Simulating the spread of COVID-19 via a spatially-resolved susceptible-exposed-infected-recovered-deceased (SEIRD) model with heterogeneous diffusion

On quasi-linear reaction diffusion systems arising from compartmental SEIR models

The global existence and boundedness of solutions to quasi-linear reaction-diffusion systems are investigated. The system arises from compartmental models describing the spread of infectious diseases proposed in Viguerie et al. (Appl Math Lett 111:106617, 2021); Viguerie et al. (Comput Mech 66(5):1131-1152, 2020), where the diffusion rate is assumed to depend on the total population, leading to quasilinear diffusion with possible degeneracy. The mathematical analysis of this model has been addressed recently in Auricchio et al. (Math Methods Appl Sci 46:12529-12548, 2023) where it was essentially assumed that all sub-populations diffuse at the same rate, which yields a positive lower bound of the total population, thus removing the degeneracy. In this work, we remove this assumption completely and show the global existence and boundedness of solutions by exploiting a recently developed L p -energy method. Our approach is applicable to a larger class of systems and is sufficiently robust to allow model variants and different boundary conditions.

SIRS epidemics with individual heterogeneity of immunity waning

In the current paper we analyse an extended SIRS epidemic model in which immunity at the individual level wanes gradually at exponential rate, but where the waning rate may differ between individuals, for instance as an effect of differences in immune systems. The model also includes vaccination schemes aimed to reach and maintain herd immunity. We consider both the informed situation where the individual waning parameters are known, thus allowing selection of vaccinees being based on both time since last vaccination as well as on the individual waning rate, and the more likely uninformed situation where individual waning parameters are unobserved, thus only allowing vaccination schemes to depend on time since last vaccination. The optimal vaccination policies for both the informed and uniformed heterogeneous situation are derived and compared with the homogeneous waning model (meaning all individuals have the same immunity waning rate), as well as to the classic SIRS model where immunity at the individual level drops from complete immunity to complete susceptibility in one leap. It is shown that the classic SIRS model requires least vaccines, followed by the SIRS with homogeneous gradual waning, followed by the informed situation for the model with heterogeneous gradual waning. The situation requiring most vaccines for herd immunity is the most likely scenario, that immunity wanes gradually with unobserved individual heterogeneity. For parameter values chosen to mimic COVID-19 and assuming perfect initial immunity and cumulative immunity of 12 months, the classic homogeneous SIRS epidemic suggests that vaccinating individuals every 15 months is sufficient to reach and maintain herd immunity, whereas the uninformed case for exponential waning with rate heterogeneity corresponding to a coefficient of variation being 0.5, requires that individuals instead need to be vaccinated every 4.4 months.

Quantitative analysis of social influence and digital piracy contagion with differential equations on networks

Illegal file sharing of copyrighted contents through popular file sharing networks poses an enormous threat to providers of digital contents, such as, games, softwares, music and movies. Though empirical studies of network effects on piracy is a well-studied domain, the dynamics of peer effect in the context of evolving social contagion has not been enough explored using dynamical models. In this research, we methodically study the trends of online piracy with a continuous ODE approach and differential equations on graphs to have a clear comparative view. We first formulate a compartmental model to study bifurcations and thresholds mathematically. We later move on with a network-based analysis to illustrate the proliferation of online piracy dynamics with an epidemiological approach over a social network. We figure out a solution for this online piracy problem by developing awareness among individuals and introducing media campaigns, which could be a valuable factor in eradicating and controlling online piracy. Next, using degree-block approximation, network analysis has been performed to investigate the phenomena from a heterogeneous approach and to derive the threshold condition for the persistence of piracy in the population in a steady state. Considering the dual control of positive peer influence and media-driven awareness, we examine the system through realistic parameter selection to better understand the complexity of the dynamics and suggest policy implications.

K-Track-Covid: interactive web-based dashboard for analyzing geographical and temporal spread of COVID-19 in South Korea

The COVID-19 pandemic has necessitated the development of robust tools for tracking and modeling the spread of the virus. We present 'K-Track-Covid,' an interactive web-based dashboard developed using the R Shiny framework, to offer users an intuitive dashboard for analyzing the geographical and temporal spread of COVID-19 in South Korea. Our dashboard employs dynamic user interface elements, employs validated epidemiological models, and integrates regional data to offer tailored visual displays. The dashboard allows users to customize their data views by selecting specific time frames, geographic regions, and demographic groups. This customization enables the generation of charts and statistical summaries pertinent to both daily fluctuations and cumulative counts of COVID-19 cases, as well as mortality statistics. Additionally, the dashboard offers a simulation model based on mathematical models, enabling users to make predictions under various parameter settings. The dashboard is designed to assist researchers, policymakers, and the public in understanding the spread and impact of COVID-19, thereby facilitating informed decision-making. All data and resources related to this study are publicly available to ensure transparency and facilitate further research.

Heterogeneous risk tolerance, in-groups, and epidemic waves

There is a growing interest in the joint modeling of the dynamics of disease and health-related beliefs and attitudes, but coupling mechanisms are yet to be understood. We introduce a model where risk information, which can be delayed, comes in two flavors, including historical risk derived from perceived incidence data and predicted risk information. Our model also includes an interpretation domain where the behavioral response to risk information is subject to in-group pressure. We then simulate how the strength of behavioral reaction impacts epidemic severity as measured by epidemic peak size, number of waves, and final size. Simulated behavioral response is not effective when the level of protection that prophylactic behavior provides is as small as 50% or lower. At a higher level of 75% or more, we see the emergence of multiple epidemic waves. In addition, simulations show that different behavioral response profiles can lead to various epidemic outcomes that are non-monotonic with the strength of reaction to risk information. We also modeled heterogeneity in the response profile of a population and find they can lead to less severe epidemic outcome in terms of peak size.

Vaccination compartmental epidemiological models for the delta and omicron SARS-CoV-2 variants

We explore the inclusion of vaccination in compartmental epidemiological models concerning the delta and omicron variants of the SARS-CoV-2 virus that caused the COVID-19 pandemic. We expand on our earlier compartmental-model work by incorporating vaccinated populations. We present two classes of models that differ depending on the immunological properties of the variant. The first one is for the delta variant, where we do not follow the dynamics of the vaccinated individuals since infections of vaccinated individuals were rare. The second one for the far more contagious omicron variant incorporates the evolution of the infections within the vaccinated cohort. We explore comparisons with available data involving two possible classes of counts, fatalities and hospitalizations. We present our results for two regions, Andalusia and Switzerland (including the Principality of Liechtenstein), where the necessary data are available. In the majority of the considered cases, the models are found to yield good agreement with the data and have a reasonable predictive capability beyond their training window, rendering them potentially useful tools for the interpretation of the COVID-19 and further pandemic waves, and for the design of intervention strategies during these waves.

