The epidemicity index of recurrent SARS-CoV-2 infections

Significance of supervision sampling in control of communicable respiratory disease simulated by a new model during different stages of the disease

The coronavirus disease 2019 (COVID-19) interventions in interrupting transmission have paid heavy losses politically and economically. The Chinese government has replaced scaling up testing with monitoring focus groups and randomly supervising sampling, encouraging scientific research on the COVID-19 transmission curve to be confirmed by constructing epidemiological models, which include statistical models, computer simulations, mathematical illustrations of the pathogen and its effects, and several other methodologies. Although predicting and forecasting the propagation of COVID-19 are valuable, they nevertheless present an enormous challenge. This paper emphasis on pandemic simulation models by introduced respiratory-specific transmission to extend and complement the classical Susceptible-Exposed-(Asymptomatic)-Infected-Recovered SE(A)IR model to assess the significance of the COVID-19 transmission control features to provide an explanation of the rationale for the government policy. A novel epidemiological model is developed using mean-field theory. Utilizing the SE(A)IR extended framework, which is a suitable method for describing the progression of epidemics over actual or genuine landscapes, we have developed a novel model named SEIAPUFR. This model effectively detects the connections between various stages of infection. Subsequently, we formulated eight ordinary differential equations that precisely depict the population's temporal development inside each segment. Furthermore, we calibrated the transmission and clearance rates by considering the impact of various control strategies on the epidemiological dynamics, which we used to project the future course of COVID-19. Based on these parameter values, our emphasis was on determining the criteria for stabilizing the disease-free equilibrium (DEF). We also developed model parameters that are appropriate for COVID-19 outbreaks, taking into account varied population sizes. Ultimately, we conducted simulations and predictions for other prominent cities in China, such as Wuhan, Shanghai, Guangzhou, and Shenzhen, that have recently been affected by the COVID-19 outbreak. By integrating different control measures, respiratory-specific modeling, and disease supervision sampling into an expanded SEI (A) R epidemic model, we found that supervision sampling can improve early warning of viral activity levels and superspreading events, and explained the significance of containments in controlling COVID-19 transmission and the rationality of policy by the influence of different containment measures on the transmission rate. These results indicate that the control measures during the pandemic interrupted the transmission chain mainly by inhibiting respiratory transmission, and the proportion of supervision sampling should be proportional to the transmission rate, especially only aimed at preventing a resurgence of SARS-CoV-2 transmission in low-prevalence areas. Furthermore, The incidence hazard of Males and Females was 1.39(1.23-1.58), and 1.43(1.26-1.63), respectively. Our investigation found that the ratio of peak sampling is directly related to the transmission rate, and both decrease when control measures are implemented. Consequently, the control measures during the pandemic interrupted the transmission chain mainly by inhibiting respiratory transmission. Reasonable and effective interventions during the early stage can flatten the transmission curve, which will slow the momentum of the outbreak to reduce medical pressure.

Balancing mitigation strategies for viral outbreaks

Control and prevention strategies are indispensable tools for managing the spread of infectious diseases. This paper examined biological models for the post-vaccination stage of a viral outbreak that integrate two important mitigation tools: social distancing, aimed at reducing the disease transmission rate, and vaccination, which boosts the immune system. Five different scenarios of epidemic progression were considered: (ⅰ) the "no control" scenario, reflecting the natural evolution of a disease without any safety measures in place, (ⅱ) the "reconstructed" scenario, representing real-world data and interventions, (ⅲ) the "social distancing control" scenario covering a broad set of behavioral changes, (ⅳ) the "vaccine control" scenario demonstrating the impact of vaccination on epidemic spread, and (ⅴ) the "both controls concurrently" scenario incorporating social distancing and vaccine controls simultaneously. By comparing these scenarios, we provided a comprehensive analysis of various intervention strategies, offering valuable insights into disease dynamics. Our innovative approach to modeling the cost of control gave rise to a robust computational algorithm for solving optimal control problems associated with different public health regulations. Numerical results were supported by real data for the Delta variant of the COVID-19 pandemic in the United States.

