Spatial heterogeneity and infection patterns on epidemic transmission disclosed by a combined contact-dependent dynamics and compartmental model.

Epidemics, such as COVID-19, have caused significant harm to human society worldwide. A better understanding of epidemic transmission dynamics can contribute to more efficient prevention and control measures. Compartmental models, which assume homogeneous mixing of the population, have been widely used in the study of epidemic transmission dynamics, while agent-based models rely on a network definition for individuals. In this study, we developed a real-scale contact-dependent dynamic (CDD) model and combined it with the traditional susceptible-exposed-infectious-recovered (SEIR) compartment model. By considering individual random movement and disease spread, our simulations using the CDD-SEIR model reveal that the distribution of agent types in the community exhibits spatial heterogeneity. The estimated basic reproduction number R0 depends on group mobility, increasing logarithmically in strongly heterogeneous cases and saturating in weakly heterogeneous conditions. Notably, R0 is approximately independent of virus virulence when group mobility is low. We also show that transmission through small amounts of long-term contact is possible due to short-term contact patterns. The dependence of R0 on environment and individual movement patterns implies that reduced contact time and vaccination policies can significantly reduce the virus transmission capacity in situations where the virus is highly transmissible (i.e., R0 is relatively large). This work provides new insights into how individual movement patterns affect virus spreading and how to protect people more efficiently.

Impacts of observation frequency on proximity contact data and modeled transmission dynamics.

Transmission of many communicable diseases depends on proximity contacts among humans. Modeling the dynamics of proximity contacts can help determine whether an outbreak is likely to trigger an epidemic. While the advent of commodity mobile devices has eased the collection of proximity contact data, battery capacity and associated costs impose tradeoffs between the observation frequency and scanning duration used for contact detection. The choice of observation frequency should depend on the characteristics of a particular pathogen and accompanying disease. We downsampled data from five contact network studies, each measuring participant-participant contact every 5 minutes for durations of four or more weeks. These studies included a total of 284 participants and exhibited different community structures. We found that for epidemiological models employing high-resolution proximity data, both the observation method and observation frequency configured to collect proximity data impact the simulation results. This impact is subject to the population's characteristics as well as pathogen infectiousness. By comparing the performance of two observation methods, we found that in most cases, half-hourly Bluetooth discovery for one minute can collect proximity data that allows agent-based transmission models to produce a reasonable estimation of the attack rate, but more frequent Bluetooth discovery is preferred to model individual infection risks or for highly transmissible pathogens. Our findings inform the empirical basis for guidelines to inform data collection that is both efficient and effective.

Managing sources of error during pandemics.

The COVID-19 pandemic has highlighted important considerations for modeling future pandemics.

Determination of significant immunological timescales from mRNA-LNP-based vaccines in humans.

A compartment model for an in-host liquid nanoparticle delivered mRNA vaccine is presented. Through non-dimensionalisation, five timescales are identified that dictate the lifetime of the vaccine in-host: decay of interferon gamma, antibody priming, autocatalytic growth, antibody peak and decay, and interleukin cessation. Through asymptotic analysis we are able to obtain semi-analytical solutions in each of the time regimes which allows us to predict maximal concentrations and better understand parameter dependence in the model. We compare our model to 22 data sets for the BNT162b2 and mRNA-1273 mRNA vaccines demonstrating good agreement. Using our analysis, we estimate the values for each of the five timescales in each data set and predict maximal concentrations of plasma B-cells, antibody, and interleukin. Through our comparison, we do not observe any discernible differences between vaccine candidates and sex. However, we do identify an age dependence, specifically that vaccine activation takes longer and that peak antibody occurs sooner in patients aged 55 and greater.

[SIR model of the COVID-19 pandemic in Colombia]. / Modelo SIR de la pandemia de COVID-19 en Colombia.

OBJECTIVE: To develop a prognostic SIR model of the COVID-19 pandemic in Colombia. MATERIALS AND METHODS: A SIR model with a deterministic approach was used to forecast the development of the COVID-19 pandemic in Colombia. The states considered were susceptible (S), infectious (i) and recovered or deceased (R). Population data were obtained from the National Administrative Department of Statistics (DANE) - Population Projections 2018-2020, released in January 2020-, and data on daily confirmed cases of COVID-19 from the National Institute of Health. Different models were proposed varying the basic reproduction number (R0). RESULTS: Based on the cases reported by the Ministry of Health, 4 simulated environments were created in an epidemiological SIR model. The time series was extended until May 30, the probable date when 99% of the population will be infected. R0=2 is the basic reproduction number and the closest approximation to the behavior of the pandemic during the first 15 days since the first case report; the worst scenario would occur in the first week of April with R0=3. CONCLUSIONS: Further mitigation and suppression measures are necessary in the containment and sustained transmission phases, such as increased diagnostic capacity through testing and disinfection of populated areas and homes in isolation.

