through our novel formulation. Additionally, we have shown that increasing the shape parameter of the Erlang distributed sojourn times increases the skewness of the epidemic curves in entire dynamics.

A general modeling framework for quantitative tracking, accurate prediction of ICU, and assessing vaccination for COVID-19 in Chile.

Background: One of the main lessons of the COVID-19 pandemic is that we must prepare to face another pandemic like it. Consequently, this article aims to develop a general framework consisting of epidemiological modeling and a practical identifiability approach to assess combined vaccination and non-pharmaceutical intervention (NPI) strategies for the dynamics of any transmissible disease. Materials and methods: Epidemiological modeling of the present work relies on delay differential equations describing time variation and transitions between suitable compartments. The practical identifiability approach relies on parameter optimization, a parametric bootstrap technique, and data processing. We implemented a careful parameter optimization algorithm by searching for suitable initialization according to each processed dataset. In addition, we implemented a parametric bootstrap technique to accurately predict the ICU curve trend in the medium term and assess vaccination. Results: We show the framework's calibration capabilities for several processed COVID-19 datasets of different regions of Chile. We found a unique range of parameters that works well for every dataset and provides overall numerical stability and convergence for parameter optimization. Consequently, the framework produces outstanding results concerning quantitative tracking of COVID-19 dynamics. In addition, it allows us to accurately predict the ICU curve trend in the medium term and assess vaccination. Finally, it is reproducible since we provide open-source codes that consider parameter initialization standardized for every dataset. Conclusion: This work attempts to implement a holistic and general modeling framework for quantitative tracking of the dynamics of any transmissible disease, focusing on accurately predicting the ICU curve trend in the medium term and assessing vaccination. The scientific community could adapt it to evaluate the impact of combined vaccination and NPIs strategies for COVID-19 or any transmissible disease in any country and help visualize the potential effects of implemented plans by policymakers. In future work, we want to improve the computational cost of the parametric bootstrap technique or use another more efficient technique. The aim would be to reconstruct epidemiological curves to predict the combined NPIs and vaccination policies' impact on the ICU curve trend in real-time, providing scientific evidence to help anticipate policymakers' decisions.

A spatiotemporal spread of COVID-19 pandemic with vaccination optimal control strategy: A case study in Morocco

On March 2, 2020, the Moroccan Ministry of Health announced the first case of COVID-19 in the city of Casablanca for a Moroccan tourist who came from Italy. The SARS-COV-2 virus has spread throughout the Kingdom of Morocco. In this paper, we study the spatiotemporal transmission of the COVID-19 virus in the Kingdom of Morocco. By sup-porting a SIW IHR partial differential equation for the spread of the COVID-19 pandemic in Morocco as a case study. Our main goal is to characterize the optimum order of control-ling the spread of the COVID-19 pandemic by adopting a vaccination strategy, the aim of which is to reduce the number of susceptible and infected individuals without vaccination and to maximize the recovered individuals by reducing the cost of vaccination using one of the vaccines approved by the World Health Organization. To do this, we proved the existence of a pair of control. It provides a description of the optimal controls in terms of state and auxiliary functions. Finally, we provided numerical simulations of data related to the transmission of the COVID-19 pandemic. Numerical results are presented to illustrate the effectiveness of the adopted approach. ©2023 Lviv Polytechnic National University.

Policy Driven Epidemiological (PDE) Model for Prediction of COVID-19 in India

The fast spread of COVID-19 has made it a global issue. Despite various efforts, proper forecasting of COVID-19 spread is still in question. Government lockdown policies play a critical role in controlling the spread of coronavirus. However, existing prediction models have ignored lockdown policies and only focused on other features such as age, sex ratio, travel history, daily cases etc. This work proposes a Policy Driven Epidemiological (PDE) Model with Temporal, Structural, Profile, Policy and Interaction Features to forecast COVID-19 in India and its 6 states. PDE model integrates two models: Susceptible-Infected-Recovered-Deceased (SIRD) and Topical affinity propagation (TAP) model to predict the infection spread within a network for a given set of infected users. The performance of PDE model is assessed with respect to linear regression model, three epidemiological models (Susceptible-Infectious-Recovered-Model (SIR), Susceptible-Exposed-Infectious-Recovered-Model (SEIR) and SIRD) and two diffusion models (Time Constant Cascade Model and Time Decay Feature Cascade Model). Experimental evaluation for India and six Indian states with respect to different government policies from 15th June to 30th June, i.e., Maharashtra, Gujarat, Tamil Nadu, Delhi, Rajasthan and Uttar Pradesh divulge that prediction accuracy of PDE model is in close proximity with the real time for the considered time frame. Results illustrate that PDE model predicted the COVID-19 cases up to 94% accuracy and reduced the Normalize Mean Squared Error (NMSE) up to 50%, 35% and 42% with respect to linear regression, epidemiological models and diffusion models, respectively. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Epidemiological Modeling with Sir and Arima Dynamic Models and Machine Learning to Predict the Future Behavior of Covid-19 in Panama

