Stochastic transmission in epidemiological models.

Recent empirical evidence suggests that the transmission coefficient in susceptible-exposed-infected-removed-like (SEIR-like) models evolves with time, presenting random patterns, and some stylized facts, such as mean-reversion and jumps. To address such observations we propose the use of jump-diffusion stochastic processes to parameterize the transmission coefficient in an SEIR-like model that accounts for death and time-dependent parameters. We provide a detailed theoretical analysis of the proposed model proving the existence and uniqueness of solutions as well as studying its asymptotic behavior. We also compare the proposed model with some variations possibly including jumps. The forecast performance of the considered models, using reported COVID-19 infections from New York City, is then tested in different scenarios. Despite the simplicity of the epidemiological model, by considering stochastic transmission, the forecasted scenarios were fairly accurate.

Time-dependent vaccine efficacy estimation quantified by a mathematical model.

In this paper we calculate the variation of the estimated vaccine efficacy (VE) due to the time-dependent force of infection resulting from the difference between the moment the Clinical Trial (CT) begins and the peak in the outbreak intensity. Using a simple mathematical model we tested the hypothesis that the time difference between the moment the CT begins and the peak in the outbreak intensity determines substantially different values for VE. We exemplify the method with the case of the VE efficacy estimation for one of the vaccines against the new coronavirus SARS-CoV-2.

Time-dependent vaccine efficacy estimation quantified by a mathematical model

In this paper we calculate the variation of the estimated vaccine efficacy (VE) due to the time-dependent force of infection resulting from the difference between the moment the Clinical Trial (CT) begins and the peak in the outbreak intensity. Using a simple mathematical model we tested the hypothesis that the time difference between the moment the CT begins and the peak in the outbreak intensity determines substantially different values for VE. We exemplify the method with the case of the VE efficacy estimation for one of the vaccines against the new coronavirus SARS-CoV-2.

Time-dependent vaccine efficacy estimation quantified by a mathematical model

In this paper we calculate the variation of the estimated vaccine efficacy (VE) due to the time-dependent force of infection resulting from the difference between the moment the Clinical Trial (CT) begins and the peak in the outbreak intensity. Using a simple mathematical model we tested the hypothesis that the time difference between the moment the CT begins and the peak in the outbreak intensity determines substantially different values for VE. We exemplify the method with the case of the VE efficacy estimation for one of the vaccines against the new coronavirus SARS-CoV-2.

Performance of a novel risk model for deep sternal wound infection after coronary artery bypass grafting.

Clinical prediction models for deep sternal wound infections (DSWI) after coronary artery bypass graft (CABG) surgery exist, although they have a poor impact in external validation studies. We developed and validated a new predictive model for 30-day DSWI after CABG (REPINF) and compared it with the Society of Thoracic Surgeons model (STS). The REPINF model was created through a multicenter cohort of adults undergoing CABG surgery (REPLICCAR II Study) database, using least absolute shrinkage and selection operator (LASSO) logistic regression, internally and externally validated comparing discrimination, calibration in-the-large (CL), net reclassification improvement (NRI) and integrated discrimination improvement (IDI), trained between the new model and the STS PredDeep, a validated model for DSWI after cardiac surgery. In the validation data, c-index = 0.83 (95% CI 0.72-0.95). Compared to the STS PredDeep, predictions improved by 6.5% (IDI). However, both STS and REPINF had limited calibration. Different populations require independent scoring systems to achieve the best predictive effect. The external validation of REPINF across multiple centers is an important quality improvement tool to generalize the model and to guide healthcare professionals in the prevention of DSWI after CABG surgery.

On the role of financial support programs in mitigating the SARS-CoV-2 spread in Brazil.