Graph Theory Based Large-Scale Machine Learning With Multi-Dimensional Constrained Optimization Approaches for Exact Epidemiological Modeling of Pandemic Diseases.

Multi-dimensional prediction models of the pandemic diseases should be constructed in a way to reflect their peculiar epidemiological characters. In this paper, a graph theory-based constrained multi-dimensional (CM) mathematical and meta-heuristic algorithms (MA) are formed to learn the unknown parameters of a large-scale epidemiological model. The specified parameter signs and the coupling parameters of the sub-models constitute the constraints of the optimization problem. In addition, magnitude constraints on the unknown parameters are imposed to proportionally weight the input-output data importance. To learn these parameters, a gradient-based CM recursive least square (CM-RLS) algorithm, and three search-based MAs; namely, the CM particle swarm optimization (CM-PSO), the CM success history-based adaptive differential evolution (CM-SHADE), and the CM-SHADEWO enriched with the whale optimization (WO) algorithms are constructed. The traditional SHADE algorithm was the winner of the 2018 IEEE congress on evolutionary computation (CEC) and its versions in this paper are modified to create more certain parameter search spaces. The results obtained under the equal conditions show that the mathematical optimization algorithm CM-RLS outperforms the MA algorithms, which is expected since it uses the available gradient information. However, the search-based CM-SHADEWO algorithm is able to capture the dominant character of the CM optimization solution and produce satisfactory estimates in the presence of the hard constraints, uncertainties and lack of gradient information.

[Impact of the COVID-19 pandemic on the Colombian population according to mitigation measures. Preliminary data from epidemiological models for the period March 18 to April 18, 2020]. / Proyecciones de impacto de la pandemia COVID-19 en la población colombiana, según medidas de mitigación. Datos preliminares de modelos epidemiológicos para el periodo del 18 de marzo al 18 de abril de 2020.

INTRODUCTION: First case of COVID-19 in Colombia was diagnosed on March 6th. Two weeks later, cases have rapidly increased, leading the government to establish some mitigation measures. OBJECTIVES: The first objective is to estimate and model the number of cases, use of hospital resources and mortality by using different R0 scenarios in a 1-month scenario (from March 18 to April 18, 2020), based on the different isolation measures applied. This work also aims to model, without establishing a time horizon, the same outcomes given the assumption that eventually 70% of the population will be infected. MATERIALS AND METHODS: Data on the number of confirmed cases in the country as of March 18, 2020 (n=93) were taken as the basis for the achievement of the first objective. An initial transmission rate of R0= 2.5 and a factor of 27 for undetected infections per each confirmed case were taken as assumptions for the model. The proportion of patients who may need intensive care or other in-hospital care was based on data from the Imperial College of London. On the other hand, an age-specific mortality rate provided by the Instituto Superiore di Sanità in Italy was used for the second objective. RESULTS: Based on the 93 cases reported as of March 18, if no mitigation measures were applied, by April 18, the country would have 613 037 cases. Mitigation measures that reduce R0 by 10% generate a 50% reduction in the number of cases. However, despite halving the number of cases, there would still be a shortfall in the number of beds required and only one in two patients would have access to this resource. CONCLUSION: This model found that the mitigation measures implemented to date by the Colombian government and analyzed in this article are based on sufficient evidence and will help to slow the spread of SARS-CoV-2 in Colombia. Although a time horizon of one month was used for this model, it is plausible to believe that, if the current measures are sustained, the mitigation effect will also be sustained over time.

The effect of medical innovation on the cost-effectiveness of Covid 19-related policies in the United States using a SIR model.