Mathematical models SIR and ARIMA were used, within an epidemiological approach, to adjust them to the COVID-19 pandemic data in Panama to establish a scientific criterion for taking decisions for the effects control that this pandemic has brought. Based on the predictions made from the adjustments of these models, it was concluded that they can be adjusted correctly to the data, allowing to make short-term predictions in a satisfactory way, however, if a more accurate model were to be carried out, independent variables could be included, besides time, such as mobility restrictions. This work lays down the foundations for future investigations of epidemiological models in Panama due to its exposition of mathematical model's comparison used to analyze the behavior of the COVID-19 Pandemic. Jupyter Notebook, GitHub, Machine Learning libraries and mathematical software such as Wolfram Mathematica were used. Adjustment of data was performed through statistical techniques and, for this prediction, statistical software Minitab and E-Views were also used. © 2022 IEEE.

Individual-based epidemiological model of COVID19 using location data

Because human movement spreads infection, and mobility is a good proxy for other social distancing measures, human mobility has been an important factor in the COVID19 epidemic. Therefore, the control of human mobility is one of the countermeasures used to suppress an epidemic.As a notable feature, COVID19 has had multiple waves (subepidemics). Understanding the causes of the start and end of each wave has important implications for a policy evaluation and the timely implementation of countermeasures. Some of the waves have been correlated with the changes in mobility, and some can be attributed to the emergence of new variants. However, the start and end of some of the waves are difficult to explain through known factors.To evaluate the effect of human mobility, we built a stochastic model incorporating individual movements of 500,000 people obtained from anonymized, user-approved location data of smartphones throughout Japan. Instead of using aggregate values of human mobility, our model tracks the movements of individuals and predicts the infection of all persons within the entire country. Although the model only has a single static parameter, it successfully reproduced the occurrence of three waves of the number of confirmed cases within the study period of March 01 to December 31, 2020 in Japan. It was previously difficult to explain the end of the second wave and the start of the third wave in the study period by human mobility alone. Our results suggest the importance of tracking individual movements instead of relaying the aggregate values of human mobility. © 2022 IEEE.

Human Mobility Driven Modeling of an Infectious Disease

In conventional disease models, disease properties are dominant parameters (e.g., infection rate, incubation pe-riod). As seen in the recent literature on infectious diseases, human behavior - particularly mobility - plays a crucial role in spreading diseases. This paper proposes an epidemiological model named SEIRD+m that considers human mobility instead of modeling disease properties alone. SEIRD+m relies on the core deterministic epidemic model SEIR (Susceptible, Exposed, Infected, and Recovered), adds a new compartment D - Dead, and enhances each SEIRD component by human mobility information (such as time, location, and movements) retrieved from cell-phone data collected by SafeGraph. We demonstrate a way to reduce the number of infections and deaths due to COVID-19 by restricting mobility on specific Census Block Groups (CBGs) detected as COVID-19 hotspots. A case study in this paper depicts that a reduction of mobility by 50 % could help reduce the number of infections and deaths in significant percentages in different population groups based on race, income, and age. © 2022 IEEE.

Projection of healthcare demand in Germany and Switzerland urged by Omicron wave (January-March 2022).