A fractional mathematical model with nonlinear partial differential equations for transmission dynamics of severe acute respiratory syndrome coronavirus 2 infection

This study presents a fractional mathematical model based on nonlinear Partial Differential Equations (PDEs) of fractional variable-order derivatives for the host populations experiencing transmission and evolution of the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) pandemic. Five host population groups have been considered, the Susceptible, Exposed, Infected, Recovered, and Deceased (SEIRD). The new model, not introduced before in its current formulation, is governed by nonlinear PDEs with fractional variable-order derivatives. As a result, the proposed model is not compared with other models or real scenarios. The advantage of the proposed fractional partial derivatives of variable orders is that they can model the rate of change of subpopulation for the proposed model. As an efficient tool to obtain the solution of the proposed model, a modified analytical technique based on the homotopy and Adomian decomposition methods is introduced. Then again, the present study is general and is applicable to a host population in any country.

Modelling the spatial spread of COVID-19 in a German district using a diffusion model

In this study, we focus on modeling the local spread of COVID-19 infections. As the pandemic continues and new variants or future pandemics can emerge, modelling the early stages of infection spread becomes crucial, especially as limited medical data might be available initially. Therefore, our aim is to gain a better understanding of the diffusion dynamics on smaller scales using partial differential equation (PDE) models. Previous works have already presented various methods to model the spatial spread of diseases, but, due to a lack of data on regional or even local scale, few actually applied their models on real disease courses in order to describe the behaviour of the disease or estimate parameters. We use medical data from both the Robert-Koch-Institute (RKI) and the Birkenfeld district government for parameter estimation within a single German district, Birkenfeld in Rhineland-Palatinate, during the second wave of the pandemic in autumn 2020 and winter 2020-21. This district can be seen as a typical middle-European region, characterized by its (mainly) rural nature and daily commuter movements towards metropolitan areas. A basic reaction-diffusion model used for spatial COVID spread, which includes compartments for susceptibles, exposed, infected, recovered, and the total population, is used to describe the spatio-temporal spread of infections. The transmission rate, recovery rate, initial infected values, detection rate, and diffusivity rate are considered as parameters to be estimated using the reported daily data and least square fit. This work also features an emphasis on numerical methods which will be used to describe the diffusion on arbitrary two-dimensional domains. Two numerical optimization techniques for parameter fitting are used: the Metropolis algorithm and the adjoint method. Two different methods, the Crank-Nicholson method and a finite element method, which are used according to the requirements of the respective optimization method are used to solve the PDE system. This way, the two methods are compared and validated and provide similar results with good approximation of the infected in both the district and the respective sub-districts.

A data-driven framework to assess population dynamics during novel coronavirus outbreaks: A case study on Xiamen Island, China

The outbreak of the Coronavirus Disease 2019 (COVID-19) has profoundly influenced daily life, necessitating the understanding of the relationship between the epidemic's progression and population dynamics. In this study, we present a data-driven framework that integrates GIS-based data mining technology and a Susceptible, Exposed, Infected and Recovered (SEIR) model. This approach helps delineate population dynamics at the grid and community scales and analyze the impacts of government policies, urban functional areas, and intercity flows on population dynamics during the pandemic. Xiamen Island was selected as a case study to validate the effectiveness of the data-driven framework. The results of the high/low cluster analysis provide 99% certainty (P < 0.01) that the population distribution between January 23 and March 16, 2020, was not random, a phenomenon referred to as high-value clustering. The SEIR model predicts that a ten-day delay in implementing a lockdown policy during an epidemic can lead to a significant increase in the number of individuals infected by the virus. Throughout the epidemic prevention and control period (January 23 to February 21, 2020), residential and transportation areas housed more residents. After the resumption of regular activities, the population was mainly concentrated in residential, industrial, and transportation, as well as road facility areas. Notably, the migration patterns into and out of Xiamen were primarily centered on neighboring cities both before and after the outbreak. However, migration indices from cities outside the affected province drastically decreased and approached zero following the COVID-19 outbreak. Our findings offer new insights into the interplay between the epidemic's development and population dynamics, which enhances the prevention and control of the coronavirus epidemic.

Combining the dynamic model and deep neural networks to identify the intensity of interventions during COVID-19 pandemic

During the COVID-19 pandemic, control measures, especially massive contact tracing following prompt quarantine and isolation, play an important role in mitigating the disease spread, and quantifying the dynamic contact rate and quarantine rate and estimate their impacts remain challenging. To precisely quantify the intensity of interventions, we develop the mechanism of physics-informed neural network (PINN) to propose the extended transmission-dynamics-informed neural network (TDINN) algorithm by combining scattered observational data with deep learning and epidemic models. The TDINN algorithm can not only avoid assuming the specific rate functions in advance but also make neural networks follow the rules of epidemic systems in the process of learning. We show that the proposed algorithm can fit the multi-source epidemic data in Xi'an, Guangzhou and Yangzhou cities well, and moreover reconstruct the epidemic development trend in Hainan and Xinjiang with incomplete reported data. We inferred the temporal evolution patterns of contact/quarantine rates, selected the best combination from the family of functions to accurately simulate the contact/quarantine time series learned by TDINN algorithm, and consequently reconstructed the epidemic process. The selected rate functions based on the time series inferred by deep learning have epidemiologically reasonable meanings. In addition, the proposed TDINN algorithm has also been verified by COVID-19 epidemic data with multiple waves in Liaoning province and shows good performance. We find the significant fluctuations in estimated contact/quarantine rates, and a feedback loop between the strengthening/relaxation of intervention strategies and the recurrence of the outbreaks. Moreover, the findings show that there is diversity in the shape of the temporal evolution curves of the inferred contact/quarantine rates in the considered regions, which indicates variation in the intensity of control strategies adopted in various regions.

A two-phase fluid model for epidemic flow

We propose a new mathematical and computational modeling framework that incorporates fluid dynamics to study the spatial spread of infectious diseases. We model the susceptible and infected populations as two inviscid fluids which interact with each other. Their motion at the macroscopic level characterizes the progression and spread of the epidemic. To implement the two-phase flow model, we employ high-order numerical methods from computational fluid dynamics. We apply this model to simulate the COVID-19 outbreaks in the city of Wuhan in China and the state of Tennessee in the US. Our modeling and simulation framework allows us to conduct a detailed investigation into the complex spatiotemporal dynamics related to the transmission and spread of COVID-19.