A Physics-Informed Neural Network approach for compartmental epidemiological models

Compartmental models provide simple and efficient tools to analyze the relevant transmission processes during an outbreak, to produce short-term forecasts or transmission scenarios, and to assess the impact of vaccination campaigns. However, their calibration is not straightforward, since many factors contribute to the rapid change of the transmission dynamics. For example, there might be changes in the individual awareness, the imposition of non-pharmacological interventions and the emergence of new variants. As a consequence, model parameters such as the transmission rate are doomed to vary in time, making their assessment more challenging. Here, we propose to use Physics-Informed Neural Networks (PINNs) to track the temporal changes in the model parameters and the state variables. PINNs recently gained attention in many engineering applications thanks to their ability to consider both the information from data (typically uncertain) and the governing equations of the system. The ability of PINNs to identify unknown model parameters makes them particularly suitable to solve ill-posed inverse problems, such as those arising in the application of epidemiological models. Here, we develop a reduced-split approach for the implementation of PINNs to estimate the temporal changes in the state variables and transmission rate of an epidemic based on the SIR model equation and infectious data. The main idea is to split the training first on the epidemiological data, and then on the residual of the system equations. The proposed method is applied to five synthetic test cases and two real scenarios reproducing the first months of the Italian COVID-19 pandemic. Our results show that the split implementation of PINNs outperforms the joint approach in terms of accuracy (up to one order of magnitude) and computational times (speed up of 20%). Finally, we illustrate that the proposed PINN-method can also be adopted to produced short-term forecasts of the dynamics of an epidemic.

Emergence of the reproduction matrix in epidemic forecasting

During the recent COVID-19 pandemic, the instantaneous reproduction number, R(t), has surged as a widely used measure to target public health interventions aiming at curbing the infection rate. In analogy with the basic reproduction number that arises from the linear stability analysis, R(t) is typically interpreted as a threshold parameter that separates exponential growth (R(t) > 1) from exponential decay (R(t) < 1). In real epidemics, however, the finite number of susceptibles, the stratification of the population (e.g. by age or vaccination state), and heterogeneous mixing lead to more complex epidemic courses. In the context of the multidimensional renewal equation, we generalize the scalar R(t) to a reproduction matrix, [Formula: see text], which details the epidemic state of the stratified population, and offers a concise epidemic forecasting scheme. First, the reproduction matrix is computed from the available incidence data (subject to some a priori assumptions), then it is projected into the future by a transfer functional to predict the epidemic course. We demonstrate that this simple scheme allows realistic and accurate epidemic trajectories both in synthetic test cases and with reported incidence data from the COVID-19 pandemic. Accounting for the full heterogeneity and nonlinearity of the infection process, the reproduction matrix improves the prediction of the infection peak. In contrast, the scalar reproduction number overestimates the possibility of sustaining the initial infection rate and leads to an overshoot in the incidence peak. Besides its simplicity, the devised forecasting scheme offers rich flexibility to be generalized to time-dependent mitigation measures, contact rate, infectivity and vaccine protection.

R 0 May Not Tell Us Everything: Transient Disease Dynamics of Some SIR Models Over Patchy Environments

This paper examines the short-term or transient dynamics of SIR infectious disease models in patch environments. We employ reactivity of an equilibrium and amplification rates, concepts from ecology, to analyze how dispersals/travels between patches, spatial heterogeneity, and other disease-related parameters impact short-term dynamics. Our findings reveal that in certain scenarios, due to the impact of spatial heterogeneity and the dispersals, the short-term disease dynamics over a patch environment may disagree with the long-term disease dynamics that is typically reflected by the basic reproduction number. Such an inconsistence can mislead the public, public healthy agencies and governments when making public health policy and decisions, and hence, these findings are of practical importance.