BACKGROUND: During 2020-21, the United States used a multifaceted approach to control SARS-CoV-2 (Covid-19) and reduce mortality and morbidity. This included non-medical interventions (NMIs), aggressive vaccine development and deployment, and research into more effective approaches to medically treat Covid-19. Each approach had both costs and benefits. The objective of this study was to calculate the Incremental Cost Effectiveness Ratio (ICER) for three major Covid-19 policies: NMIs, vaccine development and deployment (Vaccines), and therapeutics and care improvements within the hospital setting (HTCI). METHODS: To simulate the number of QALYs lost per scenario, we developed a multi-risk Susceptible-Infected-Recovered (SIR) model where infection and fatality rates vary between regions. We use a two equation SIR model. The first equation represents changes in the number of infections and is a function of the susceptible population, the infection rate and the recovery rate. The second equation shows the changes in the susceptible population as people recover. Key costs included loss of economic productivity, reduced future earnings due to educational closures, inpatient spending and the cost of vaccine development. Benefits included reductions in Covid-19 related deaths, which were offset in some models by additional cancer deaths due to care delays. RESULTS: The largest cost is the reduction in economic output associated with NMI ($1.7 trillion); the second most significant cost is the educational shutdowns, with estimated reduced lifetime earnings of $523B. The total estimated cost of vaccine development is $55B. HTCI had the lowest cost per QALY gained vs "do nothing" with a cost of $2,089 per QALY gained. Vaccines cost $34,777 per QALY gained in isolation, while NMIs alone were dominated by other options. HTCI alone dominated most alternatives, except the combination of HTCI and Vaccines ($58,528 per QALY gained) and HTCI, Vaccines and NMIs ($3.4 m per QALY gained). CONCLUSIONS: HTCI was the most cost effective and was well justified under any standard cost effectiveness threshold. The cost per QALY gained for vaccine development, either alone or in concert with other approaches, is well within the standard for cost effectiveness. NMIs reduced deaths and saved QALYs, but the cost per QALY gained is well outside the usual accepted limits.

Fractional order SEIQRD epidemic model of Covid-19: A case study of Italy.

The fractional order SEIQRD compartmental model of COVID-19 is explored in this manuscript with six different categories in the Caputo approach. A few findings for the new model's existence and uniqueness criterion, as well as non-negativity and boundedness of the solution, have been established. When RCovid19<1 at infection-free equilibrium, we prove that the system is locally asymptotically stable. We also observed that RCovid 19<1, the system is globally asymptotically stable in the absence of disease. The main objective of this study is to investigate the COVID-19 transmission dynamics in Italy, in which the first case of Coronavirus infection 2019 (COVID-19) was identified on January 31st in 2020. We used the fractional order SEIQRD compartmental model in a fractional order framework to account for the uncertainty caused by the lack of information regarding the Coronavirus (COVID-19). The Routh-Hurwitz consistency criteria and La-Salle invariant principle are used to analyze the dynamics of the equilibrium. In addition, the fractional-order Taylor's approach is utilized to approximate the solution to the proposed model. The model's validity is demonstrated by comparing real-world data with simulation outcomes. This study considered the consequences of wearing face masks, and it was discovered that consistent use of face masks can help reduce the propagation of the COVID-19 disease.

Validation framework for epidemiological models with application to COVID-19 models.

Mathematical models have been an important tool during the COVID-19 pandemic, for example to predict demand of critical resources such as medical devices, personal protective equipment and diagnostic tests. Many COVID-19 models have been developed. However, there is relatively little information available regarding reliability of model predictions. Here we present a general model validation framework for epidemiological models focused around predictive capability for questions relevant to decision-making end-users. COVID-19 models are typically comprised of multiple releases, and provide predictions for multiple localities, and these characteristics are systematically accounted for in the framework, which is based around a set of validation scores or metrics that quantify model accuracy of specific quantities of interest including: date of peak, magnitude of peak, rate of recovery, and monthly cumulative counts. We applied the framework to retrospectively assess accuracy of death predictions for four COVID-19 models, and accuracy of hospitalization predictions for one COVID-19 model (models for which sufficient data was publicly available). When predicting date of peak deaths, the most accurate model had errors of approximately 15 days or less, for releases 3-6 weeks in advance of the peak. Death peak magnitude relative errors were generally in the 50% range 3-6 weeks before peak. Hospitalization predictions were less accurate than death predictions. All models were highly variable in predictive accuracy across regions. Overall, our framework provides a wealth of information on the predictive accuracy of epidemiological models and could be used in future epidemics to evaluate new models or support existing modeling methodologies, and thereby aid in informed model-based public health decision making. The code for the validation framework is available at https://doi.org/10.5281/zenodo.7102854.

The dynamics of novel corona virus disease via stochastic epidemiological model with vaccination.

During the past two years, the novel coronavirus pandemic has dramatically affected the world by producing 4.8 million deaths. Mathematical modeling is one of the useful mathematical tools which has been used frequently to investigate the dynamics of various infectious diseases. It has been observed that the nature of the novel disease of coronavirus transmission differs everywhere, implying that it is not deterministic while having stochastic nature. In this paper, a stochastic mathematical model has been investigated to study the transmission dynamics of novel coronavirus disease under the effect of fluctuated disease propagation and vaccination because effective vaccination programs and interaction of humans play a significant role in every infectious disease prevention. We develop the epidemic problem by taking into account the extended version of the susceptible-infected-recovered model and with the aid of a stochastic differential equation. We then study the fundamental axioms for existence and uniqueness to show that the problem is mathematically and biologically feasible. The extinction of novel coronavirus and persistency are examined, and sufficient conditions resulted from our investigation. In the end, some graphical representations support the analytical findings and present the effect of vaccination and fluctuated environmental variation.

