A SIR model assumption for the spread of COVID-19 in different communities

Long-term trend prediction of pandemic combining the compartmental and deep learning models

Predicting the spread trends of a pandemic is crucial, but long-term prediction remains challenging due to complex relationships among disease spread stages and preventive policies. To address this issue, we propose a novel approach that utilizes data augmentation techniques, compartmental model features, and disease preventive policies. We also use a breakpoint detection method to divide the disease spread into distinct stages and weight these stages using a self-attention mechanism to account for variations in virus transmission capabilities. Finally, we introduce a long-term spread trend prediction model for infectious diseases based on a bi-directional gated recurrent unit network. To evaluate the effectiveness of our model, we conducted experiments using public datasets, focusing on the prediction of COVID-19 cases in four countries over a period of 210 days. Experiments shown that the Adjust-R2 index of our model exceeds 0.9914, outperforming existing models. Furthermore, our model reduces the mean absolute error by 0.85-4.52% compared to other models. Our combined approach of using both the compartmental and deep learning models provides valuable insights into the dynamics of disease spread.

Deep learning infused SIRVD model for COVID-19 prediction: XGBoost-SIRVD-LSTM approach

The global impact of the ongoing COVID-19 pandemic, while somewhat contained, remains a critical challenge that has tested the resilience of humanity. Accurate and timely prediction of COVID-19 transmission dynamics and future trends is essential for informed decision-making in public health. Deep learning and mathematical models have emerged as promising tools, yet concerns regarding accuracy persist. This research suggests a novel model for forecasting the COVID-19's future trajectory. The model combines the benefits of machine learning models and mathematical models. The SIRVD model, a mathematical based model that depicts the reach of the infection via population, serves as basis for the proposed model. A deep prediction model for COVID-19 using XGBoost-SIRVD-LSTM is presented. The suggested approach combines Susceptible-Infected-Recovered-Vaccinated-Deceased (SIRVD), and a deep learning model, which includes Long Short-Term Memory (LSTM) and other prediction models, including feature selection using XGBoost method. The model keeps track of changes in each group's membership over time. To increase the SIRVD model's accuracy, machine learning is applied. The key properties for forecasting the spread of the infection are found using a method called feature selection. Then, in order to learn from these features and create predictions, a model involving deep learning is applied. The performance of the model proposed was assessed with prediction metrics such as R 2, root mean square error (RMSE), mean absolute percentage error (MAPE), and normalized root mean square error (NRMSE). The results are also validated to those of other prediction models. The empirical results show that the suggested model outperforms similar models. Findings suggest its potential as a valuable tool for pandemic management and public health decision-making.

Computational investigation of stochastic Zika virus optimal control model using Legendre spectral method

This study presents a computational investigation of a stochastic Zika virus along with optimal control model using the Legendre spectral collocation method (LSCM). By accumulation of stochasticity into the model through the proposed stochastic differential equations, we appropriating the random fluctuations essential in the progression and disease transmission. The stability, convergence and accuracy properties of the LSCM are conscientiously analyzed and also demonstrating its strength for solving the complex epidemiological models. Moreover, the study evaluates the various control strategies, such as treatment, prevention and treatment pesticide control, and identifies optimal combinations that the intervention costs and also minimize the proposed infection rates. The basic properties of the given model, such as the reproduction number, were determined with and without the presence of the control strategies. ForR 0 < 0 , the model satisfies the disease-free equilibrium, in this case the disease die out after some time, while forR 0 > 1 , then endemic equilibrium is satisfied, in this case the disease spread in the population at higher scale. The fundamental findings acknowledge the significant impact of stochastic phonemes on the robustness and effectiveness of control strategies that accelerating the need for cost-effective and multi-faceted approaches. In last the results provide the valuable insights for public health department to enabling more impressive mitigation of Zika virus outbreaks and management in real-world scenarios.

Bayesian model selection for COVID-19 pandemic state estimation using extended Kalman filters: Case study for Saudi Arabia

Quantifying the uncertainty in data-driven mechanistic models is fundamental in public health applications. COVID-19 is a complex disease that had a significant impact on global health and economies. Several mathematical models were used to understand the complexity of the transmission dynamics under different hypotheses to support the decision-making for disease management. This paper highlights various scenarios of a 6D epidemiological model known as SEIQRD (Susceptible-Exposed-Infected-Quarantined-Recovered-Deceased) to evaluate its effectiveness in prediction and state estimation during the spread of COVID-19 pandemic. Then we investigate the suitability of the classical 4D epidemiological model known as SIRD (Susceptible-Infected-Recovered-Deceased) in the long-term behaviour in order to make a comparison between these models. The primary aim of this paper is to establish a foundational basis for the validity and epidemiological model comparisons in long-term behaviour which may help identify the degree of model complexity that is required based on two approaches viz. the Bayesian inference employing the nested sampling algorithm and recursive state estimation utilizing the Extended Kalman Filter (EKF). Our approach acknowledges the potential imperfections and uncertainties inherent in compartmental epidemiological models. By integrating our proposed methodology, these models can consistently generate predictions closely aligned with the observed data on active cases and deaths. This framework, implemented within the EKF algorithm, offers a robust tool for addressing future, unknown pandemics. Moreover, we present a systematic methodology for time-varying parameter estimation along with uncertainty quantification using Saudi Arabia COVID-19 data and obtain the credible confidence intervals of the epidemiological nonlinear dynamical system model parameters.

Physical Chemistry Lab for Data Analysis of COVID-19 Spreading Kinetics in Different Countries

The COVID-19 pandemic has passed. It gives us a real-world example of kinetic data analysis practice for our undergraduate physical chemistry laboratory class. It is a great example to connect this seemingly very different problem to the kinetic theories for chemical reactions that the students have learned in the lecture class. At the beginning of the spring 2023 semester, we obtained COVID-19 kinetic data from the "Our World in Data" database, which summarizes the World Health Organization (WHO) data reported from different countries. We analyzed the effective spreading kinetics based on the susceptible-infectious-recovered-vaccinated (SIR-V) model. We then compared the effective rate constants represented by the real-time reproduction numbers (R t ) underlining the reported data for these countries and discussed the results and the limitations of the model with the students.

Integrate-and-fire model of disease transmission

We create an epidemiological susceptible-infected-susceptible model of disease transmission using integrate-and-fire nodes on a network, allowing memory of previous interactions and infections. Agents in the network sum infectious matter from their nearest neighbors at every time step, until they exceed their infection threshold, at which point they "fire" and become infected for as long as the recovery time. The model has memory of previous interactions by tracking the amount of infectious matter carried by agents as well as just binary infected or susceptible states, and the model has memory of previous infections by modeling immunity as increasing the infection threshold after recovery. Creating a simulation of the model on networks with a power-law degree distribution and homogeneous agent parameters, we find a single strain version of the model matches well with the England COVID-19 case data, with a root-mean-squared error of 0.014%. A simulation of a multistrain version of the model (where there is cross-strain immunity) matches well with the influenza strain A and strain B case numbers in Canada, with a root-mean-squared error of 0.002% and 0.0012%, respectively, though due to the coupling in the model, both strains peak in phase. Since the dynamics of the model successfully capture real-life transmission dynamics, we test interventions to study their effect on case numbers, with both quarantining and social gathering restrictions lowering the peak. Since the model has memory, the stricter the intervention, the higher the secondary peak when the restriction is removed, showing that interventions change only the shape of the curves and not the overall number infected in the population.