Epidemic Management via Imperfect Testing: A Multi-criterial Perspective

Diagnostic testing may represent a key component in response to an ongoing epidemic, especially if coupled with containment measures, such as mandatory self-isolation, aimed to prevent infectious individuals from furthering onward transmission while allowing non-infected individuals to go about their lives. However, by its own nature as an imperfect binary classifier, testing can produce false negative or false positive results. Both types of misclassification are problematic: while the former may exacerbate the spread of disease, the latter may result in unnecessary isolation mandates and socioeconomic burden. As clearly shown by the COVID-19 pandemic, achieving adequate protection for both people and society is a crucial, yet highly challenging task that needs to be addressed in managing large-scale epidemic transmission. To explore the trade-offs imposed by diagnostic testing and mandatory isolation as tools for epidemic containment, here we present an extension of the classical Susceptible-Infected-Recovered model that accounts for an additional stratification of the population based on the results of diagnostic testing. We show that, under suitable epidemiological conditions, a careful assessment of testing and isolation protocols can contribute to epidemic containment, even in the presence of false negative/positive results. Also, using a multi-criterial framework, we identify simple, yet Pareto-efficient testing and isolation scenarios that can minimize case count, isolation time, or seek a trade-off solution for these often contrasting epidemic management objectives.

Testing a simple and frugal model of health protective behaviour in epidemic times

The COVID-19 epidemic highlighted the necessity to integrate dynamic human behaviour change into infectious disease transmission models. The adoption of health protective behaviour, such as handwashing or staying at home, depends on both epidemiological and personal variables. However, only a few models have been proposed in the recent literature to account for behavioural change in response to the health threat over time. This study aims to estimate the relevance of TELL ME, a simple and frugal agent-based model developed following the 2009 H1N1 outbreak to explain individual engagement in health protective behaviours in epidemic times and how communication can influence this. Basically, TELL ME includes a behavioural rule to simulate individual decisions to adopt health protective behaviours. To test this rule, we used behavioural data from a series of 12 cross-sectional surveys in France over a 6-month period (May to November 2020). Samples were representative of the French population (N = 24,003). We found the TELL ME behavioural rule to be associated with a moderate to high error rate in representing the adoption of behaviours, indicating that parameter values are not constant over time and that other key variables influence individual decisions. These results highlight the crucial need for longitudinal behavioural data to better calibrate epidemiological models accounting for public responses to infectious disease threats.

Data-driven multiscale dynamical framework to control a pandemic evolution with non-pharmaceutical interventions

Before the availability of vaccines, many countries have resorted multiple times to drastic social restrictions to prevent saturation of their health care system, and to regain control over an otherwise exponentially increasing COVID-19 pandemic. With the advent of data-sharing, computational approaches are key to efficiently control a pandemic with non-pharmaceutical interventions (NPIs). Here we develop a data-driven computational framework based on a time discrete and age-stratified compartmental model to control a pandemic evolution inside and outside hospitals in a constantly changing environment with NPIs. Besides the calendrical time, we introduce a second time-scale for the infection history, which allows for non-exponential transition probabilities. We develop inference methods and feedback procedures to successively recalibrate model parameters as new data becomes available. As a showcase, we calibrate the framework to study the pandemic evolution inside and outside hospitals in France until February 2021. We combine national hospitalization statistics from governmental websites with clinical data from a single hospital to calibrate hospitalization parameters. We infer changes in social contact matrices as a function of NPIs from positive testing and new hospitalization data. We use simulations to infer hidden pandemic properties such as the fraction of infected population, the hospitalisation probability, or the infection fatality ratio. We show how reproduction numbers and herd immunity levels depend on the underlying social dynamics.

Epidemicity of cholera spread and the fate of infection control measures

The fate of ongoing infectious disease outbreaks is predicted through reproduction numbers, defining the long-term establishment of the infection, and epidemicity indices, tackling the reactivity of the infectious pool to new contagions. Prognostic metrics of unfolding outbreaks are of particular importance when designing adaptive emergency interventions facing real-time assimilation of epidemiological evidence. Our aim here is twofold. First, we propose a novel form of the epidemicity index for the characterization of cholera epidemics in spatial models of disease spread. Second, we examine in hindsight the survey of infections, treatments and containment measures carried out for the now extinct 2010–2019 Haiti cholera outbreak, to suggest that magnitude and timing of non-pharmaceutical and vaccination interventions imply epidemiological responses recapped by the evolution of epidemicity indices. Achieving negative epidemicity greatly accelerates fading of infections and thus proves a worthwhile target of containment measures. We also show that, in our model, effective reproduction numbers and epidemicity indices are explicitly related. Therefore, providing an upper bound to the effective reproduction number (significantly lower than the unit threshold) warrants negative epidemicity and, in turn, a rapidly fading outbreak preventing coalescence of sparse local sub-threshold flare-ups.