Scalable computational algorithms for geospatial COVID-19 spread using high performance computing

A nonlinear partial differential equation (PDE) based compartmental model of COVID-19 provides a continuous trace of infection over space and time. Finer resolutions in the spatial discretization, the inclusion of additional model compartments and model stratifications based on clinically relevant categories contribute to an increase in the number of unknowns to the order of millions. We adopt a parallel scalable solver that permits faster solutions for these high fidelity models. The solver combines domain decomposition and algebraic multigrid preconditioners at multiple levels to achieve the desired strong and weak scalabilities. As a numerical illustration of this general methodology, a five-compartment susceptible-exposed-infected-recovered-deceased (SEIRD) model of COVID-19 is used to demonstrate the scalability and effectiveness of the proposed solver for a large geographical domain (Southern Ontario). It is possible to predict the infections for a period of three months for a system size of 186 million (using 3200 processes) within 12 hours saving months of computational effort needed for the conventional solvers.

Role of immigration and emigration on the spread of COVID-19 in a multipatch environment: a case study of India

Human mobility has played a critical role in the spread of COVID-19. The understanding of mobility helps in getting information on the acceleration or control of the spread of disease. The COVID-19 virus has been spreading among several locations despite all the best efforts related to its isolation. To comprehend this, a multi-patch mathematical model of COVID-19 is proposed and analysed in this work, where-in limited medical resources, quarantining, and inhibitory behaviour of healthy individuals are incorporated into the model. Furthermore, as an example, the impact of mobility in a three-patch model is studied considering the three worst-hit states of India, i.e. Kerala, Maharashtra and Tamil Nadu, as three patches. Key parameters and the basic reproduction number are estimated from the available data. Through results and analyses, it is seen that Kerala has a higher effective contact rate and has the highest prevalence. Moreover, if Kerala is isolated from Maharashtra or Tamil Nadu, the number of active cases will increase in Kerala but reduce in the other two states. Our findings indicate that the number of active cases will decrease in the high prevalence state and increase in the lower prevalence states if the emigration rate is higher than the immigration rate in the high prevalence state. Overall, proper travel restrictions are to be implemented to reduce or control the spread of disease from the high-prevalence state to other states with lower prevalence rates.

Spatial-temporal diffusion model of aggregated infectious diseases based on population life characteristics: a case study of COVID-19

Outbreaks of infectious diseases pose significant threats to human life, and countries around the world need to implement more precise prevention and control measures to contain the spread of viruses. In this study, we propose a spatial-temporal diffusion model of infectious diseases under a discrete grid, based on the time series prediction of infectious diseases, to model the diffusion process of viruses in population. This model uses the estimated outbreak origin as the center of transmission, employing a tree-like structure of daily human travel to generalize the process of viral spread within the population. By incorporating diverse data, it simulates the congregation of people, thus quantifying the flow weights between grids for population movement. The model is validated with some Chinese cities with COVID-19 outbreaks, and the results show that the outbreak point estimation method could better estimate the virus transmission center of the epidemic. The estimated location of the outbreak point in Xi'an was only 0.965 km different from the actual one, and the results were more satisfactory. The spatiotemporal diffusion model for infectious diseases simulates daily newly infected areas, which effectively cover the actual patient infection zones on the same day. During the mid-stage of viral transmission, the coverage rate can increase to over 90%, compared to related research, this method has improved simulation accuracy by approximately 18%. This study can provide technical support for epidemic prevention and control, and assist decision-makers in developing more scientific and efficient epidemic prevention and control policies.

The Role of Mobility in the Dynamics of the COVID-19 Epidemic in Andalusia

Metapopulation models have been a popular tool for the study of epidemic spread over a network of highly populated nodes (cities, provinces, countries) and have been extensively used in the context of the ongoing COVID-19 pandemic. In the present work, we revisit such a model, bearing a particular case example in mind, namely that of the region of Andalusia in Spain during the period of the summer-fall of 2020 (i.e., between the first and second pandemic waves). Our aim is to consider the possibility of incorporation of mobility across the province nodes focusing on mobile-phone time-dependent data, but also discussing the comparison for our case example with a gravity model, as well as with the dynamics in the absence of mobility. Our main finding is that mobility is key toward a quantitative understanding of the emergence of the second wave of the pandemic and that the most accurate way to capture it involves dynamic (rather than static) inclusion of time-dependent mobility matrices based on cell-phone data. Alternatives bearing no mobility are unable to capture the trends revealed by the data in the context of the metapopulation model considered herein.

Dynamic parameterization of a modified SEIRD model to analyze and forecast the dynamics of COVID-19 outbreaks in the United States

The rapid spread of the numerous outbreaks of the coronavirus disease 2019 (COVID-19) pandemic has fueled interest in mathematical models designed to understand and predict infectious disease spread, with the ultimate goal of contributing to the decision making of public health authorities. Here, we propose a computational pipeline that dynamically parameterizes a modified SEIRD (susceptible-exposed-infected-recovered-deceased) model using standard daily series of COVID-19 cases and deaths, along with isolated estimates of population-level seroprevalence. We test our pipeline in five heavily impacted states of the US (New York, California, Florida, Illinois, and Texas) between March and August 2020, considering two scenarios with different calibration time horizons to assess the update in model performance as new epidemiologic data become available. Our results show a median normalized root mean squared error (NRMSE) of 2.38% and 4.28% in calibrating cumulative cases and deaths in the first scenario, and 2.41% and 2.30% when new data are assimilated in the second scenario, respectively. Then, 2-week (4-week) forecasts of the calibrated model resulted in median NRMSE of cumulative cases and deaths of 5.85% and 4.68% (8.60% and 17.94%) in the first scenario, and 1.86% and 1.93% (2.21% and 1.45%) in the second. Additionally, we show that our method provides significantly more accurate predictions of cases and deaths than a constant parameterization in the second scenario (p < 0.05). Thus, we posit that our methodology is a promising approach to analyze the dynamics of infectious disease outbreaks, and that our forecasts could contribute to designing effective pandemic-arresting public health policies.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00366-023-01816-9.

Modeling the SARS-CoV-2 Omicron variant dynamics in the United States with booster dose vaccination and waning immunity

We carried out a theoretical and numerical analysis for an epidemic model to analyze the dynamics of the SARS-CoV-2 Omicron variant and the impact of vaccination campaigns in the United States. The model proposed here includes asymptomatic and hospitalized compartments, vaccination with booster doses, and the waning of natural and vaccine-acquired immunity. We also consider the influence of face mask usage and efficiency. We found that enhancing booster doses and using N95 face masks are associated with a reduction in the number of new infections, hospitalizations and deaths. We highly recommend the use of surgical face masks as well, if usage of N95 is not a possibility due to the price range. Our simulations show that there might be two upcoming Omicron waves (in mid-2022 and late 2022), caused by natural and acquired immunity waning with respect to time. The magnitude of these waves will be 53% and 25% lower than the peak in January 2022, respectively. Hence, we recommend continuing to use face masks to decrease the peak of the upcoming COVID-19 waves.