Advancing the understanding and treatment of post-traumatic stress disorder with computational modelling

The existing theories of post-traumatic stress disorder (PTSD) have inspired large volumes of research and have contributed substantially to our current knowledge base. However, most of the theories are of a qualitative and verbal nature, and may be difficult to evaluate and compare with each other. In this paper, we propose that one way forward is to use computational modelling to formulate more precise theories of PTSD that can be evaluated by (1) assessing whether the model can explain fundamental phenomena related to PTSD, and (2) comparing simulated outcomes with real data. Computational modelling can force us to describe processes more precisely and achieve stronger theories that are viable for testing. Establishing the theoretical groundwork before undertaking empirical studies can help us to avoid doing research with low probability of valid results, and counteract the replicability crisis in psychology. In conclusion, computational modelling is a promising avenue for advancing the understanding and treatment of PTSD.

Precision epidemiology at the nexus of mathematics and nanotechnology: Unraveling the dance of viral dynamics

The intersection of mathematical modeling, nanotechnology, and epidemiology marks a paradigm shift in our battle against infectious diseases, aligning with the focus of the journal on the regulation, expression, function, and evolution of genes in diverse biological contexts. This exploration navigates the intricate dance of viral transmission dynamics, highlighting mathematical models as dual tools of insight and precision instruments, a theme relevant to the diverse sections of Gene. In the context of virology, ethical considerations loom large, necessitating robust frameworks to protect individual rights, an aspect essential in infectious disease research. Global collaboration emerges as a critical pillar in our response to emerging infectious diseases, fortified by the predictive prowess of mathematical models enriched by nanotechnology. The synergy of interdisciplinary collaboration, training the next generation to bridge mathematical rigor, biology, and epidemiology, promises accelerated discoveries and robust models that account for real-world complexities, fostering innovation and exploration in the field. In this intricate review, mathematical modeling in viral transmission dynamics and epidemiology serves as a guiding beacon, illuminating the path toward precision interventions, global preparedness, and the collective endeavor to safeguard human health, resonating with the aim of advancing knowledge in gene regulation and expression.

Forecasting the spread of COVID-19 based on policy, vaccination, and Omicron data

The COVID-19 pandemic caused by the novel SARS-COV-2 virus poses a great risk to the world. During the COVID-19 pandemic, observing and forecasting several important indicators of the epidemic (like new confirmed cases, new cases in intensive care unit, and new deaths for each day) helped prepare the appropriate response (e.g., creating additional intensive care unit beds, and implementing strict interventions). Various predictive models and predictor variables have been used to forecast these indicators. However, the impact of prediction models and predictor variables on forecasting performance has not been systematically well analyzed. Here, we compared the forecasting performance using a linear mixed model in terms of prediction models (mathematical, statistical, and AI/machine learning models) and predictor variables (vaccination rate, stringency index, and Omicron variant rate) for seven selected countries with the highest vaccination rates. We decided on our best models based on the Bayesian Information Criterion (BIC) and analyzed the significance of each predictor. Simple models were preferred. The selection of the best prediction models and the use of Omicron variant rate were considered essential in improving prediction accuracies. For the test data period before Omicron variant emergence, the selection of the best models was the most significant factor in improving prediction accuracy. For the test period after Omicron emergence, Omicron variant rate use was considered essential in deciding forecasting accuracy. For prediction models, ARIMA, lightGBM, and TSGLM generally performed well in both test periods. Linear mixed models with country as a random effect has proven that the choice of prediction models and the use of Omicron data was significant in determining forecasting accuracies for the highly vaccinated countries. Relatively simple models, fit with either prediction model or Omicron data, produced best results in enhancing forecasting accuracies with test data.

Use of bio-information and communication technology shortens time to peak at a lower height of the epidemic curve: An alternative to flattening for countries with early COVID-19 outbreaks

INTRODUCTION

The traditional approach to epidemic control has been to slow down the rate of infection while building up healthcare capacity, resulting in a flattened epidemic curve. Advancements in bio-information-communication technology (BICT) have enabled the preemptive isolation of infected cases through efficient testing and contact tracing. This study aimed to conceptualize the BICT-enabled epidemic control (BICTEC) and to document its relationships with epidemic curve shaping and epidemic mitigation performance.

METHODS

Daily COVID-19 incidences were collected from outbreak to Aug. 12, 2020, for nine countries reporting the first outbreak on or before Feb. 1, 2020. Key epidemic curve determinants-peak height (PH), time to peak (TTP), and area under the curve (AUC)-were estimated for each country, and their relationships were analyzed to test if epidemic curves peak quickly at a shorter height. CFR (Case Fatality Rate) and CI (Cumulative Incidence) were compared across the countries to identify relationships between epidemic curve shapes and epidemic mitigation performance.

RESULTS

China and South Korea had the quickest TTPs (40.70 and 45.37 days since outbreak, respectively) and the shortest PHs (2.95 and 4.65 cases per day, respectively). Sweden, known for its laissez-faire approach, had the longest TTP (120.36) and the highest PH (279.74). Quicker TTPs were correlated with shorter PHs (ρ = 0·896, p = 0·0026) and lower AUCs (0.790, p = 0.0028), indicating that epidemic curves do not follow a flattened trajectory. During the study period, countries with quicker TTPs tended to have lower CIs (ρ = .855, P = .006) and CFRs (ρ = 0.684, P = .061). For example, South Korea, with the second-quickest TTP, reported the second lowest CI and the lowest CFR.

CONCLUSIONS

Countries that experienced early COVID-19 outbreaks demonstrated the epidemic curves that quickly peak at a shorter height, indicating a departure from the traditional flattened trajectory. South Korea's BICTEC was found to be at least as effective as most lockdowns in reducing CI and CFR.

A New Auto-Regressive Multi-Variable Modified Auto-Encoder for Multivariate Time-Series Prediction: A Case Study with Application to COVID-19 Pandemics

The SARS-CoV-2 global pandemic prompted governments, institutions, and researchers to investigate its impact, developing strategies based on general indicators to make the most precise predictions possible. Approaches based on epidemiological models were used but the outcomes demonstrated forecasting with uncertainty due to insufficient or missing data. Besides the lack of data, machine-learning models including random forest, support vector regression, LSTM, Auto-encoders, and traditional time-series models such as Prophet and ARIMA were employed in the task, achieving remarkable results with limited effectiveness. Some of these methodologies have precision constraints in dealing with multi-variable inputs, which are important for problems like pandemics that require short and long-term forecasting. Given the under-supply in this scenario, we propose a novel approach for time-series prediction based on stacking auto-encoder structures using three variations of the same model for the training step and weight adjustment to evaluate its forecasting performance. We conducted comparison experiments with previously published data on COVID-19 cases, deaths, temperature, humidity, and air quality index (AQI) in São Paulo City, Brazil. Additionally, we used the percentage of COVID-19 cases from the top ten affected countries worldwide until May 4th, 2020. The results show 80.7% and 10.3% decrease in RMSE to entire and test data over the distribution of 50 trial-trained models, respectively, compared to the first experiment comparison. Also, model type#3 achieved 4th better overall ranking performance, overcoming the NBEATS, Prophet, and Glounts time-series models in the second experiment comparison. This model shows promising forecast capacity and versatility across different input dataset lengths, making it a prominent forecasting model for time-series tasks.

