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.

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.

COVID-19 Vaccination and Healthcare Demand.

One of the driving concerns during any epidemic is the strain on the healthcare system. As we have seen many times over the globe with the COVID-19 pandemic, hospitals and ICUs can quickly become overwhelmed by cases. While strict periods of public health mitigation have certainly helped decrease incidence and thus healthcare demand, vaccination is the only clear long-term solution. In this paper, we develop a two-module model to forecast the effects of relaxation of non-pharmaceutical intervention and vaccine uptake on daily incidence, and the cascade effects on healthcare demand. The first module is a simple epidemiological model which incorporates non-pharmaceutical intervention, the relaxation of such measures and vaccination campaigns to predict caseloads into the Fall of 2021. This module is then fed into a healthcare module which can forecast the number of doctor visits, the number of occupied hospital beds, number of occupied ICU beds and any excess demand of these. From this module, we can also estimate the length of stay of individuals in ICU. For model verification and forecasting, we use the four most populous Canadian provinces as a case study.

Coupling the Within-Host Process and Between-Host Transmission of COVID-19 Suggests Vaccination and School Closures are Critical.

Most models of COVID-19 are implemented at a single micro or macro scale, ignoring the interplay between immune response, viral dynamics, individual infectiousness and epidemiological contact networks. Here we develop a data-driven model linking the within-host viral dynamics to the between-host transmission dynamics on a multilayer contact network to investigate the potential factors driving transmission dynamics and to inform how school closures and antiviral treatment can influence the epidemic. Using multi-source data, we initially determine the viral dynamics and estimate the relationship between viral load and infectiousness. Then, we embed the viral dynamics model into a four-layer contact network and formulate an agent-based model to simulate between-host transmission. The results illustrate that the heterogeneity of immune response between children and adults and between vaccinated and unvaccinated infections can produce different transmission patterns. We find that school closures play a significant effect on mitigating the pandemic as more adults get vaccinated and the virus mutates. If enough infected individuals are diagnosed by testing before symptom onset and then treated quickly, the transmission can be effectively curbed. Our multiscale model reveals the critical role played by younger individuals and antiviral treatment with testing in controlling the epidemic.

Comparing Short-Term Univariate and Multivariate Time-Series Forecasting Models in Infectious Disease Outbreak.

Predicting infectious disease outbreak impacts on population, healthcare resources and economics and has received a special academic focus during coronavirus (COVID-19) pandemic. Focus on human disease outbreak prediction techniques in current literature, Marques et al. (Predictive models for decision support in the COVID-19 crisis. Springer, Switzerland, 2021) state that there are four main methods to address forecasting problem: compartmental models, classic statistical models, space-state models and machine learning models. We adopt their framework to compare our research with previous works. Besides being divided by methods, forecasting problems can also be divided by the number of variables that are considered to make predictions. Considering this number of variables, forecasting problems can be classified as univariate, causal and multivariate models. Multivariate approaches have been applied in less than 10% of research found. This research is the first attempt to evaluate, over real time-series data of 3 different countries with univariate and multivariate methods to provide a short-term prediction. In literature we found no research with that scope and aim. A comparison of univariate and multivariate methods has been conducted and we concluded that besides the strong potential of multivariate methods, in our research univariate models presented best results in almost all regions' predictions.

A Multiscale Model of COVID-19 Dynamics.

COVID-19, caused by the infection of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has been a global pandemic and created unprecedented public health challenges throughout the world. Despite significant progresses in understanding the disease pathogenesis and progression, the epidemiological triad of pathogen, host, and environment remains unclear. In this paper, we develop a multiscale model to study the coupled within-host and between-host dynamics of COVID-19. The model includes multiple transmission routes (both human-to-human and environment-to-human) and connects multiple scales (both the population and individual levels). A detailed analysis on the local and global dynamics of the fast system, slow system and full system shows that rich dynamics, including both forward and backward bifurcations, emerge with the coupling of viral infection and epidemiological models. Model fitting to both virological and epidemiological data facilitates the evaluation of the influence of a few infection characteristics and antiviral treatment on the spread of the disease. Our work underlines the potential role that the environment can play in the transmission of COVID-19. Antiviral treatment of infected individuals can delay but cannot prevent the emergence of disease outbreaks. These results highlight the implementation of comprehensive intervention measures such as social distancing and wearing masks that aim to stop airborne transmission, combined with surface disinfection and hand hygiene that can prevent environmental transmission. The model also provides a multiscale modeling framework to study other infectious diseases when the environment can serve as a reservoir of pathogens.

Modeling and Global Sensitivity Analysis of Strategies to Mitigate Covid-19 Transmission on a Structured College Campus.