New compartment model for COVID-19.

The SIR or susceptible-infected-recovered model is the standard compartment model for understanding epidemics and has been used all over the world for COVID-19. While the SIR model assumes that infected patients are identical to symptomatic and infectious patients, it is now known that in COVID-19 pre-symptomatic patients are infectious and there are significant number of asymptomatic patients who are infectious. In this paper, population is separated into five compartments for COVID-19; susceptible individuals (S), pre-symptomatic patients (P), asymptomatic patients (A), quarantined patients (Q) and recovered and/or dead patients (R). The time evolution of population in each compartment is described by a set of ordinary differential equations. Numerical solution to the set of differential equations shows that quarantining pre-symptomatic and asymptomatic patients is effective in controlling the pandemic.

Tuberculosis in the Russian Federation: Prognosis and Epidemiological Models in a Situation After the COVID-19 Pandemic.

AIM: Because of the COVID-19 pandemic, many support programs for tuberculosis (TB) patients have been discontinued and TB mass screening activities decreased worldwide, resulting in a decrease in new case detection and an increase in TB deaths (WHO, WHO global lists of high burden countries for TB, multidrug/rifampicin-resistant TB (MDR/RR-TB) and TB/HIV, 2021-2025, 2021). The study aimed to assess changes in epidemiological indicators of tuberculosis in the Russian Federation and to simulate these indicators in the post-COVID-19 period. MATERIALS AND METHODS: The main epidemiological indicators of tuberculosis were analyzed with the use of government statistical data for the period from 2009 to 2021. Further mathematical modeling of epidemiological indicators for the coming years was carried out, taking into account the TB screening by chest X-ray. Statistical analysis was carried out using the software environment R (v.3.5.1) for statistical computing and the commercial software Statistical Package for the Social Sciences (SPSS Statistics for Windows, version 24.0, IBM Corp., 2016). Time series forecasting was performed using the programming language for statistical calculations R, version 4.1.2 and the bsts package, version 0.9.8. STUDY RESULTS: The study has found that the mean regression coefficient of a single predictor differs in the model for TB incidence and mortality (0.0098 and 0.0002, respectively). Forecast of overall incidence, the incidence of children and the forecast for mortality using the basic scenario (screening 75-78%) for the period from 2022 to 2026 was characterized by a mean decrease rate of 23.1%, 15.6% and 6.0% per year, respectively. A conservative scenario (screening 47-63%) of overall incidence indicates that the incidence of children and the forecast for mortality will continue to decrease with a mean decrease rate of 23.2%, 15.6% and 6.0% per year, respectively. Comparable data were obtained from the forecast of overall incidence, the incidence of children and the forecast for mortality using the optimistic scenario (screening 82-89%) with a mean decrease rate of 22.9%, 15.4% and 6.0% per year, respectively. CONCLUSIONS: It has been proven that the significance of screening with chest X-ray as a predictor of mortality is minimal. However, TB screening at least 60% of the population (chest X-ray in adults and immunological tests in children) have provided relationship between the TB screening rate and TB mortality rate (TB mortality rate increases with an increase in the population coverage and, conversely, decreases with a decrease in the population coverage).

The Structural Identifiability of a Humidity-Driven Epidemiological Model of Influenza Transmission.

Influenza epidemics cause considerable morbidity and mortality every year worldwide. Climate-driven epidemiological models are mainstream tools to understand seasonal transmission dynamics and predict future trends of influenza activity, especially in temperate regions. Testing the structural identifiability of these models is a fundamental prerequisite for the model to be applied in practice, by assessing whether the unknown model parameters can be uniquely determined from epidemic data. In this study, we applied a scaling method to analyse the structural identifiability of four types of commonly used humidity-driven epidemiological models. Specifically, we investigated whether the key epidemiological parameters (i.e., infectious period, the average duration of immunity, the average latency period, and the maximum and minimum daily basic reproductive number) can be uniquely determined simultaneously when prevalence data is observable. We found that each model is identifiable when the prevalence of infection is observable. The structural identifiability of these models will lay the foundation for testing practical identifiability in the future using synthetic prevalence data when considering observation noise. In practice, epidemiological models should be examined with caution before using them to estimate model parameters from epidemic data.

A contact tracing SIR model for randomly mixed populations.