MPSTAN: Metapopulation-Based Spatio-Temporal Attention Network for Epidemic Forecasting

Accurate epidemic forecasting plays a vital role for governments to develop effective prevention measures for suppressing epidemics. Most of the present spatio-temporal models cannot provide a general framework for stable and accurate forecasting of epidemics with diverse evolutionary trends. Incorporating epidemiological domain knowledge ranging from single-patch to multi-patch into neural networks is expected to improve forecasting accuracy. However, relying solely on single-patch knowledge neglects inter-patch interactions, while constructing multi-patch knowledge is challenging without population mobility data. To address the aforementioned problems, we propose a novel hybrid model called metapopulation-based spatio-temporal attention network (MPSTAN). This model aims to improve the accuracy of epidemic forecasting by incorporating multi-patch epidemiological knowledge into a spatio-temporal model and adaptively defining inter-patch interactions. Moreover, we incorporate inter-patch epidemiological knowledge into both model construction and the loss function to help the model learn epidemic transmission dynamics. Extensive experiments conducted on two representative datasets with different epidemiological evolution trends demonstrate that our proposed model outperforms the baselines and provides more accurate and stable short- and long-term forecasting. We confirm the effectiveness of domain knowledge in the learning model and investigate the impact of different ways of integrating domain knowledge on forecasting. We observe that using domain knowledge in both model construction and the loss function leads to more efficient forecasting, and selecting appropriate domain knowledge can improve accuracy further.

Social and economic variables explain COVID-19 diffusion in European regions

At the beginning of 2020, Italy was the country with the highest number of COVID-19 cases, not only in Europe, but also in the rest of the world, and Lombardy was the most heavily hit region of Italy. The objective of this research is to understand which variables have determined the prevalence of cases in Lombardy and in other highly-affected European regions. We consider the first and second waves of the COVID-19 pandemic, using a set of 22 variables related to economy, population, healthcare and education. Regions with a high prevalence of cases are extracted by means of binary classifiers, then the most relevant variables for the classification are determined, and the robustness of the analysis is assessed. Our results show that the most meaningful features to identify high-prevalence regions include high number of hours spent in work environments, high life expectancy, and low number of people leaving from education and neither employed nor educated or trained.

A dynamic approach to support outbreak management using reinforcement learning and semi-connected SEIQR models

BACKGROUND

Containment measures slowed the spread of COVID-19 but led to a global economic crisis. We establish a reinforcement learning (RL) algorithm that balances disease control and economic activities.

METHODS

To train the RL agent, we design an RL environment with 4 semi-connected regions to represent the COVID-19 epidemic in Tokyo, Osaka, Okinawa, and Hokkaido, Japan. Every region is governed by a Susceptible-Exposed-Infected-Quarantined-Removed (SEIQR) model and has a transport hub to connect with other regions. The allocation of the synthetic population and inter-regional traveling is determined by population-weighted density. The agent learns the best policy from interacting with the RL environment, which involves obtaining daily observations, performing actions on individual movement and screening, and receiving feedback from the reward function. After training, we implement the agent into RL environments describing the actual epidemic waves of the four regions to observe the agent's performance.

RESULTS

For all epidemic waves covered by our study, the trained agent reduces the peak number of infectious cases and shortens the epidemics (from 165 to 35 cases and 148 to 131 days for the 5th wave). The agent is generally strict on screening but easy on movement, except for Okinawa, where the agent is easy on both actions. Action timing analyses indicate that restriction on movement is elevated when the number of exposed or infectious cases remains high or infectious cases increase rapidly, and stringency on screening is eased when the number of exposed or infectious cases drops quickly or to a regional low. For Okinawa, action on screening is tightened when the number of exposed or infectious cases increases rapidly.

CONCLUSIONS

Our experiments exhibit the potential of the RL in assisting policy-making and how the semi-connected SEIQR models establish an interactive environment for imitating cross-regional human flows.

Multi-feature SEIR model for epidemic analysis and vaccine prioritization

The SEIR (susceptible-exposed-infected-recovered) model has become a valuable tool for studying infectious disease dynamics and predicting the spread of diseases, particularly concerning the COVID pandemic. However, existing models often oversimplify population characteristics and fail to account for differences in disease sensitivity and social contact rates that can vary significantly among individuals. To address these limitations, we have developed a new multi-feature SEIR model that considers the heterogeneity of health conditions (disease sensitivity) and social activity levels (contact rates) among populations affected by infectious diseases. Our model has been validated using the data of the confirmed COVID cases in Allegheny County (Pennsylvania, USA) and Hamilton County (Ohio, USA). The results demonstrate that our model outperforms traditional SEIR models regarding predictive accuracy. In addition, we have used our multi-feature SEIR model to propose and evaluate different vaccine prioritization strategies tailored to the characteristics of heterogeneous populations. We have formulated optimization problems to determine effective vaccine distribution strategies. We have designed extensive numerical simulations to compare vaccine distribution strategies in different scenarios. Overall, our multi-feature SEIR model enhances the existing models and provides a more accurate picture of disease dynamics. It can help to inform public health interventions during pandemics/epidemics.

Hospital capacities and response to COVID-19 pandemic surges in Iran: A quantitative model-based study

The coronavirus 2019 (COVID-19) pandemic resulted in serious limitations for healthcare systems, and this study aimed to investigate the impact of COVID-19 surges on in-patient care capacities in Iran employing the Adaptt tool. Using a cross-sectional study design, our study was carried out in the year 2022 using 1-year epidemiologic (polymerase chain reaction-positive COVID-19 cases) and hospital capacity (beds and human resource) data from the official declaration of the pandemic in Iran in February 2020. We populated several scenarios, and in each scenario, a proportion of hospital capacity is assumed to be allocated to the COVID-19 patients. In most of the scenarios, no significant shortage was found in terms of bed and human resources. However, considering the need for treatment of non- COVID-19 cases, in one of the scenarios, it can be observed that during the peak period, the number of required and available specialists is exactly equal, which was a challenge during surge periods and resulted in extra hours of working and workforce burnout in hospitals. The shortage of intensive care unit beds and doctors specializing in internal medicine, infectious diseases, and anesthesiology also requires more attention for planning during the peak days of COVID-19.

Drawing a parallel between the trend of confirmed COVID-19 deaths in the winters of 2022/2023 and 2023/2024 in Italy, with a prediction

We studied the weekly number and the growth/decline rates of COVID-19 deaths of the period from October 31, 2022, to February 9, 2023, in Italy. We found that the COVID-19 winter wave reached its peak during the three holiday weeks from December 16, 2022, to January 5, 2023, and it was definitely trending downward, returning to the same number of deaths as the end of October 2022, in the first week February 2023. During this period of 15 weeks, that wave caused a number of deaths as large as 8,526. Its average growth rate was +7.89% deaths per week (10 weeks), while the average weekly decline rate was -15.85% (5 weeks). At the time of writing of this paper, Italy has been experiencing a new COVID-19 wave, with the latest 7 weekly bulletins (October 26, 2023 - December 13, 2023) showing that deaths have climbed from 148 to 322. The weekly growth rate had risen by +14.08% deaths, on average. Hypothesizing that this 2023/2024 wave will have a total duration similar to that of 2022/2023, with comparable extensions of both the growth period and the decline period and similar growth/decline rates, we predict that the number of COVID-19 deaths of the period from the end of October 2023 to the beginning of February 2024 should be less than 4100. A preliminary assessment of this forecast, based on 11 of the 15 weeks of the period, has already confirmed the accuracy of this approach.