BACKGROUND: During 2020, there were no effective treatments or vaccines against SARS-CoV-2. The most common disease contention measures were social distance (social isolation), the use of face masks and lockdowns. In the beginning, numerous countries have succeeded to control and reduce COVID-19 infections at a high economic cost. Thus, to alleviate such side effects, many countries have implemented socioeconomic programs to fund individuals that lost their jobs and to help endangered businesses to survive. METHODS: We assess the role of a socioeconomic program, so-called "Auxilio Emergencial" (AE), during 2020 as a measure to mitigate the Coronavirus Disease 2019 (COVID-19) outbreak in Brazil. For each Brazilian State, we estimate the time-dependent reproduction number from daily reports of COVID-19 infections and deaths using a Susceptible-Exposed-Infected-Recovered-like (SEIR-like) model. Then, we analyse the correlations between the reproduction number, the amount of individuals receiving governmental aid, and the index of social isolation based on mobile phone information. RESULTS: We observed significant positive correlation values between the average values by the AE and median values of an index accounting for individual mobility. We also observed significantly negative correlation values between the reproduction number and this index on individual mobility. Using the simulations of a susceptible-exposed-infected-removed-like model, if the AE was not operational during the first wave of COVID-19 infections, the accumulated number of infections and deaths could be 6.5 (90% CI: 1.3-21) and 7.9 (90% CI: 1.5-23) times higher, respectively, in comparison with the actual implementation of AE. CONCLUSIONS: Our results suggest that the AE implemented in Brazil had a significant influence on social isolation by allowing those in need to stay at home, which would reduce the expected numbers of infections and deaths.

COVID-19 underreporting and its impact on vaccination strategies.

BACKGROUND: Underreporting cases of infectious diseases poses a major challenge in the analysis of their epidemiological characteristics and dynamical aspects. Without accurate numerical estimates it is difficult to precisely quantify the proportions of severe and critical cases, as well as the mortality rate. Such estimates can be provided for instance by testing the presence of the virus. However, during an ongoing epidemic, such tests' implementation is a daunting task. This work addresses this issue by presenting a methodology to estimate underreported infections based on approximations of the stable rates of hospitalization and death. METHODS: We present a novel methodology for the stable rate estimation of hospitalization and death related to the Corona Virus Disease 2019 (COVID-19) using publicly available reports from various distinct communities. These rates are then used to estimate underreported infections on the corresponding areas by making use of reported daily hospitalizations and deaths. The impact of underreporting infections on vaccination strategies is estimated under different disease-transmission scenarios using a Susceptible-Exposed-Infective-Removed-like (SEIR) epidemiological model. RESULTS: For the considered locations, during the period of study, the estimations suggest that the number of infected individuals could reach 30% of the population of these places, representing, in some cases, more than six times the observed numbers. These results are in close agreement with estimates from independent seroprevalence studies, thus providing a strong validation of the proposed methodology. Moreover, the presence of large numbers of underreported infections can reduce the perceived impact of vaccination strategies in reducing rates of mortality and hospitalization. CONCLUSIONS: pBy using the proposed methodology and employing a judiciously chosen data analysis implementation, we estimate COVID-19 underreporting from publicly available data. This leads to a powerful way of quantifying underreporting impact on the efficacy of vaccination strategies. As a byproduct, we evaluate the impact of underreporting in the designing of vaccination strategies.

The impact of COVID-19 vaccination delay: A data-driven modeling analysis for Chicago and New York City.

BACKGROUND: By the beginning of December 2020, some vaccines against COVID-19 already presented efficacy and security, which qualify them to be used in mass vaccination campaigns. Thus, setting up strategies of vaccination became crucial to control the COVID-19 pandemic. METHODS: We use daily COVID-19 reports from Chicago and New York City (NYC) from 01-Mar2020 to 28-Nov-2020 to estimate the parameters of an SEIR-like epidemiological model that accounts for different severity levels. To achieve data adherent predictions, we let the model parameters to be time-dependent. The model is used to forecast different vaccination scenarios, where the campaign starts at different dates, from 01-Oct-2020 to 01-Apr-2021. To generate realistic scenarios, disease control strategies are implemented whenever the number of predicted daily hospitalizations reaches a preset threshold. RESULTS: The model reproduces the empirical data with remarkable accuracy. Delaying the vaccination severely affects the mortality, hospitalization, and recovery projections. In Chicago, the disease spread was under control, reducing the mortality increment as the start of the vaccination was postponed. In NYC, the number of cases was increasing, thus, the estimated model predicted a much larger impact, despite the implementation of contention measures. The earlier the vaccination campaign begins, the larger is its potential impact in reducing the COVID-19 cases, as well as in the hospitalizations and deaths. Moreover, the rate at which cases, hospitalizations and deaths increase with the delay in the vaccination beginning strongly depends on the shape of the incidence of infection in each city.