In response to the COVID-19 pandemic, many higher educational institutions moved their courses on-line in hopes of slowing disease spread. The advent of multiple highly-effective vaccines offers the promise of a return to "normal" in-person operations, but it is not clear if-or for how long-campuses should employ non-pharmaceutical interventions such as requiring masks or capping the size of in-person courses. In this study, we develop and fine-tune a model of COVID-19 spread to UC Merced's student and faculty population. We perform a global sensitivity analysis to consider how both pharmaceutical and non-pharmaceutical interventions impact disease spread. Our work reveals that vaccines alone may not be sufficient to eradicate disease dynamics and that significant contact with an infectious surrounding community will maintain infections on-campus. Our work provides a foundation for higher-education planning allowing campuses to balance the benefits of in-person instruction with the ability to quarantine/isolate infectious individuals.

Analysis of a COVID-19 Epidemic Model with Seasonality.

The statistics of COVID-19 cases exhibits seasonal fluctuations in many countries. In this paper, we propose a COVID-19 epidemic model with seasonality and define the basic reproduction number [Formula: see text] for the disease transmission. It is proved that the disease-free equilibrium is globally asymptotically stable when [Formula: see text], while the disease is uniformly persistent and there exists at least one positive periodic solution when [Formula: see text]. Numerically, we observe that there is a globally asymptotically stable positive periodic solution in the case of [Formula: see text]. Further, we conduct a case study of the COVID-19 transmission in the USA by using statistical data.

Effect of Human Behavior on the Evolution of Viral Strains During an Epidemic.

It is well known in the literature that human behavior can change as a reaction to disease observed in others, and that such behavioral changes can be an important factor in the spread of an epidemic. It has been noted that human behavioral traits in disease avoidance are under selection in the presence of infectious diseases. Here, we explore a complementary trend: the pathogen itself might experience a force of selection to become less "visible," or less "symptomatic," in the presence of such human behavioral trends. Using a stochastic SIR agent-based model, we investigated the co-evolution of two viral strains with cross-immunity, where the resident strain is symptomatic while the mutant strain is asymptomatic. We assumed that individuals exercised self-regulated social distancing (SD) behavior if one of their neighbors was infected with a symptomatic strain. We observed that the proportion of asymptomatic carriers increased over time with a stronger effect corresponding to higher levels of self-regulated SD. Adding mandated SD made the effect more significant, while the existence of a time-delay between the onset of infection and the change of behavior reduced the advantage of the asymptomatic strain. These results were consistent under random geometric networks, scale-free networks, and a synthetic network that represented the social behavior of the residents of New Orleans.

Model Dynamics and Optimal Control for Intervention Policy of COVID-19 Epidemic with Quarantine and Immigrating Disturbances.

A dynamic model called SqEAIIR for the COVID-19 epidemic is investigated with the effects of vaccination, quarantine and precaution promotion when the traveling and immigrating individuals are considered as unknown disturbances. By utilizing only daily sampling data of isolated symptomatic individuals collected by Mexican government agents, an equivalent model is established by an adaptive fuzzy-rules network with the proposed learning law to guarantee the convergence of the model's error. Thereafter, the optimal controller is developed to determine the adequate intervention policy. The main theorem is conducted to demonstrate the setting of all designed parameters regarding the closed-loop performance. The numerical systems validate the efficiency of the proposed scheme to control the epidemic and prevent the overflow of requiring healthcare facilities. Moreover, the sufficient performance of the proposed scheme is achieved with the effect of traveling and immigrating individuals.

Discrete Models in Epidemiology: New Contagion Probability Functions Based on Real Data Behavior.

Mathematical modeling is a tool used for understanding diseases dynamics. The discrete-time model is an especial case in modeling that satisfactorily describes the epidemiological dynamics because of the discrete nature of the real data. However, discrete models reduce their descriptive and fitting potential because of assuming a homogeneous population. Thus, in this paper, we proposed contagion probability functions according to two infection paradigms that consider factors associated with transmission dynamics. For example, we introduced probabilities of establishing an infectious interaction, the number of contacts with infectious and the level of connectivity or social distance within populations. Through the probabilities design, we overcame the homogeneity assumption. Also, we evaluated the proposed probabilities through their introduction into discrete-time models for two diseases and different study zones with real data, COVID-19 for Germany and South Korea, and dengue for Colombia. Also, we described the oscillatory dynamics for the last one using the contagion probabilities alongside parameters with a biological sense. Finally, we highlight the implementation of the proposed probabilities would improve the simulation of the public policy effect of control strategies over an infectious disease outbreak.

Understanding the Role of Environmental Transmission on COVID-19 Herd Immunity and Invasion Potential.