Applications of Machine Learning (ML) and Mathematical Modeling (MM) in Healthcare with Special Focus on Cancer Prognosis and Anticancer Therapy: Current Status and Challenges

The use of data-driven high-throughput analytical techniques, which has given rise to computational oncology, is undisputed. The widespread use of machine learning (ML) and mathematical modeling (MM)-based techniques is widely acknowledged. These two approaches have fueled the advancement in cancer research and eventually led to the uptake of telemedicine in cancer care. For diagnostic, prognostic, and treatment purposes concerning different types of cancer research, vast databases of varied information with manifold dimensions are required, and indeed, all this information can only be managed by an automated system developed utilizing ML and MM. In addition, MM is being used to probe the relationship between the pharmacokinetics and pharmacodynamics (PK/PD interactions) of anti-cancer substances to improve cancer treatment, and also to refine the quality of existing treatment models by being incorporated at all steps of research and development related to cancer and in routine patient care. This review will serve as a consolidation of the advancement and benefits of ML and MM techniques with a special focus on the area of cancer prognosis and anticancer therapy, leading to the identification of challenges (data quantity, ethical consideration, and data privacy) which are yet to be fully addressed in current studies.

Taking cues from machine learning, compartmental and time series models for SARS-CoV-2 omicron infection in Indian provinces

SARS-CoV-2, the virus responsible for COVID-19, posed a significant threat to the world. We analyzed COVID-19 dissemination data in the top ten Indian provinces by infection incidences using the Susceptible-Infectious-Removed (SIR) model, an Autoregressive Integrated Moving Average (ARIMA) time series model, a machine learning model based on the Random Forest, and distribution fitting. Outbreaks are expected to continue if the Basic Reproduction Number (R0) > 1, and infection waves are anticipated to end if the R0 < 1, as determined by the SIR model. Different parametric probability distributions are also fitted. Data collected from December 12, 2021, to March 31, 2022, encompassing data from both before and during the implementation of strict control measures. Based on the estimates of the model parameters, health agencies and government policymakers can develop strategies to combat the spread of the disease in the future, and the most effective technique can be recommended for real-world application for other outbreaks of COVID-19. The best method out of these could be also implemented further on the epidemiological data of other similar infectious agents.

Simulating real-life scenarios to better understand the spread of diseases under different contexts

Current statistical models to simulate pandemics miss the most relevant information about the close atomic interactions between individuals which is the key aspect of virus spread. Thus, they lack a proper visualization of such interactions and their impact on virus spread. In the field of computer graphics, and more specifically in computer animation, there have been many crowd simulation models to populate virtual environments. However, the focus has typically been to simulate reasonable paths between random or semi-random locations in a map, without any possibility of analyzing specific individual behavior. We propose a crowd simulation framework to accurately simulate the interactions in a city environment at the individual level, with the purpose of recording and analyzing the spread of human diseases. By simulating the whereabouts of agents throughout the day by mimicking the actual activities of a population in their daily routines, we can accurately predict the location and duration of interactions between individuals, thus having a model that can reproduce the spread of the virus due to human-to-human contact. Our results show the potential of our framework to closely simulate the virus spread based on real agent-to-agent contacts. We believe that this could become a powerful tool for policymakers to make informed decisions in future pandemics and to better communicate the impact of such decisions to the general public.

Network-based uncertainty quantification for mathematical models in epidemiology

After the new Coronavirus disease (COVID-19) emerged in the end of January 2020 in Germany, a large number of individuals suffered from severe symptoms and eventually needed intensive care in hospitals. Due to the rapid spread of the disease, the number of deceased individuals increased as well, which is a motivation to prevent as many new infections as possible. Therefore, the knowledge about the current evolution of the virus spread is crucial to predict its future behavior and to react with suitable interventions. In this paper, the evolution of the COVID-19 pandemic in Germany is forecasted by a network-based inference method, in which the interactions of individuals are taken into account using a contact matrix. Then the results are compared to the predictions without considering a contact matrix as well as to the logistic regression, which shows the advantage of incorporating the contact matrix. Furthermore, the basic reproduction number of the pandemic in Germany using a neural network approach is estimated and used for further predictions of the evolution of COVID-19 in Germany. In order to mathematically model the different compartments of the population in the considered regions, the classical SIR model is employed. In this work, we deploy the LASSO (Least Absolute Shrinkage and Selection Operator) for the unknown parameter estimation. Furthermore, we calculate and illustrate the MAPE (Mean Absolute Percentage Error) of the estimations to show the accuracy of the predictions. The results include model parameter estimation and model validation, as well as the outbreak forecasting using network-informed algorithms. Our findings show that the network-inference based approach outperforms the logistic regression as well as the neural network approach and the SIR model calibration without a contact network. Furthermore according to the results, the network-inference based approach is particularly suitable for short- to mid-term predictions, even when there is not much information about the new disease. Moreover, the predictions based on the estimation of the reproduction number in Germany can yield more reliable results with increasing the availability of data, but could not outperform the network-inference based algorithm.

Stochastic intelligent computing solvers for the SIR dynamical prototype epidemic model using the impacts of the hospital bed

The present investigations are related to design a stochastic intelligent solver using the infrastructure of artificial neural networks (ANNs) and scaled conjugate gradient (SCG), i.e. ANNs-SCG for the numerical simulations of SIR dynamical prototype system based impacts of hospital bed. The SIR dynamical model is defined into three classes, susceptible patients in the hospital, infected population and recovered people. The proposed results are obtained through the sample statics of verification, testing and training of the dataset. The selection of the statics for training, testing and validation is chosen as 80%, 8% and 12%. A dataset is proposed based on the Adams scheme for the comparison of dynamical SIR prototype using the impacts of hospital bed. The numerical solutions are presented through the ANNs-SCG in order to reduce the values of the mean square error. To achieve the reliability, capability, accuracy, and competence of ANNs-SCG, the mathematical solutions are presented in the form of error histograms (EHs), regression, state transitions (STs) and correlation.

Impact of periodic vaccination in SEIRS seasonal model

We study three different strategies of vaccination in an SEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible) seasonal forced model, which are (i) continuous vaccination; (ii) periodic short-time localized vaccination, and (iii) periodic pulsed width campaign. Considering the first strategy, we obtain an expression for the basic reproduction number and infer a minimum vaccination rate necessary to ensure the stability of the disease-free equilibrium (DFE) solution. In the second strategy, short duration pulses are added to a constant baseline vaccination rate. The pulse is applied according to the seasonal forcing phases. The best outcome is obtained by locating intensive immunization at inflection of the transmissivity curve. Therefore, a vaccination rate of 44.4% of susceptible individuals is enough to ensure DFE. For the third vaccination proposal, additionally to the amplitude, the pulses have a prolonged time width. We obtain a non-linear relationship between vaccination rates and the duration of the campaign. Our simulations show that the baseline rates, as well as the pulse duration, can substantially improve the vaccination campaign effectiveness. These findings are in agreement with our analytical expression. We show a relationship between the vaccination parameters and the accumulated number of infected individuals, over the years, and show the relevance of the immunization campaign annual reaching for controlling the infection spreading. Regarding the dynamical behavior of the model, our simulations show that chaotic and periodic solutions as well as bi-stable regions depend on the vaccination parameters range.