Kinetic Models for Epidemic Dynamics in the Presence of Opinion Polarization

Understanding the impact of collective social phenomena in epidemic dynamics is a crucial task to effectively contain the disease spread. In this work, we build a mathematical description for assessing the interplay between opinion polarization and the evolution of a disease. The proposed kinetic approach describes the evolution of aggregate quantities characterizing the agents belonging to epidemiologically relevant states and will show that the spread of the disease is closely related to consensus dynamics distribution in which opinion polarization may emerge. In the present modelling framework, microscopic consensus formation dynamics can be linked to macroscopic epidemic trends to trigger the collective adherence to protective measures. We conduct numerical investigations which confirm the ability of the model to describe different phenomena related to the spread of an epidemic.

Numerical Investigation of Time-Fractional Phi-Four Equation via Novel Transform

This paper examines two methods for solving the nonlinear fractional Phi-four problem with variable coefficients. One of the distinct states of the Klein–Gordon model yields the Phi-four equation. It is also used to simulate the kink and anti-kink solitary wave connections that have recently emerged in biological systems and nuclear particle physics. The approaches that are being suggested consist of the Yang transform, the homotopy perturbation approach, the decomposition approach, and the fractional derivative as stated by Caputo. The advantages of the proposed techniques are their capability of combining two dominant approaches for attaining precise and approximate solutions of nonlinear equations. It is important to keep in mind that the suggested methods can perform better in general as they need less computational effort than the alternative methods, while keeping a high level of numerical precision. The actual and estimated outcomes are demonstrated in graphs and tables to be quite similar, demonstrating the usefulness of the proposed approaches. Additionally, several simulations are used to show the physical behaviors of the found solutions with regard to fractional order. The article’s results possess complimentary properties that relate to the symmetry of partial differential equations.

Epi-DNNs: Epidemiological priors informed deep neural networks for modeling COVID-19 dynamics

Differential equations-based epidemic compartmental models and deep neural networks-based artificial intelligence (AI) models are powerful tools for analyzing and fighting the transmission of COVID-19. However, the capability of compartmental models is limited by the challenges of parameter estimation, while AI models fail to discover the evolutionary pattern of COVID-19 and lack explainability. This paper aims to provide a novel method (called Epi-DNNs) by integrating compartmental models and deep neural networks (DNNs) to model the complex dynamics of COVID-19. In the proposed Epi-DNNs method, the neural network is designed to express the unknown parameters in the compartmental model and the Runge–Kutta method is implemented to solve the ordinary differential equations (ODEs) so as to give the values of the ODEs at a given time. Specifically, the discrepancy between predictions and observations is incorporated into the loss function, then the defined loss is minimized and applied to identify the best-fitted parameters governing the compartmental model. Furthermore, we verify the performance of Epi-DNNs on the real-world reported COVID-19 data on the Omicron epidemic in Shanghai covering February 25 to May 27, 2022. The experimental findings on the synthesized data have revealed its effectiveness in COVID-19 transmission modeling. Moreover, the inferred parameters from the proposed Epi-DNNs method yield a predictive compartmental model, which can serve to forecast future dynamics.

Investigating the effect of vaccinated population on the COVID-19 prediction using FA and ABC-based feed-forward neural networks

Since 2019, the coronavirus outbreak has caused many catastrophic events all over the world. At the current time, the massive vaccination has been considered as the most efficient way to fight against the pandemic. This study schemes to explain and model COVID-19 cases by considering the vaccination rate. We utilized an amalgamation of neural network (NN) with two powerful optimization algorithms, i.e., firefly algorithm and artificial bee colony. For validating the models, we employed the COVID-19 datasets regarding the vaccination rate and the total confirmed cases for 51 states since the beginning of vaccination in the US. The numerical experiment indicated that by considering the vaccinated population, the accuracy of NN increases exponentially when compared with the same NN in the absence of the vaccinated population. During the next stage, the NN with vaccinated input data is elected for firefly and bee optimizing. Based upon the firefly optimizing, 93.75% of COVID-19 cases can be explained in all states. According to the bee optimizing, 92.3% of COVID-19 cases is explained since the massive vaccination. Overall, it can be concluded that the massive vaccination is the key predictor of COVID-19 cases on a grand scale.

Syndromic Surveillance Using Structured Telehealth Data: Case Study of the First Wave of COVID-19 in Brazil

BACKGROUND

Telehealth has been widely used for new case detection and telemonitoring during the COVID-19 pandemic. It safely provides access to health care services and expands assistance to remote, rural areas and underserved communities in situations of shortage of specialized health professionals. Qualified data are systematically collected by health care workers containing information on suspected cases and can be used as a proxy of disease spread for surveillance purposes. However, the use of this approach for syndromic surveillance has yet to be explored. Besides, the mathematical modeling of epidemics is a well-established field that has been successfully used for tracking the spread of SARS-CoV-2 infection, supporting the decision-making process on diverse aspects of public health response to the COVID-19 pandemic. The response of the current models depends on the quality of input data, particularly the transmission rate, initial conditions, and other parameters present in compartmental models. Telehealth systems may feed numerical models developed to model virus spread in a specific region.

OBJECTIVE

Herein, we evaluated whether a high-quality data set obtained from a state-based telehealth service could be used to forecast the geographical spread of new cases of COVID-19 and to feed computational models of disease spread.

METHODS

We analyzed structured data obtained from a statewide toll-free telehealth service during 4 months following the first notification of COVID-19 in the Bahia state, Brazil. Structured data were collected during teletriage by a health team of medical students supervised by physicians. Data were registered in a responsive web application for planning and surveillance purposes. The data set was designed to quickly identify users, city, residence neighborhood, date, sex, age, and COVID-19-like symptoms. We performed a temporal-spatial comparison of calls reporting COVID-19-like symptoms and notification of COVID-19 cases. The number of calls was used as a proxy of exposed individuals to feed a mathematical model called "susceptible, exposed, infected, recovered, deceased."