In January 2022, after the implementation of broad vaccination programs, the Omicron wave was propagating across Europe. There was an urgent need to understand how population immunity affects the dynamics of the COVID-19 pandemic when the loss of vaccine protection was concurrent with the emergence of a new variant of concern. In particular, assessing the risk of saturation of the healthcare systems was crucial to manage the pandemic and allow a transition towards the endemic course of SARS-CoV-2 by implementing more refined mitigation strategies that shield the most vulnerable groups and protect the healthcare systems. We investigated the epidemic dynamics by means of compartmental models that describe the age-stratified social-mixing and consider vaccination status, type, and waning of the efficacy. In response to the acute situation, our model aimed at (i) providing insight into the plausible scenarios that were likely to occur in Switzerland and Germany in the midst of the Omicron wave, (ii) informing public health authorities, and (iii) helping take informed decisions to minimize negative consequences of the pandemic. Despite the unprecedented numbers of new positive cases, our results suggested that, in all plausible scenarios, the wave was unlikely to create an overwhelming healthcare demand; due to the lower hospitalization rate and the effectiveness of the vaccines in preventing a severe course of the disease. This prediction came true and the healthcare systems in Switzerland and Germany were not pushed to the limit, despite the unprecedentedly large number of infections. By retrospective comparison of the model predictions with the official reported data of the epidemic dynamic, we demonstrate the ability of the model to capture the main features of the epidemic dynamic and the corresponding healthcare demand. In a broader context, our framework can be applied also to endemic scenarios, offering quantitative support for refined public health interventions in response to recurring waves of COVID-19 or other infectious diseases.

Recent progress on wastewater-based epidemiology for COVID-19 surveillance: A systematic review of analytical procedures and epidemiological modeling.

On March 11, 2020, the World Health Organization declared the coronavirus disease 2019 (COVID-19), whose causative agent is the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), a pandemic. This virus is predominantly transmitted via respiratory droplets and shed via sputum, saliva, urine, and stool. Wastewater-based epidemiology (WBE) has been able to monitor the circulation of viral pathogens in the population. This tool demands both in-lab and computational work to be meaningful for, among other purposes, the prediction of outbreaks. In this context, we present a systematic review that organizes and discusses laboratory procedures for SARS-CoV-2 RNA quantification from a wastewater matrix, along with modeling techniques applied to the development of WBE for COVID-19 surveillance. The goal of this review is to present the current panorama of WBE operational aspects as well as to identify current challenges related to it. Our review was conducted in a reproducible manner by following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines for systematic reviews. We identified a lack of standardization in wastewater analytical procedures. Regardless, the reverse transcription-quantitative polymerase chain reaction (RT-qPCR) approach was the most reported technique employed to detect and quantify viral RNA in wastewater samples. As a more convenient sample matrix, we suggest the solid portion of wastewater to be considered in future investigations due to its higher viral load compared to the liquid fraction. Regarding the epidemiological modeling, the data-driven approach was consistently used for the prediction of variables associated with outbreaks. Future efforts should also be directed toward the development of rapid, more economical, portable, and accurate detection devices.

Optimizing non-pharmaceutical intervention strategies against COVID-19 using artificial intelligence.

One key task in the early fight against the COVID-19 pandemic was to plan non-pharmaceutical interventions to reduce the spread of the infection while limiting the burden on the society and economy. With more data on the pandemic being generated, it became possible to model both the infection trends and intervention costs, transforming the creation of an intervention plan into a computational optimization problem. This paper proposes a framework developed to help policy-makers plan the best combination of non-pharmaceutical interventions and to change them over time. We developed a hybrid machine-learning epidemiological model to forecast the infection trends, aggregated the socio-economic costs from the literature and expert knowledge, and used a multi-objective optimization algorithm to find and evaluate various intervention plans. The framework is modular and easily adjustable to a real-world situation, it is trained and tested on data collected from almost all countries in the world, and its proposed intervention plans generally outperform those used in real life in terms of both the number of infections and intervention costs.