A non-autonomous time-delayed SIR model for COVID-19 epidemics prediction in China during the transmission of Omicron variant

<abstract><p>With the continuous evolution of the coronavirus, the Omicron variant has gradually replaced the Delta variant as the prevalent strain. Their inducing epidemics last longer, have a higher number of asymptomatic cases, and are more serious. In this article, we proposed a nonautonomous time-delayed susceptible-infected-removed (NATD-SIR) model to predict them in different regions of China. We obtained the maximum and its time of current infected persons, the final size, and the end time of COVID-19 epidemics from January 2022 in China. The method of the fifth-order moving average was used to preprocess the time series of the numbers of current infected and removed cases to obtain more accurate parameter estimations. We found that usually the transmission rate $ \beta(t) $ was a piecewise exponential decay function, but due to multiple bounces in Shanghai City, $ \beta(t) $ was approximately a piecewise quadratic function. In most regions, the removed rate $ \gamma(t) $ was approximately equal to a piecewise linear increasing function of (a*t+b)*H(t-k), but in a few areas, $ \gamma(t) $ displayed an exponential increasing trend. For cases where the removed rate cannot be obtained, we proposed a method for setting the removed rate, which has a good approximation. Using the numerical solution, we obtained the prediction results of the epidemics. By analyzing those important indicators of COVID-19, we provided valuable suggestions for epidemic prevention and control and the resumption of work and production.</p></abstract>

Modelling the Potential Public Health Impact of Different COVID-19 Vaccination Strategies with an Adapted Vaccine in Singapore

BACKGROUND

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) causing COVID-19 has been a dynamically changing virus, requiring the development of adapted vaccines. This study estimated the potential public health impact alternative vaccination strategies for COVID-19 in Singapore.

RESEARCH DESIGN AND METHODS

The outcomes of alternative vaccination strategies with a future adapted vaccine were estimated using a combined Markov decision tree model. The population was stratified by high- and standard-risk. Using age-specific inputs informed by local surveillance data and published sources, the model estimated health (case numbers, hospitalizations, and deaths) and economic (medical costs and productivity losses) outcomes in different age and risk subpopulations.

RESULTS

Booster vaccination in only the elderly and high-risk subpopulation was estimated to avert 278,614 cases 21,558 hospitalizations, 239 deaths, Singapore dollars (SGD) 277 million in direct medical costs, and SGD 684 million in indirect medical costs. These benefits increased as vaccination was expanded to other subpopulations. Increasing the booster vaccination coverage to 75% of the standard-risk population averted more deaths (3%), hospitalizations (29%), infections (145%), direct costs (90%), and indirect costs (192%) compared to the base case.

CONCLUSIONS

Broader vaccination strategies using an adapted booster vaccine could have substantial public health and economic impact in Singapore.

Modeling the potential public health impact of different vaccination strategies with an adapted vaccine in South Africa

BACKGROUND

COVID-19 vaccines adapted to newly emerging circulating variants are necessary to better protect the population due to the evolving nature of the SARS-CoV-2 virus.

RESEARCH DESIGN AND METHODS

The South African population was stratified by age and risk (defined by comorbidities such as diabetes, obesity, smoking, cancer, and asthma), and HIV status. The outcomes of different vaccination strategies based on age, risk, and HIV status were estimated using a Markov-decision tree model based on age-specific inputs derived from the literature and South African surveillance data.

RESULTS

Vaccinating older adults and those with comorbidities was estimated to avert 111,179 infections 18,281 hospitalizations, and 3,868 deaths, resulting in savings of ZAR 1,260 million (USD 67 million) and ZAR 3,205 million (USD 170 million) in direct and indirect costs, respectively. Similar results were obtained when considering strategies targeting older adults and the HIV population. Expanding vaccination to 75% of the standard-risk population prevented more infections (401%), hospitalizations (167%), and deaths (67%) and increased the direct (232%) and indirect (455%) cost savings compared to the base case.

CONCLUSIONS

Implementing widespread vaccination strategies that utilize a vaccine adapted to the prevailing circulating variant in South Africa would result in significant public health and economic gains.

A data-driven epidemic model with human mobility and vaccination protection for COVID-19 prediction

Epidemiological models allow for quantifying the dynamic characteristics of large-scale outbreaks. However, capturing detailed and accurate epidemiological information often requires consideration of multiple kinetic mechanisms and parameters. Due to the uncertainty of pandemic evolution, such as pathogen variation, host immune response and changes in mitigation strategies, the parameter evaluation and state prediction of complex epidemiological models are challenging. Here, we develop a data-driven epidemic model with a generalized SEIR mechanistic structure that includes new compartments, human mobility and vaccination protection. To address the issue of model complexity, we embed the epidemiological model dynamics into physics-informed neural networks (PINN), taking the observed series of time instances as direct input of the network to simultaneously infer unknown parameters and unobserved dynamics of the underlying model. Using actual data during the COVID-19 outbreak in Australia, Israel, and Switzerland, our model framework demonstrates satisfactory performance in multi-step ahead predictions compared to several benchmark models. Moreover, our model infers time-varying parameters such as transmission rates, hospitalization ratios, and effective reproduction numbers, as well as calculates the latent period and asymptomatic infection count, which are typically unreported in public data. Finally, we employ the proposed data-driven model to analyze the impact of different mitigation strategies on COVID-19.

Modeling the potential public health and economic impact of different COVID-19 booster dose vaccination strategies with an adapted vaccine in the United Kingdom

BACKGROUND

Updating vaccines is essential for combatting emerging coronavirus disease 2019 (COVID-19) variants. This study assessed the public health and economic impact of a booster dose of an adapted vaccine in the United Kingdom (UK).

METHODS

A Markov-decision tree model estimated the outcomes of vaccination strategies targeting various age and risk groups in the UK. Age-specific data derived from published sources were used. The model estimated case numbers, deaths, hospitalizations, medical costs, and societal costs. Scenario analyses were conducted to explore uncertainty.

RESULTS

Vaccination targeting individuals aged ≥ 65 years and the high-risk population aged 12-64 years was estimated to avert 701,549 symptomatic cases, 5,599 deaths, 18,086 hospitalizations, 56,326 post-COVID condition cases, and 38,263 lost quality-adjusted life years (QALYs), translating into direct and societal cost savings of £112,174,054 and £542,758,682, respectively. The estimated economically justifiable price at willingness-to-pay thresholds of £20,000 and £30,000 per QALY was £43 and £61, respectively, from the payer perspective and £64 and £82, respectively, from the societal perspective. Expanding to additional age groups improved the public health impact.

CONCLUSIONS

Targeting individuals aged ≥ 65 years and those aged 12-64 years at high risk yields public health gains, but expansion to additional age groups provides additional gains.

An artificial neural network approach for the language learning model

The current study provides the numerical solutions of the language-based model through the artificial intelligence (AI) procedure based on the scale conjugate gradient neural network (SCJGNN). The mathematical learning language differential model is characterized into three classes, named as unknown, familiar, and mastered. A dataset is generalized by using the performance of the Adam scheme, which is used to reduce to mean square error. The AI based SCJGNN procedure works by taking the data with the ratio of testing (12%), validation (13%), and training (75%). An activation log-sigmoid function, twelve numbers of neurons, SCJG optimization, hidden and output layers are presented in this stochastic computing work for solving the learning language model. The correctness of AI based SCJGNN is noted through the overlapping of the results along with the small calculated absolute error that are around 10-06 to 10-08 for each class of the model. Moreover, the regression performances for each case of the model is performed as one that shows the perfect model. Additionally, the dependability of AI based SCJGNN is approved using the histogram, and function fitness.