Estimating, monitoring, and forecasting COVID-19 epidemics: a spatiotemporal approach applied to NYC data.

We propose a susceptible-exposed-infective-recovered-type (SEIR-type) meta-population model to simulate and monitor the (COVID-19) epidemic evolution. The basic model consists of seven categories, namely, susceptible (S), exposed (E), three infective classes, recovered (R), and deceased (D). We define these categories for n age and sex groups in m different spatial locations. Therefore, the resulting model contains all epidemiological classes for each age group, sex, and location. The mixing between them is accomplished by means of time-dependent infection rate matrices. The model is calibrated with the curve of daily new infections in New York City and its boroughs, including census data, and the proportions of infections, hospitalizations, and deaths for each age range. We finally obtain a model that matches the reported curves and predicts accurate infection information for different locations and age classes.

Validation and quality measurements for STS, EuroSCORE II and a regional risk model in Brazilian patients.

OBJECTIVES: The objectives of this study were to describe a novel statewide registry for cardiac surgery in Brazil (REPLICCAR), to compare a regional risk model (SPScore) with EuroSCORE II and STS, and to understand where quality improvement and safety initiatives can be implemented. METHODS: A total of 11 sites in the state of São Paulo, Brazil, formed an online registry platform to capture information on risk factors and outcomes after cardiac surgery procedures for all consecutive patients. EuroSCORE II and STS values were calculated for each patient. An SPScore model was designed and compared with EuroSCORE II and STS to predict 30-day outcomes: death, reoperation, readmission, and any morbidity. RESULTS: A total of 5222 patients were enrolled in this study between November 2013 and December 2017. The observed 30-day mortality rate was 7.6%. Most patients were older, overweight, and classified as New York Heart Association (NYHA) functional class III; 14.5% of the patient population had a positive diagnosis of rheumatic heart disease, 10.9% had insulin-dependent diabetes, and 19 individuals had a positive diagnosis of Chagas disease. When evaluating the prediction performance, we found that SPScore outperformed EuroSCORE II and STS in the prediction of mortality (0.90 vs. 0.76 and 0.77), reoperation (0.84 vs. 0.60 and 0.56), readmission (0.84 vs. 0.55 and 0.51), and any morbidity (0.80 vs. 0.65 and 0.64), respectively (p<0.001). CONCLUSIONS: The REPLICCAR registry might stimulate the creation of other cardiac surgery registries in developing countries, ultimately improving the regional quality of care provided to patients.

Special issue: mathematical methods in the biosciences.

The special issue is available from: https://www.aimspress.com/newsinfo/1079.html/.

The role of self-loops and link removal in evolutionary games on networks.

Recently, a new mathematical formulation of evolutionary game dynamics [1] has been introduced accounting for a finite number of players organized over a network, where the players are located at the nodes of a graph and edges represent connections between them. Internal steady states are particularly interesting in control and consensus problems, especially in a networked context where they are related to the coexistence of different strategies. In this paper we consider this model including self-loops. Existence of internal steady states is studied for different graph topologies in two-strategy games. Results on the effect of removing links from central players are also presented.

Quantifying the survival uncertainty of Wolbachia-infected mosquitoes in a spatial model.

Artificial releases of Wolbachia-infected Aedes mosquitoes have been under study in the past yearsfor fighting vector-borne diseases such as dengue, chikungunya and zika.Several strains of this bacterium cause cytoplasmic incompatibility (CI) and can also affect their host's fecundity or lifespan, while highly reducing vector competence for the main arboviruses. We consider and answer the following questions: 1) what should be the initial condition (i.e. size of the initial mosquito population) to have invasion with one mosquito release source? We note that it is hard to have an invasion in such case. 2) How many release points does one need to have sufficiently high probability of invasion? 3) What happens if one accounts for uncertainty in the release protocol (e.g. unequal spacing among release points)? We build a framework based on existing reaction-diffusion models for the uncertainty quantification in this context,obtain both theoretical and numerical lower bounds for the probability of release successand give new quantitative results on the one dimensional case.