RESULTS

For 181 (43%) out of 417 municipalities of Bahia, the first call to the telehealth service reporting COVID-19-like symptoms preceded the first notification of the disease. The calls preceded, on average, 30 days of the notification of COVID-19 in the municipalities of the state of Bahia, Brazil. Additionally, data obtained by the telehealth service were used to effectively reproduce the spread of COVID-19 in Salvador, the capital of the state, using the "susceptible, exposed, infected, recovered, deceased" model to simulate the spatiotemporal spread of the disease.

CONCLUSIONS

Data from telehealth services confer high effectiveness in anticipating new waves of COVID-19 and may help understand the epidemic dynamics.

A Comparative Study of Fractional Partial Differential Equations with the Help of Yang Transform

In applied sciences and engineering, partial differential equations (PDE) of integer and non-integer order play a crucial role. It can be challenging to determine these equations’ exact solutions. As a result, developing numerical approaches to obtain precise numerical solutions to these kinds of differential equations takes time. The homotopy perturbation transform method (HPTM) and Yang transform decomposition method (YTDM) are the subjects of several recent findings that we describe. These techniques work well for fractional calculus applications. We also examine fractional differential equations’ precise and approximative solutions. The Caputo derivative is employed because it enables the inclusion of traditional initial and boundary conditions in the formulation of the issue. This has major implications for complicated problems. The paper lists the important characteristics of the YTDM and HPTM. Our research has numerous applications in the disciplines of science and engineering and might be seen as a substitute for current methods.

Multi-regional COVID-19 epidemic forecast in Sweden

The novel coronavirus disease 2019 (COVID-19) is a contagious disease with high transmissibility to spread worldwide, reported to present a certain burden on worldwide public health. This study aimed to determine epidemic occurrence probability at any reasonable time horizon in any region of interest by applying modern novel statistical methods directly to raw clinical data. This paper describes a novel bio-system reliability approach, particularly suitable for multi-regional health and stationary environmental systems, observed over a sufficient period of time, resulting in a reliable long-term forecast of the highly pathogenic virus outbreak probability. For this study, COVID-19 daily recorded patient numbers in most affected Sweden regions were chosen. This work aims to benchmark state-of-the-art methods, making it possible to extract necessary information from dynamically observed patient numbers while considering relevant territorial mapping. The method proposed in this paper opens up the possibility of accurately predicting epidemic outbreak probability for multi-regional biological systems. Based on their clinical survey data, the suggested methodology can be used in various public health applications. Key findings are: A novel spatiotemporal health system reliability method has been developed and applied to COVID-19 epidemic data.Accurate multi-regional epidemic occurrence prediction is made.Epidemic threshold confidence bands given.

Dynamical analysis of a stochastic delayed epidemic model with lévy jumps and regime switching

In this paper a delayed stochastic SLVIQR epidemic model, which can be applied for modeling the new coronavirus COVID-19 after a calibration, is derived. Model is constructed by assuming that transmission rate satisfies the mean-reverting Ornstain-Uhlenbeck process and, besides a standard Brownian motion, another two driving processes are considered: a stationary Poisson point process and a continuous finite-state Markov chain. For the constructed model, the existence and uniqueness of positive global solution is proven. Also, sufficient conditions under which the disease would lead to extinction or be persistent in the mean are established and it is shown that constructed model has a richer dynamic analysis compared to existing models. In addition, numerical simulations are given to illustrate the theoretical results.

Assessing the medical resources in COVID-19 based on evolutionary game

COVID-19 has brought a great challenge to the medical system. A key scientific question is how to make a balance between home quarantine and staying in the hospital. To this end, we propose a game-based susceptible-exposed-asymptomatic -symptomatic- hospitalized-recovery-dead model to reveal such a situation. In this new framework, time-varying cure rate and mortality are employed and a parameter m is introduced to regulate the probability that individuals are willing to go to the hospital. Through extensive simulations, we find that (1) for low transmission rates (β < 0.2), the high value of m (the willingness to stay in the hospital) indicates the full use of medical resources, and thus the pandemic can be easily contained; (2) for high transmission rates (β > 0.2), large values of m lead to breakdown of the healthcare system, which will further increase the cumulative number of confirmed cases and death cases. Finally, we conduct the empirical analysis using the data from Japan and other typical countries to illustrate the proposed model and to test how our model explains reality.

Data Assimilation Predictive GAN (DA-PredGAN) Applied to a Spatio-Temporal Compartmental Model in Epidemiology

We propose a novel use of generative adversarial networks (GANs) (i) to make predictions in time (PredGAN) and (ii) to assimilate measurements (DA-PredGAN). In the latter case, we take advantage of the natural adjoint-like properties of generative models and the ability to simulate forwards and backwards in time. GANs have received much attention recently, after achieving excellent results for their generation of realistic-looking images. We wish to explore how this property translates to new applications in computational modelling and to exploit the adjoint-like properties for efficient data assimilation. We apply these methods to a compartmental model in epidemiology that is able to model space and time variations, and that mimics the spread of COVID-19 in an idealised town. To do this, the GAN is set within a reduced-order model, which uses a low-dimensional space for the spatial distribution of the simulation states. Then the GAN learns the evolution of the low-dimensional states over time. The results show that the proposed methods can accurately predict the evolution of the high-fidelity numerical simulation, and can efficiently assimilate observed data and determine the corresponding model parameters.

Responses to COVID-19 with probabilistic programming

The COVID-19 pandemic left its unique mark on the twenty-first century as one of the most significant disasters in history, triggering governments all over the world to respond with a wide range of interventions. However, these restrictions come with a substantial price tag. It is crucial for governments to form anti-virus strategies that balance the trade-off between protecting public health and minimizing the economic cost. This work proposes a probabilistic programming method to quantify the efficiency of major initial non-pharmaceutical interventions. We present a generative simulation model that accounts for the economic and human capital cost of adopting such strategies, and provide an end-to-end pipeline to simulate the virus spread and the incurred loss of various policy combinations. By investigating the national response in 10 countries covering four continents, we found that social distancing coupled with contact tracing is the most successful policy, reducing the virus transmission rate by 96% along with a 98% reduction in economic and human capital loss. Together with experimental results, we open-sourced a framework to test the efficacy of each policy combination.