Project-based learning for an online course of simulation engineering: From bioreactor to epidemiological modeling

Before the pandemic, distance learning was not a widely adopted option for science and engineering programs where in some courses, such as chemistry, electromagnetism, or fluid mechanics, etc., attending to laboratories and workshops was in most cases mandatory. The lockdown forced us to innovate, searching alternative ways to teach experimental phenomena, suddenly replaced with simulation science and technology, subjects that although rely on computers, also suffered changes from the transition. In this contribution, we propose an undergraduate course on simulation for chemical engineering, departing from the fact that modeling, and simulation are multipurpose and multidisciplinary tools. The course aims to reinforce the concepts of dynamical systems by using analogies between process engineering examples and other disciplines, particularly, epidemiology. For this purpose, a final project on modeling the dynamics of the COVID 19 pandemic in Mexico was designed and validated with a public database from the Mexican Secretariat of Health. By doing this, the students got in touch with the evolution of the dynamics outside of school hours, since it was common to see weekly updates and extrapolation trends of the pandemic, thus applying their skills to the final project. It was found that success factors were the use of official data, the use of Graphical User Interfaces to explore diverse simulation scenarios and the final project. The transition to the Distance Learning faced several challenges that were partially coped with the redesign of the course. © 2023 Institution of Chemical Engineers

COVID-19 Test Allocation Strategy to Mitigate SARS-CoV-2 Infections across School Districts.

In response to COVID-19, schools across the United States closed in early 2020; many did not fully reopen until late 2021. Although regular testing of asymptomatic students, teachers, and staff can reduce transmission risks, few school systems consistently used proactive testing to safeguard return to classrooms. Socioeconomically diverse public school districts might vary testing levels across campuses to ensure fair, effective use of limited resources. We describe a test allocation approach to reduce overall infections and disparities across school districts. Using a model of SARS-CoV-2 transmission in schools fit to data from a large metropolitan school district in Texas, we reduced incidence between the highest and lowest risk schools from a 5.6-fold difference under proportional test allocation to 1.8-fold difference under our optimized test allocation. This approach provides a roadmap to help school districts deploy proactive testing and mitigate risks of future SARS-CoV-2 variants and other pathogen threats.

A Predictive Model for R0(SARS-COV2)

Due to the rapid spread of the COVID-19, scientists are constantly monitoring the evolution of the number of infections in a region. In particular, the basic reproductive number (R0) is studied, because it indicates if the number of cases will increase and the infection will last, or if it will decrease and stability will be reached. The present contribution is focused on forecasting this ratio, based on the extreme gradient boosting tree approach. Gradient reinforcement trees are used. Using public data of the COVID-19 outbreak in the Caribbean and some countries, this value is computed. © 2022 IEEE.

Age-specific contribution of contacts to transmission of SARS-CoV-2 in Germany.

Current estimates of pandemic SARS-CoV-2 spread in Germany using infectious disease models often do not use age-specific infection parameters and are not always based on age-specific contact matrices of the population. They also do usually not include setting- or pandemic phase-based information from epidemiological studies of reported cases and do not account for age-specific underdetection of reported cases. Here, we report likely pandemic spread using an age-structured model to understand the age- and setting-specific contribution of contacts to transmission during different phases of the COVID-19 pandemic in Germany. We developed a deterministic SEIRS model using a pre-pandemic contact matrix. The model was optimized to fit age-specific SARS-CoV-2 incidences reported by the German National Public Health Institute (Robert Koch Institute), includes information on setting-specific reported cases in schools and integrates age- and pandemic period-specific parameters for underdetection of reported cases deduced from a large population-based seroprevalence studies. Taking age-specific underreporting into account, younger adults and teenagers were identified in the modeling study as relevant contributors to infections during the first three pandemic waves in Germany. For the fifth wave, the Delta to Omicron transition, only age-specific parametrization reproduces the observed relative and absolute increase in pediatric hospitalizations in Germany. Taking into account age-specific underdetection did not change considerably how much contacts in schools contributed to the total burden of infection in the population (up to 12% with open schools under hygiene measures in the third wave). Accounting for the pandemic phase and age-specific underreporting is important to correctly identify those groups of the population in which quarantine, testing, vaccination, and contact-reduction measures are likely to be most effective and efficient. Age-specific parametrization is also highly relevant to generate informative age-specific output for decision makers and resource planers.

Integrated Extended SIR-type Epidemiological Modeling Platform for Covid-19

In these conditions of Covid-19 pandemic, the design and implementation of an epidemiological modeling platform with an API-type integration with beneficiary entities and data providers is a priority for the healthcare system and other organizations. An epidemiological platform (PLIS), replicable and adaptable for managing an epidemic, based on an integrated extended SIR-type model, is presented in this paper. This solution has an open architecture, respecting the scalability and interoperability, requirements, and is based on international communication standards and protocols, and SOA technology. © 2022 IEEE.