Inference and forecasting phase shift regime of COVID-19 sub-lineages with a Markov-switching model

IMPORTANCE

Using regime-switching models, we attempted to determine whether there is a link between changes in severe acute respiratory syndrome coronavirus 2 (SARS-Cov-2) variants and infection waves, as well as forecasting new SARS-Cov-2 variants. We believe that our study makes a significant contribution to the field because it proposes a new approach for forecasting the ongoing pandemic, and the spread of other infectious diseases, using a statistical model which incorporates unpredictable factors such as human behavior, political factors, and cultural beliefs.

Natural and socio-environmental factors contribute to the transmissibility of COVID-19: evidence from an improved SEIR model

COVID-19 has ravaged Brazil, and its spread showed spatial heterogeneity. Changes in the environment have been implicated as potential factors involved in COVID-19 transmission. However, considerable research efforts have not elucidated the risk of environmental factors on COVID-19 transmission from the perspective of infectious disease dynamics. The aim of this study is to model the influence of the environment on COVID-19 transmission and to analyze how the socio-ecological factors affecting the probability of virus transmission in 10 states dramatically shifted during the early stages of the epidemic in Brazil. First, this study used a Pearson correlation to analyze the interconnection between COVID-19 morbidity and socio-ecological factors and identified factors with significant correlations as the dominant factors affecting COVID-19 transmission. Then, the time-lag effect of dominant factors on the morbidity of COVID-19 was investigated by constructing a distributed lag nonlinear model and standard two-stage meta-analytic model, and the results were considered in the improved SEIR model. Lastly, a machine learning method was introduced to explore the nonlinear relationship between the environmental propagation probability and socio-ecological factors. By analyzing the impact of environmental factors on virus transmission, it can be found that population mobility directly caused by human activities had a greater impact on virus transmission than temperature and humidity. The heterogeneity of meteorological factors can be accounted for by the diverse climate patterns in Brazil. The improved SEIR model was adopted to explore the interconnection of COVID-19 transmission and the environment, which revealed a new strategy to probe the causal links between them.

Production-sharing of critical resources with dynamic demand under pandemic situation: The COVID-19 pandemic

The COVID-19 virus's high transmissibility has resulted in the virus's rapid spread throughout the world, which has brought several repercussions, ranging from a lack of sanitary and medical products to the collapse of medical systems. Hence, governments attempt to re-plan the production of medical products and reallocate limited health resources to combat the pandemic. This paper addresses a multi-period production-inventory-sharing problem (PISP) to overcome such a circumstance, considering two consumable and reusable products. We introduce a new formulation to decide on production, inventory, delivery, and sharing quantities. The sharing will depend on net supply balance, allowable demand overload, unmet demand, and the reuse cycle of reusable products. Undeniably, the dynamic demand for products during pandemic situations must be reflected effectively in addressing the multi-period PISP. A bespoke compartmental susceptible-exposed-infectious-hospitalized-recovered-susceptible (SEIHRS) epidemiological model with a control policy is proposed, which also accounts for the influence of people's behavioral response as a result of the knowledge of adequate precautions. An accelerated Benders decomposition-based algorithm with tailored valid inequalities is offered to solve the model. Finally, we consider a realistic case study - the COVID-19 pandemic in France - to examine the computational proficiency of the decomposition method. The computational results reveal that the proposed decomposition method coupled with effective valid inequalities can solve large-sized test problems in a reasonable computational time and 9.88 times faster than the commercial Gurobi solver. Moreover, the sharing mechanism reduces the total cost of the system and the unmet demand on the average up to 32.98% and 20.96%, respectively.

A model-based strategy for the COVID-19 vaccine roll-out in the Philippines

COVID-19 has affected millions of people worldwide, causing illness and death, and disrupting daily life while imposing a significant social and economic burden. Vaccination is an important control measure that significantly reduces mortality if properly and efficiently distributed. In this work, an age-structured model of COVID-19 transmission, incorporating an unreported infectious compartment, is developed. Three age groups are considered: young (0-19 years), adult (20-64 years), and elderly (65+ years). The transmission rate and reporting rate are determined for each group by utilizing the number of COVID-19 cases in the National Capital Region in the Philippines. Optimal control theory is employed to identify the best vaccine allocation to different age groups. Further, three different vaccination periods are considered to reflect phases of vaccination priority groups: the first, second, and third account for the inoculation of the elderly, adult and elderly, and all three age groups, respectively. This study could guide in making informed decisions in mitigating a population-structured disease transmission under limited resources.

A comparative study of compartmental models for COVID-19 transmission in Ontario, Canada

The number of confirmed COVID-19 cases reached over 1.3 million in Ontario, Canada by June 4, 2022. The continued spread of the virus underlying COVID-19 has been spurred by the emergence of variants since the initial outbreak in December, 2019. Much attention has thus been devoted to tracking and modelling the transmission of COVID-19. Compartmental models are commonly used to mimic epidemic transmission mechanisms and are easy to understand. Their performance in real-world settings, however, needs to be more thoroughly assessed. In this comparative study, we examine five compartmental models-four existing ones and an extended model that we propose-and analyze their ability to describe COVID-19 transmission in Ontario from January 2022 to June 2022.

Population-Level Immunity for Transient Suppression of COVID-19 Waves in Japan from April 2021 to September 2022

Multiple COVID-19 waves have been observed worldwide, with varying numbers of positive cases. Population-level immunity can partly explain a transient suppression of epidemic waves, including immunity acquired after vaccination strategies. In this study, we aimed to estimate population-level immunity in 47 Japanese prefectures during the three waves from April 2021 to September 2022. For each wave, characterized by the predominant variants, namely, Delta, Omicron, and BA.5, the estimated rates of population-level immunity in the 10-64-years age group, wherein the most positive cases were observed, were 20%, 35%, and 45%, respectively. The number of infected cases in the BA.5 wave was inversely associated with the vaccination rates for the second and third injections. We employed machine learning to replicate positive cases in three Japanese prefectures to validate the reliability of our model for population-level immunity. Using interpolation based on machine learning, we estimated the impact of behavioral factors and vaccination on the fifth wave of new positive cases that occurred during the Tokyo 2020 Olympic Games. Our computational results highlighted the critical role of population-level immunity, such as vaccination, in infection suppression. These findings underscore the importance of estimating and monitoring population-level immunity to predict the number of infected cases in future waves. Such estimations that combine numerical derivation and machine learning are of utmost significance for effective management of medical resources, including the vaccination strategy.

Biochemical models of SIR and SIRS: Effects of bilinear incidence rate on infection-free and endemic states

Understanding and forecasting the progression of disease epidemics is possible through the study of nonlinear epidemic biochemical models that describe the relationship among susceptible, infected, and immune individuals in a population. In this paper, by determining the algebraic invariant planes and studying the Hopf bifurcation on these invariant planes, we study the stability of the Hopf bifurcation in the infection-free and endemic states of the SIR and SIRS epidemic models with bilinear incidence rate. We analyze the stability of the limit cycles of the bilinear incidence SIR and SIRS models at the steady state point where infection vanishes and at the endemic steady state point where the system behaves in an oscillatory manner. We demonstrate the algebraic results by numerical simulations for parameter values that satisfy the conditions for both free and endemic states.