The numerical solution of a mathematical model of the Covid-19 pandemic utilizing a meshless local discrete Galerkin method

It was in early December 2019 that the terrible news of the outbreak of new coronavirus disease (Covid-19) was reported by the world media, which appeared in Wuhan, China, and is rapidly spreading to other parts of China and several overseas countries. In the field of infectious diseases, modeling, evaluating, and predicting the rate of disease transmission are very important for epidemic prevention and control. Several preliminary mathematical models for Covid-19 are formulated by various international study groups. In this article, the SEIHR(D) compartmental model is proposed to study this epidemic and the factors affecting it, including vaccination. The proposed model can be used to compute the trajectory of the spread of the disease in different countries. Most importantly, it can be used to predict the impact of different inhibition strategies on the development of Covid-19. A computational approach is applied to solve the offered model utilizing the Galerkin method based on the moving least squares approximation constructed on a set of scattered points as a locally weighted least square polynomial fitting. As the method does not need any background meshes, its algorithm can be easily implemented on computers. Finally, illustrative examples clearly show the reliability and efficiency of the new technique and the obtained results are in good agreement with the known facts about the Covid-19 pandemic.

Modeling nonlocal behavior in epidemics via a reaction-diffusion system incorporating population movement along a network

The outbreak of COVID-19, beginning in 2019 and continuing through the time of writing, has led to renewed interest in the mathematical modeling of infectious disease. Recent works have focused on partial differential equation (PDE) models, particularly reaction-diffusion models, able to describe the progression of an epidemic in both space and time. These studies have shown generally promising results in describing and predicting COVID-19 progression. However, people often travel long distances in short periods of time, leading to nonlocal transmission of the disease. Such contagion dynamics are not well-represented by diffusion alone. In contrast, ordinary differential equation (ODE) models may easily account for this behavior by considering disparate regions as nodes in a network, with the edges defining nonlocal transmission. In this work, we attempt to combine these modeling paradigms via the introduction of a network structure within a reaction-diffusion PDE system. This is achieved through the definition of a population-transfer operator, which couples disjoint and potentially distant geographic regions, facilitating nonlocal population movement between them. We provide analytical results demonstrating that this operator does not disrupt the physical consistency or mathematical well-posedness of the system, and verify these results through numerical experiments. We then use this technique to simulate the COVID-19 epidemic in the Brazilian region of Rio de Janeiro, showcasing its ability to capture important nonlocal behaviors, while maintaining the advantages of a reaction-diffusion model for describing local dynamics.

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

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

A data-validated temporary immunity model of COVID-19 spread in Michigan

We introduce a distributed-delay differential equation disease spread model for COVID-19 spread. The model explicitly incorporates the population's time-dependent vaccine uptake and incorporates a gamma-distributed temporary immunity period for both vaccination and previous infection. We validate the model on COVID-19 cases and deaths data from the state of Michigan and use the calibrated model to forecast the spread and impact of the disease under a variety of realistic booster vaccine strategies. The model suggests that the mean immunity duration for individuals after vaccination is 350 days and after a prior infection is 242 days. Simulations suggest that both high population-wide adherence to vaccination mandates and a more-than-annually frequency of booster doses will be required to contain outbreaks in the future.

Modelling the impact of health care providers in transmission dynamics of COVID-19

In this paper, a mathematical model is proposed and analysed to assess the impacts of health care providers in transmission dynamics of COVID-19. The stability theory of differential equations is used to examine a mathematical model. The results of both local and global stability of disease-free equilibrium points were determined by using Routh-Hurwitz criteria and Metzler matrix method which verified that was locally and globally asymptotically stable. Also, the endemic equilibrium point was determined by the Lyapunov function which showed that E ∗ was globally asymptotically stable under strict conditions. The findings revealed that non-diagnosed and undetected health care providers seems to contribute to high spread of COVID-19 in a community. Also, it illustrates that an increase in the number of non-diagnostic testing rates of health care providers may result in high infection rates in the community and contaminations of hospitals' equipment. Therefore, the particular study recommend that there is a necessity of applying early diagnostic testing to curtail the COVID-19 transmission in the health care providers' community and reduce contaminations of hospital's equipment.

Optimizing Spatio-Temporal Allocation of the COVID-19 Vaccine Under Different Epidemiological Landscapes

An efficient and safe vaccine is expected to allow people to return to normal life as soon as possible. However, vaccines for new diseases are likely to be in short supply during the initial deployment due to narrow production capacity and logistics. There is an urgent need to optimize the allocation of limited vaccines to improve the population effectiveness of vaccination. Existing studies mostly address a single epidemiological landscape. The robustness of the effectiveness of other proposed strategies is difficult to guarantee under other landscapes. In this study, a novel vaccination allocation model based on spatio-temporal heterogeneity of epidemiological landscapes is proposed. This model was combined with optimization algorithms to determine the near-optimal spatio-temporal allocation for vaccines with different effectiveness and coverage. We fully simulated the epidemiological landscapes during vaccination, and then minimized objective functions independently under various epidemiological landscapes and degrees of viral transmission. We find that if all subregions are in the middle or late stages of the pandemic, the difference between the effectiveness of the near-optimal and pro-rata strategies is very small in most cases. In contrast, under other epidemiological landscapes, when minimizing deaths, the optimizer tends to allocate the remaining doses to sub-regions with relatively higher risk and expected coverage after covering the elderly. While to minimize symptomatic infections, allocating vaccines first to the higher-risk sub-regions is near-optimal. This means that the pro-rata allocation is a good option when the subregions are all in the middle to late stages of the pandemic. Moreover, we suggest that if all subregions are in the period of rapid virus transmission, vaccines should be administered to older adults in all subregions simultaneously, while when the epidemiological dynamics of the subregions are significantly different, priority can be given to older adults in subregions that are still in the early stages of the pandemic. After covering the elderly in the region, high-risk sub-regions can be prioritized.

Modeling epidemic flow with fluid dynamics

In this paper, a new mathematical model based on partial differential equations is proposed to study the spatial spread of infectious diseases. The model incorporates fluid dynamics theory and represents the epidemic spread as a fluid motion generated through the interaction between the susceptible and infected hosts. At the macroscopic level, the spread of the infection is modeled as an inviscid flow described by the Euler equation. Nontrivial numerical methods from computational fluid dynamics (CFD) are applied to investigate the model. In particular, a fifth-order weighted essentially non-oscillatory (WENO) scheme is employed for the spatial discretization. As an application, this mathematical and computational framework is used in a simulation study for the COVID-19 outbreak in Wuhan, China. The simulation results match the reported data for the cumulative cases with high accuracy and generate new insight into the complex spatial dynamics of COVID-19.