Contact tracing is an important intervention measure to control infectious diseases. We present a new approach that borrows the edge dynamics idea from network models to track contacts included in a compartmental SIR model for an epidemic spreading in a randomly mixed population. Unlike network models, our approach does not require statistical information of the contact network, data that are usually not readily available. The model resulting from this new approach allows us to study the effect of contact tracing and isolation of diagnosed patients on the control reproduction number and number of infected individuals. We estimate the effects of tracing coverage and capacity on the effectiveness of contact tracing. Our approach can be extended to more realistic models that incorporate latent and asymptomatic compartments.

An age-dependent immuno-epidemiological model with distributed recovery and death rates.

The work is devoted to a new immuno-epidemiological model with distributed recovery and death rates considered as functions of time after the infection onset. Disease transmission rate depends on the intra-subject viral load determined from the immunological submodel. The age-dependent model includes the viral load, recovery and death rates as functions of age considered as a continuous variable. Equations for susceptible, infected, recovered and dead compartments are expressed in terms of the number of newly infected cases. The analysis of the model includes the proof of the existence and uniqueness of solution. Furthermore, it is shown how the model can be reduced to age-dependent SIR or delay model under certain assumptions on recovery and death distributions. Basic reproduction number and final size of epidemic are determined for the reduced models. The model is validated with a COVID-19 case data. Modelling results show that proportion of young age groups can influence the epidemic progression since disease transmission rate for them is higher than for other age groups.

Bayesian SIR model with change points with application to the Omicron wave in Singapore.

The Omicron variant has led to a new wave of the COVID-19 pandemic worldwide, with unprecedented numbers of daily confirmed new cases in many countries and areas. To analyze the impact of society or policy changes on the development of the Omicron wave, the stochastic susceptible-infected-removed (SIR) model with change points is proposed to accommodate the situations where the transmission rate and the removal rate may vary significantly at change points. Bayesian inference based on a Markov chain Monte Carlo algorithm is developed to estimate both the locations of change points as well as the transmission rate and removal rate within each stage. Experiments on simulated data reveal the effectiveness of the proposed method, and several stages are detected in analyzing the Omicron wave data in Singapore.

Long-term benefits of nonpharmaceutical interventions for endemic infections are shaped by respiratory pathogen dynamics.

COVID-19 nonpharmaceutical interventions (NPIs), including mask wearing, have proved highly effective at reducing the transmission of endemic infections. A key public health question is whether NPIs could continue to be implemented long term to reduce the ongoing burden from endemic pathogens. Here, we use epidemiological models to explore the impact of long-term NPIs on the dynamics of endemic infections. We find that the introduction of NPIs leads to a strong initial reduction in incidence, but this effect is transient: As susceptibility increases, epidemics return while NPIs are in place. For low R0 infections, these return epidemics are of reduced equilibrium incidence and epidemic peak size. For high R0 infections, return epidemics are of similar magnitude to pre-NPI outbreaks. Our results underline that managing ongoing susceptible buildup, e.g., with vaccination, remains an important long-term goal.

Fractional model for Middle East respiratory syndrome coronavirus on a complex heterogeneous network.

In this paper, we present a new fractional epidemiological model on a heterogeneous network to investigate Middle East respiratory syndrome (MERS-CoV), which is caused by a virus in the coronavirus family. We also consider the development of equations for the camel population, given that it is the primary animal source of the virus, as well as direct human interaction with this population. The model is configured in an SIS form for both the human population and the camel population. We study the equilibrium positions of the system and the conditions for the existence of each of them, as well as the local stability of each equilibrium position. Then, we provide some numerical examples that compare real data and numerical results.

A Modified PINN Approach for Identifiable Compartmental Models in Epidemiology with Application to COVID-19.

Many approaches using compartmental models have been used to study the COVID-19 pandemic, with machine learning methods applied to these models having particularly notable success. We consider the Susceptible-Infected-Confirmed-Recovered-Deceased (SICRD) compartmental model, with the goal of estimating the unknown infected compartment I, and several unknown parameters. We apply a variation of a "Physics Informed Neural Network" (PINN), which uses knowledge of the system to aid learning. First, we ensure estimation is possible by verifying the model's identifiability. Then, we propose a wavelet transform to process data for the network training. Finally, our central result is a novel modification of the PINN's loss function to reduce the number of simultaneously considered unknowns. We find that our modified network is capable of stable, efficient, and accurate estimation, while the unmodified network consistently yields incorrect values. The modified network is also shown to be efficient enough to be applied to a model with time-varying parameters. We present an application of our model results for ranking states by their estimated relative testing efficiency. Our findings suggest the effectiveness of our modified PINN network, especially in the case of multiple unknown variables.