Fractal and fractional SIS model for syphilis data

This work studies the SIS model extended by fractional and fractal derivatives. We obtain explicit solutions for the standard and fractal formulations; for the fractional case, we study numerical solutions. As a real data example, we consider the Brazilian syphilis data from 2011 to 2021. We fit the data by considering the three variations of the model. Our fit suggests a recovery period of 11.6 days and a reproduction ratio (R0) equal to 6.5. By calculating the correlation coefficient (r) between the real data and the theoretical points, our results suggest that the fractal model presents a higher r compared to the standard or fractional case. The fractal formulation is improved when two different fractal orders with distinguishing weights are considered. This modification in the model provides a better description of the data and improves the correlation coefficient.

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

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

A data-driven Markov process for infectious disease transmission

The 2019 coronavirus pandemic exudes public health and socio-economic burden globally, raising an unprecedented concern for infectious diseases. Thus, describing the infectious disease transmission process to design effective intervention measures and restrict its spread is a critical scientific issue. We propose a level-dependent Markov model with infinite state space to characterize viral disorders like COVID-19. The levels and states in this model represent the stages of outbreak development and the possible number of infectious disease patients. The transfer of states between levels reflects the explosive transmission process of infectious disease. A simulation method with heterogeneous infection is proposed to solve the model rapidly. After that, simulation experiments were conducted using MATLAB according to the reported data on COVID-19 published by Johns Hopkins. Comparing the simulation results with the actual situation shows that our proposed model can well capture the transmission dynamics of infectious diseases with and without imposed interventions and evaluate the effectiveness of intervention strategies. Further, the influence of model parameters on transmission dynamics is analyzed, which helps to develop reasonable intervention strategies. The proposed approach extends the theoretical study of mathematical modeling of infectious diseases and contributes to developing models that can describe an infinite number of infected persons.

Assessing individual risk and the latent transmission of COVID-19 in a population with an interaction-driven temporal model

Interaction-driven modeling of diseases over real-world contact data has been shown to promote the understanding of the spread of diseases in communities. This temporal modeling follows the path-preserving order and timing of the contacts, which are essential for accurate modeling. Yet, other important aspects were overlooked. Various airborne pathogens differ in the duration of exposure needed for infection. Also, from the individual perspective, Covid-19 progression differs between individuals, and its severity is statistically correlated with age. Here, we enrich an interaction-driven model of Covid-19 and similar airborne viral diseases with (a) meetings duration and (b) personal disease progression. The enriched model enables predicting outcomes at both the population and the individual levels. It further allows predicting individual risk of engaging in social interactions as a function of the virus characteristics and its prevalence in the population. We further showed that the enigmatic nature of asymptomatic transmission stems from the latent effect of the network density on this transmission and that asymptomatic transmission has a substantial impact only in sparse communities.

Risk of Testing Positive for COVID-19 among Healthcare and Healthcare-Related Workers

Understanding the risk factors associated with COVID-19 infection among healthcare workers is crucial for infection prevention and control. The aim of this study was to examine the risk of testing positive for COVID-19 among a multicenter cohort of workers, taking into account their occupational roles (medical professionals, staff in operational and administrative roles, or laboratory personnel) in healthcare settings. The data analyzed in this study included 2163 individuals with suggestive COVID-19 symptoms who underwent laboratory testing. The incidence rate in the study sample was calculated to be 15.3 cases per 10,000 person-days. The results from the multiple regression model indicated that job roles were not significantly associated with the risk of testing positive. However, age and the duration of the pandemic were identified as significant risk factors, with increasing age and longer pandemic duration being associated with a higher risk of testing positive. Additionally, vaccination was found to reduce the risk of testing positive. These findings provide valuable insights into COVID-19 transmission among indoor healthcare workers, highlighting the influence of age, pandemic duration, and vaccination on infection risk. Further research is needed to develop evidence-based strategies aimed at protecting healthcare workers and preventing virus spread in healthcare settings.

Comparison of homemade mask designs based on calculated infection risk, using actual COVID-19 infection scenarios

During pandemics such as COVID-19, shortages of approved respirators necessitate the use of alternative masks, including homemade designs. The effectiveness of the masks is often quantified in terms of the ability to filter particles. However, to formulate public policy the efficacy of the mask in reducing the risk of infection for a given population is considerably more useful than its filtration efficiency (FE). The effect of the mask on the infection profile is complicated to estimate as it depends strongly upon the behavior of the affected population. A recently introduced tool known as the dynamic-spread model is well suited for performing population-specific risk assessment. The dynamic-spread model was used to simulate the performance of a variety of mask designs (all used for source control only) in different COVID-19 scenarios. The efficacy of different masks was found to be highly scenario dependent. Switching from a cotton T-shirt of 8% FE to a 3-layer cotton-gauze-cotton mask of 44% FE resulted in a decrease in number of new infections of about 30% in the New York State scenario and 60% in the Harris County, Texas scenario. The results are valuable to policy makers for quantifying the impact upon the infection rate for different intervention strategies, e.g., investing resources to provide the community with higher-filtration masks.

Direct numerical solutions of the SIR and SEIR models via the Dirichlet series approach

Compartment models are implemented to understand the dynamic of a system. To analyze the models, a numerical tool is required. This manuscript presents an alternative numerical tool for the SIR and SEIR models. The same idea could be applied to other compartment models. The result starts with transforming the SIR model to an equivalent differential equation. The Dirichlet series satisfying the differential equation leads to an alternative numerical method to obtain the model's solutions. The derived Dirichlet solution not only matches the numerical solution obtained by the fourth-order Runge-Kutta method (RK-4), but it also carries the long-run behavior of the system. The SIR solutions obtained by the RK-4 method, an approximated analytical solution, and the Dirichlet series approximants are graphically compared. The Dirichlet series approximants order 15 and the RK-4 method are almost perfectly matched with the mean square error less than 2 × 10-5. A specific Dirichlet series is considered in the case of the SEIR model. The process to obtain a numerical solution is done in the similar way. The graphical comparisons of the solutions achieved by the Dirichlet series approximants order 20 and the RK-4 method show that both methods produce almost the same solution. The mean square errors of the Dirichlet series approximants order 20 in this case are less than 1.2 × 10-4.

Trajectories of COVID-19: A longitudinal analysis of many nations and subnational regions

The COVID-19 pandemic is the first to be rapidly and sequentially measured by nation-wide PCR community testing for the presence of the viral RNA at a global scale. We take advantage of the novel "natural experiment" where diverse nations and major subnational regions implemented various policies including social distancing and vaccination at different times with different levels of stringency and adherence. Initially, case numbers expand exponentially with doubling times of ~1-2 weeks. In the nations where interventions were not implemented or perhaps lees effectual, case numbers increased exponentially but then stabilized around 102-to-103 new infections (per km2 built-up area per day). Dynamics under effective interventions were perturbed and infections decayed to low levels. They rebounded concomitantly with the lifting of social distancing policies or pharmaceutical efficacy decline, converging on a stable equilibrium setpoint. Here we deploy a mathematical model which captures this V-shape behavior, incorporating a direct measure of intervention efficacy. Importantly, it allows the derivation of a maximal estimate for the basic reproductive number Ro (mean 1.6-1.8). We were able to test this approach by comparing the approximated "herd immunity" to the vaccination coverage observed that corresponded to rapid declines in community infections during 2021. The estimates reported here agree with the observed phenomena. Moreover, the decay (0.4-0.5) and rebound rates (0.2-0.3) were similar throughout the pandemic and among all the nations and regions studied. Finally, a longitudinal analysis comparing multiple national and regional results provides insights on the underlying epidemiology of SARS-CoV-2 and intervention efficacy, as well as evidence for the existence of an endemic steady state of COVID-19.