Spatialized epidemiological forecasting applied to Covid-19 pandemic at departmental scale in France

In this paper, we present a spatialized extension of a SIR model that accounts for undetected infections and recoveries as well as the load on hospital services. The spatialized compartmental model we introduce is governed by a set of partial differential equations (PDEs) defined on a spatial domain with complex boundary. We propose to solve the set of PDEs defining our model by using a meshless numerical method based on a finite difference scheme in which the spatial operators are approximated by using radial basis functions. Such an approach is reputed as flexible for solving problems on complex domains. Then we calibrate our model on the French department of Isère during the first period of lockdown, using daily reports of hospital occupancy in France. Our methodology allows to simulate the spread of Covid-19 pandemic at a departmental level, and for each compartment. However, the simulation cost prevents from online short-term forecast. Therefore, we propose to rely on reduced order modeling to compute short-term forecasts of infection number. The strategy consists in learning a time-dependent reduced order model with few compartments from a collection of evaluations of our spatialized detailed model, varying initial conditions and parameter values. A set of reduced bases is learnt in an offline phase while the projection on each reduced basis and the selection of the best projection is performed online, allowing short-term forecast of the global number of infected individuals in the department. The original approach proposed in this paper is generic and could be adapted to model and simulate other dynamics described by a model with spatially distributed parameters of the type diffusion-reaction on complex domains. Also, the time-dependent model reduction techniques we introduced could be leveraged to compute control strategies related to such dynamics.

Delay differential equations for the spatially resolved simulation of epidemics with specific application to COVID-19

In the wake of the 2020 COVID-19 epidemic, much work has been performed on the development of mathematical models for the simulation of the epidemic and of disease models generally. Most works follow the susceptible-infected-removed (SIR) compartmental framework, modeling the epidemic with a system of ordinary differential equations. Alternative formulations using a partial differential equation (PDE) to incorporate both spatial and temporal resolution have also been introduced, with their numerical results showing potentially powerful descriptive and predictive capacity. In the present work, we introduce a new variation to such models by using delay differential equations (DDEs). The dynamics of many infectious diseases, including COVID-19, exhibit delays due to incubation periods and related phenomena. Accordingly, DDE models allow for a natural representation of the problem dynamics, in addition to offering advantages in terms of computational time and modeling, as they eliminate the need for additional, difficult-to-estimate, compartments (such as exposed individuals) to incorporate time delays. In the present work, we introduce a DDE epidemic model in both an ordinary and partial differential equation framework. We present a series of mathematical results assessing the stability of the formulation. We then perform several numerical experiments, validating both the mathematical results and establishing model's ability to reproduce measured data on realistic problems.

Global prediction model for COVID-19 pandemic with the characteristics of the multiple peaks and local fluctuations

Background

With the spread of COVID-19, the time-series prediction of COVID-19 has become a research hotspot. Unlike previous epidemics, COVID-19 has a new pattern of long-time series, large fluctuations, and multiple peaks. Traditional dynamical models are limited to curves with short-time series, single peak, smoothness, and symmetry. Secondly, most of these models have unknown parameters, which bring greater ambiguity and uncertainty. There are still major shortcomings in the integration of multiple factors, such as human interventions, environmental factors, and transmission mechanisms.

Methods

A dynamical model with only infected humans and removed humans was established. Then the process of COVID-19 spread was segmented using a local smoother. The change of infection rate at different stages was quantified using the continuous and periodic Logistic growth function to quantitatively describe the comprehensive effects of natural and human factors. Then, a non-linear variable and NO₂ concentrations were introduced to qualify the number of people who have been prevented from infection through human interventions.

Results

The experiments and analysis showed the R² of fitting for the US, UK, India, Brazil, Russia, and Germany was 0.841, 0.977, 0.974, 0.659, 0.992, and 0.753, respectively. The prediction accuracy of the US, UK, India, Brazil, Russia, and Germany in October was 0.331, 0.127, 0.112, 0.376, 0.043, and 0.445, respectively.

Conclusion

The model can not only better describe the effects of human interventions but also better simulate the temporal evolution of COVID-19 with local fluctuations and multiple peaks, which can provide valuable assistant decision-making information.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12874-022-01604-x.

Efficacy versus abundancy: Comparing vaccination schemes

We introduce a novel compartmental model accounting for the effects of vaccine efficacy, deployment rates and timing of initiation of deployment. We simulate different scenarios and initial conditions, and we find that higher abundancy and rate of deployment of low efficacy vaccines lowers the cumulative number of deaths in comparison to slower deployment of high efficacy vaccines. We also forecast that, at the same daily deployment rate, the earlier introduction of vaccination schemes with lower efficacy would also lower the number of deaths with respect to a delayed introduction of high efficacy vaccines, which can however, still achieve lower numbers of infections and better herd immunity.

SARS-CoV-2 rate of spread in and across tissue, groundwater and soil: A meshless algorithm for the fractional diffusion equation

The epidemiological aspects of the viral dynamic of the SARS-CoV-2 have become increasingly crucial due to major questions and uncertainties around the unaddressed issues of how corpse burial or the disposal of contaminated waste impacts nearby soil and groundwater. Here, a theoretical framework base on a meshless algorithm using the moving least squares (MLS) shape functions is adopted for solving the time-fractional model of the viral diffusion in and across three different environments including water, tissue, and soil. Our computations predict that by considering the α (order of fractional derivative) best fit to experimental data, the virus has a traveling distance of 1 m m in water after 22, regardless of the source of contamination (e.g., from tissue or soil). The outcomes and extrapolations of our study are fundamental for providing valuable benchmarks for future experimentation on this topic and ultimately for the accurate description of viral spread across different environments. In addition to COVID-19 relief efforts, our methodology can be adapted for a wide range of applications such as studying virus ecology and genomic reservoirs in freshwater and marine environments.

Generic approach for mathematical model of multi-strain pandemics

Multi-strain pandemics have emerged as a major concern. We introduce a new model for assessing the connection between multi-strain pandemics and mortality rate, basic reproduction number, and maximum infected individuals. The proposed model provides a general mathematical approach for representing multi-strain pandemics, generalizing for an arbitrary number of strains. We show that the proposed model fits well with epidemiological historical world health data over a long time period. From a theoretical point of view, we show that the increasing number of strains increases logarithmically the maximum number of infected individuals and the mean mortality rate. Moreover, the mean basic reproduction number is statistically identical to the single, most aggressive pandemic strain for multi-strain pandemics.