Predictive performance of six mortality risk scores and the development of a novel model in a prospective cohort of patients undergoing valve surgery secondary to rheumatic fever.

BACKGROUND: Mortality prediction after cardiac procedures is an essential tool in clinical decision making. Although rheumatic cardiac disease remains a major cause of heart surgery in the world no previous study validated risk scores in a sample exclusively with this condition. OBJECTIVES: Develop a novel predictive model focused on mortality prediction among patients undergoing cardiac surgery secondary to rheumatic valve conditions. METHODS: We conducted prospective consecutive all-comers patients with rheumatic heart disease (RHD) referred for surgical treatment of valve disease between May 2010 and July of 2015. Risk scores for hospital mortality were calculated using the 2000 Bernstein-Parsonnet, EuroSCORE II, InsCor, AmblerSCORE, GuaragnaSCORE, and the New York SCORE. In addition, we developed the rheumatic heart valve surgery score (RheSCORE). RESULTS: A total of 2,919 RHD patients underwent heart valve surgery. After evaluating 13 different models, the top performing areas under the curve were achieved using Random Forest (0.982) and Neural Network (0.952). Most influential predictors across all models included left atrium size, high creatinine values, a tricuspid procedure, reoperation and pulmonary hypertension. Areas under the curve for previously developed scores were all below the performance for the RheSCORE model: 2000 Bernstein-Parsonnet (0.876), EuroSCORE II (0.857), InsCor (0.835), Ambler (0.831), Guaragna (0.816) and the New York score (0.834). A web application is presented where researchers and providers can calculate predicted mortality based on the RheSCORE. CONCLUSIONS: The RheSCORE model outperformed pre-existing scores in a sample of patients with rheumatic cardiac disease.

A singularly perturbed HIV model with treatment and antigenic variation.

We study the long term dynamics and the multiscale aspects of a within-host HIV model that takes into account both mutation and treatment with enzyme inhibitors. This model generalizes a number of other models that have been extensively used to describe the HIV dynamics. Since the free virus dynamics occur on a much faster time-scale than cell dynamics, the model has two intrinsic time scales and should be viewed as a singularly perturbed system. Using Tikhonov's theorem we prove that the model can be approximated by a lower dimensional nonlinear model. Furthermore, we show that this reduced system is globally asymptotically stable by using Lyapunov's stability theory.

Global stability for a class of virus models with cytotoxic T lymphocyte immune response and antigenic variation.

We study the global stability of a class of models for in-vivo virus dynamics that take into account the Cytotoxic T Lymphocyte immune response and display antigenic variation. This class includes a number of models that have been extensively used to model HIV dynamics. We show that models in this class are globally asymptotically stable, under mild hypothesis, by using appropriate Lyapunov functions. We also characterise the stable equilibrium points for the entire biologically relevant parameter range. As a by-product, we are able to determine what is the diversity of the persistent strains.

On the calibration of a size-structured population model from experimental data.

The aim of this work is twofold. First, we survey the techniques developed in Perthame and Zubelli (Inverse Probl 23(3):1037-1052, 2007), Doumic et al. (Inverse Probl 25, 2009) to reconstruct the division (birth) rate from the cell volume distribution data in certain structured population structured population models. Secondly, we implement such techniques on experimental cell volume distributions available in the literature so as to validate the theoretical and numerical results. As a proof of concept, we use the experimental data experimental data reported in the classical work of Kubitschek (Biophys J 9(6):792-809, 1969) concerning Escherichia coli in vitro experiments measured by means of a Coulter transducer-multichannel analyzer system (Coulter Electronics, Inc., Hialeah, FL, USA). Despite the rather old measurement technology, the reconstructed division rates still display potentially useful biological features.