The Principles of SARS-CoV-2 Intervariant Competition Are Exemplified in the Pre-Omicron Era of the Colombian Epidemic

The first 18 months of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections in Colombia were characterized by three epidemic waves. During the third wave, from March through August 2021, intervariant competition resulted in Mu replacing Alpha and Gamma. We employed Bayesian phylodynamic inference and epidemiological modeling to characterize the variants in the country during this period of competition. Phylogeographic analysis indicated that Mu did not emerge in Colombia but acquired increased fitness there through local transmission and diversification, contributing to its export to North America and Europe. Despite not having the highest transmissibility, Mu's genetic composition and ability to evade preexisting immunity facilitated its domination of the Colombian epidemic landscape. Our results support previous modeling studies demonstrating that both intrinsic factors (transmissibility and genetic diversity) and extrinsic factors (time of introduction and acquired immunity) influence the outcome of intervariant competition. This analysis will help set practical expectations about the inevitable emergences of new variants and their trajectories. IMPORTANCE Before the appearance of the Omicron variant in late 2021, numerous SARS-CoV-2 variants emerged, were established, and declined, often with different outcomes in different geographic areas. In this study, we considered the trajectory of the Mu variant, which only successfully dominated the epidemic landscape of a single country: Colombia. We demonstrate that Mu competed successfully there due to its early and opportune introduction time in late 2020, combined with its ability to evade immunity granted by prior infection or the first generation of vaccines. Mu likely did not effectively spread outside of Colombia because other immune-evading variants, such as Delta, had arrived in those locales and established themselves first. On the other hand, Mu's early spread within Colombia may have prevented the successful establishment of Delta there. Our analysis highlights the geographic heterogeneity of early SARS-CoV-2 variant spread and helps to reframe the expectations for the competition behaviors of future variants.

A fractional PI observer for incommensurate fractional order systems under parametric uncertainties

The problem of state observation in incommensurate fractional order systems has been poorly studied. Currently some observers that have been proposed are based on a copy of the system, which causes them to be highly dependent on the system parameters, additionally they are redundant (estimate variables that are available). So this paper proposes a novel fractional observer against parametric uncertainties for a certain type of incommensurate fractional order systems. The fractional observer design is based on a property concerning observability in incommensurate fractional order systems which allows us to construct the observer only considering the available output and its fractional derivatives. On the other hand, the convergence analysis of the observation error is carried out using a particular approach of fractional order systems related to the Global Mittag-Leffler boundedness. We prove that there is a compact set GMLA (Globally Mittag-Leffler Attractive, according to Definition 4) where the system that represents the observation error dynamics is attractive and we also prove that the observation error is uniformly bounded. Additionally, the fractional observer is model-free i.e., a system copy is not required, this gives robustness in spite of parametric uncertainties and it is also reduced order therefore one observer must be designed for each variable that we want to estimate consequently the observer is non-redundant (no estimation of variables that are already available). Moreover, our proposed fractional observer can be designed for commensurate fractional order systems and we also show that if we consider integer derivative order, the proposed fractional observer presents certain properties. Finally, in order to show the effectiveness of the proposed fractional observer, an incommensurate fractional order Rössler hyperchaotic system is considered as a numerical example and an incommensurate fractional model of the COVID-19 pandemic as a real-world application.

Analyzing COVID-19 data in the Canadian province of Manitoba: A new approach

The basic homogeneous SEIR (susceptible-exposed-infected-removed) model is a commonly used compartmental model for analysing infectious diseases such as influenza and COVID-19. However, in the homogeneous SEIR model, it is assumed that the population of study is homogeneous and, one cannot incorporate individual-level information (e.g., location of infected people, distance between susceptible and infected individuals, vaccination status) which may be important in predicting new disease cases. Recently, a geographically-dependent individual-level model (GD-ILM) within an SEIR framework was developed for when both regional and individual-level spatial data are available. In this paper, we propose to use an SEIR GD-ILM for each health region of Manitoba (central Canadian province) population to analyse the COVID-19 data. As different health regions of the population under study may act differently, we assume that each health region has its own corresponding parameters determined by a homogeneous SEIR model (such as contact rate, latent period, infectious period). A Monte Carlo Expectation Conditional Maximization (MCECM) algorithm is used for inference. Using estimated parameters we predict the infection rate at each health region of Manitoba over time to identify highly risk local geographical areas. Performance of the proposed approach is also evaluated through simulation studies.

How to promote the diffusion of green behavior among contractors? Analysis and simulation using the SIR model

To promote the green development of the construction industry, improve resource utilization, and mitigate the environmental pollution caused by engineering projects, this study identifies the key paths and influencing factors of behavioral diffusion through the analysis of green behavior diffusion among contractors based on the behavioral decisions of the main participants. The study aims to improve positive influences among contractors with respect to the sustainable development of construction. Using the SIR (susceptible-infected-removed) model, we reconsider contractors of different states; construct state transformation paths for potential adopters, adopters, and abandoners of green behaviors among contractors; and analyze the factors that influence the diffusion of green behaviors among contractors to simulate the effects of different paths of behavior diffusion. The results show that two paths, adoption and recovery rates, have a positive influence on the diffusion of green behavior, while three other paths have a negative influence. The identified factors exhibit two types of influence, promotion and hindrance, involving both intra-firm and government regulations, and are associated with other stakeholders. This study promotes the diffusion of green behavior among contractors, which allows contractors to gain a competitive advantage in advance and has positive implications for the implementation of environmentally friendly concepts in the construction industry.

"Does a Respiratory Virus Have an Ecological Niche, and If So, Can It Be Mapped?" Yes and Yes

Although the utility of Ecological Niche Models (ENM) and Species Distribution Models (SDM) has been demonstrated in many ecological applications, their suitability for modelling epidemics or pandemics, such as SARS-Cov-2, has been questioned. In this paper, contrary to this viewpoint, we show that ENMs and SDMs can be created that can describe the evolution of pandemics, both in space and time. As an illustrative use case, we create models for predicting confirmed cases of COVID-19, viewed as our target "species", in Mexico through 2020 and 2021, showing that the models are predictive in both space and time. In order to achieve this, we extend a recently developed Bayesian framework for niche modelling, to include: (i) dynamic, non-equilibrium "species" distributions; (ii) a wider set of habitat variables, including behavioural, socio-economic and socio-demographic variables, as well as standard climatic variables; (iii) distinct models and associated niches for different species characteristics, showing how the niche, as deduced through presence-absence data, can differ from that deduced from abundance data. We show that the niche associated with those places with the highest abundance of cases has been highly conserved throughout the pandemic, while the inferred niche associated with presence of cases has been changing. Finally, we show how causal chains can be inferred and confounding identified by showing that behavioural and social factors are much more predictive than climate and that, further, the latter is confounded by the former.