Using the SARIMA Model to Forecast the Fourth Global Wave of Cumulative Deaths from COVID-19: Evidence from 12 Hard-Hit Big Countries

The COVID-19 pandemic is a serious threat to all of us. It has caused an unprecedented shock to the world’s economy, and it has interrupted the lives and livelihood of millions of people. In the last two years, a large body of literature has attempted to forecast the main dimensions of the COVID-19 outbreak using a wide set of models. In this paper, I forecast the short- to mid-term cumulative deaths from COVID-19 in 12 hard-hit big countries around the world as of 20 August 2021. The data used in the analysis were extracted from the Our World in Data COVID-19 dataset. Both non-seasonal and seasonal autoregressive integrated moving averages (ARIMA and SARIMA) were estimated. The analysis showed that: (i) ARIMA/SARIMA forecasts were sufficiently accurate in both the training and test set by always outperforming the simple alternative forecasting techniques chosen as benchmarks (Mean, Naïve, and Seasonal Naïve); (ii) SARIMA models outperformed ARIMA models in 47 out 48 metrics (in forecasting future values), i.e., on 97.9% of all the considered forecast accuracy measures (mean absolute error [MAE], mean absolute percentage error [MAPE], mean absolute scaled error [MASE], and the root mean squared error [RMSE]), suggesting a clear seasonal pattern in the data; and (iii) the forecasted values from SARIMA models fitted very well the observed (real-time) data for the period 21 August 2021–19 September 2021 for almost all the countries analyzed. This article shows that SARIMA can be safely used for both the short- and medium-term predictions of COVID-19 deaths. Thus, this approach can help government authorities to monitor and manage the huge pressure that COVID-19 is exerting on national healthcare systems.

Comprehensive compartmental model and calibration algorithm for the study of clinical implications of the population-level spread of COVID-19: a study protocol

INTRODUCTION

The complex dynamics of the coronavirus disease 2019 (COVID-19) pandemic has made obtaining reliable long-term forecasts of the disease progression difficult. Simple mechanistic models with deterministic parameters are useful for short-term predictions but have ultimately been unsuccessful in extrapolating the trajectory of the pandemic because of unmodelled dynamics and the unrealistic level of certainty that is assumed in the predictions.

METHODS AND ANALYSIS

We propose a 22-compartment epidemiological model that includes compartments not previously considered concurrently, to account for the effects of vaccination, asymptomatic individuals, inadequate access to hospital care, post-acute COVID-19 and recovery with long-term health complications. Additionally, new connections between compartments introduce new dynamics to the system and provide a framework to study the sensitivity of model outputs to several concurrent effects, including temporary immunity, vaccination rate and vaccine effectiveness. Subject to data availability for a given region, we discuss a means by which population demographics (age, comorbidity, socioeconomic status, sex and geographical location) and clinically relevant information (different variants, different vaccines) can be incorporated within the 22-compartment framework. Considering a probabilistic interpretation of the parameters allows the model's predictions to reflect the current state of uncertainty about the model parameters and model states. We propose the use of a sparse Bayesian learning algorithm for parameter calibration and model selection. This methodology considers a combination of prescribed parameter prior distributions for parameters that are known to be essential to the modelled dynamics and automatic relevance determination priors for parameters whose relevance is questionable. This is useful as it helps prevent overfitting the available epidemiological data when calibrating the parameters of the proposed model. Population-level administrative health data will serve as partial observations of the model states.

ETHICS AND DISSEMINATION

Approved by Carleton University's Research Ethics Board-B (clearance ID: 114596). Results will be made available through future publication.

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

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

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

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

A Multi-Agent-Based Simulation Model for the Spreading of Diseases Through Social Interactions During Pandemics

Epidemiological models have a vital and consolidated role in aiding decision-making during crises such as the Coronavirus Disease 2019 (COVID-19) pandemic. However, the influence of social interactions in the spreading of communicable diseases is left aside from the main models in the literature. The main contribution of this work is the introduction of a probabilistic simulation model based on a multi-agent approach that is capable of predicting the spreading of diseases. Our proposal has a simple model for the main source of infections in pandemics of respiratory viruses: social interactions. This simplicity is key for incorporating complex networks topology into the model, which is a more accurate representation for real-world interactions. This flexibility in network structure allows the evaluation of specific phenomena, such as the presence of super-spreaders. We provide the modeling for the dynamical network topology in two different simulation scenarios. Another contribution is the generic microscopic model for infection evolution that enables the evaluation of impact from more specific behaviors and interventions on the overall spreading of the disease. It also enables a more intuitive process for going from data to model parameters. This ease of changing the infection evolution model is key for performing more complete analyses than would be possible in other models from the literature. Further, we give specific parameters for a controlled scenario with quick testing and tracing. We present computational results that illustrate the model utilization for predicting the spreading of COVID-19 in a city. Also, we show the results of applying the model for assessing the risk of resuming on-site activities at a collective use facility.

Explainable Artificial Intelligence for COVID-19 Diagnosis Through Blood Test Variables

This work proposes an explainable artificial intelligence approach to help diagnose COVID-19 patients based on blood test and pathogen variables. Two glass-box models, logistic regression and explainable boosting machine, and two black-box models, random forest and support vector machine, were used to assess the disease diagnosis. Shapley additive explanations were used to explain predictions for the black-box models, while glass-box models feature importance brought insights into the most relevant features. All global explanations show the eosinophils and leukocytes, white blood cells are among the essential features to help diagnose the COVID-19. Moreover, the best model obtained an AUC of 0.87.

Modeling the Waves of Covid-19

The challenges with modeling the spread of Covid-19 are its power-type growth during the middle stages of the waves with the exponents depending on time, and that the saturation of the waves is mainly due to the protective measures and other restriction mechanisms working in the same direction. The two-phase solution we propose for modeling the total number of detected cases of Covid-19 describes the actual curves for many its waves and in many countries almost with the accuracy of physics laws. Bessel functions play the key role in our approach. The differential equations we obtain are of universal type and can be used in behavioral psychology, invasion ecology (transient processes), etc. The initial transmission rate and the intensity of the restriction mechanisms are the key parameters. This theory provides a convincing explanation of the surprising uniformity of the Covid-19 waves in many places, and can be used for forecasting the epidemic spread. For instance, the early projections for the 3rd wave in the USA appeared sufficiently exact. The Delta-waves (2021) in India, South Africa, UK, and the Netherlands are discussed at the end.

Mathematical modeling and estimation for next wave of COVID-19 in Poland

We investigate the problem of mathematical modeling of new corona virus (COVID-19) in Poland and tries to predict the upcoming wave. A Gaussian mixture model is proposed to characterize the COVID-19 disease and to predict a new / future wave of COVID-19. This prediction is very much needed to prepare for medical setup and continue with the upcoming program. Specifically, data related to the new confirmed cases of COVID-19 per day are considered, and then we attempt to predict the data and statistical activity. A close match between actual data and analytical data by using the Gaussian mixture model shows that it is a suitable model to present new cases of COVID-19. In addition, it is thought that there are N waves of COVID-19 and that information for each future wave is also present in current and previous waves as well. Using this concept, predictions of a future wave can be made.