COVID-19 is caused by the SARS-CoV-2 virus, which is mainly transmitted directly between humans. However, it is observed that this disease can also be transmitted through an indirect route via environmental fomites. The development of appropriate and effective vaccines has allowed us to target and anticipate herd immunity. Understanding of the transmission dynamics and the persistence of the virus on environmental fomites and their resistive role on indirect transmission of the virus is an important scientific and public health challenge because it is essential to consider all possible transmission routes and route specific transmission strength to accurately quantify the herd immunity threshold. In this paper, we present a mathematical model that considers both direct and indirect transmission modes. Our analysis focuses on establishing the disease invasion threshold, investigating its sensitivity to both transmission routes and isolate route-specific transmission rate. Using the tau-leap algorithm, we perform a stochastic model simulation to address the invasion potential of both transmission routes. Our analysis shows that direct transmission has a higher invasion potential than that of the indirect transmission. As a proof of this concept, we fitted our model with early epidemic data from several countries to uniquely estimate the reproduction numbers associated with direct and indirect transmission upon confirming the identifiability of the parameters. As the indirect transmission possess lower invasion potential than direct transmission, proper estimation and necessary steps toward mitigating it would help reduce vaccination requirement.

Assessing Age-Specific Vaccination Strategies and Post-vaccination Reopening Policies for COVID-19 Control Using SEIR Modeling Approach.

As the availability of COVID-19 vaccines, it is badly needed to develop vaccination guidelines to prioritize the vaccination delivery in order to effectively stop COVID-19 epidemic and minimize the loss. We evaluated the effect of age-specific vaccination strategies on the number of infections and deaths using an SEIR model, considering the age structure and social contact patterns for different age groups for each of different countries. In general, the vaccination priority should be given to those younger people who are active in social contacts to minimize the number of infections, while the vaccination priority should be given to the elderly to minimize the number of deaths. But this principle may not always apply when the interaction of age structure and age-specific social contact patterns is complicated. Partially reopening schools, workplaces or households, the vaccination priority may need to be adjusted accordingly. Prematurely reopening social contacts could initiate a new outbreak or even a new pandemic out of control if the vaccination rate and the detection rate are not high enough. Our result suggests that it requires at least nine months of vaccination (with a high vaccination rate > 0.1%) for Italy and India before fully reopening social contacts in order to avoid a new pandemic.

Controlling Multiple COVID-19 Epidemic Waves: An Insight from a Multi-scale Model Linking the Behaviour Change Dynamics to the Disease Transmission Dynamics.

COVID-19 epidemics exhibited multiple waves regionally and globally since 2020. It is important to understand the insight and underlying mechanisms of the multiple waves of COVID-19 epidemics in order to design more efficient non-pharmaceutical interventions (NPIs) and vaccination strategies to prevent future waves. We propose a multi-scale model by linking the behaviour change dynamics to the disease transmission dynamics to investigate the effect of behaviour dynamics on COVID-19 epidemics using game theory. The proposed multi-scale models are calibrated and key parameters related to disease transmission dynamics and behavioural dynamics with/without vaccination are estimated based on COVID-19 epidemic data (daily reported cases and cumulative deaths) and vaccination data. Our modeling results demonstrate that the feedback loop between behaviour changes and COVID-19 transmission dynamics plays an essential role in inducing multiple epidemic waves. We find that the long period of high-prevalence or persistent deterioration of COVID-19 epidemics could drive almost all of the population to change their behaviours and maintain the altered behaviours. However, the effect of behaviour changes fades out gradually along the progress of epidemics. This suggests that it is essential to have not only persistent, but also effective behaviour changes in order to avoid subsequent epidemic waves. In addition, our model also suggests the importance to maintain the effective altered behaviours during the initial stage of vaccination, and to counteract relaxation of NPIs, it requires quick and massive vaccination to avoid future epidemic waves.

Analysis of the Geographic Transmission Differences of COVID-19 in China Caused by Population Movement and Population Density.

The coronavirus disease (COVID-19) has led to a global pandemic and caused huge healthy and economic losses. Non-pharmaceutical interventions, especially contact tracing and social distance restrictions, play a vital role in the control of COVID-19. Understanding the spatial impact is essential for designing such a control policy. Based on epidemic data of the confirmed cases after the Wuhan lockdown, we calculate the invasive reproduction numbers of COVID-19 in the different regions of China. Statistical analysis indicates a significant positive correlation between the reproduction numbers and the population input sizes from Wuhan, which indicates that the large-scale population movement contributed a lot to the geographic spread of COVID-19 in China. Moreover, there is a significant positive correlation between reproduction numbers and local population densities, which shows that the higher population density intensifies the spread of disease. Considering that in the early stage, there were sequential imported cases that affected the estimation of reproduction numbers, we classify the imported cases and local cases through the information of epidemiological data and calculate the net invasive reproduction number to quantify the local spread of the epidemic. The results are applied to the design of border control policy on the basis of vaccination coverage.

From Policy to Prediction: Forecasting COVID-19 Dynamics Under Imperfect Vaccination.

Understanding the joint impact of vaccination and non-pharmaceutical interventions on COVID-19 development is important for making public health decisions that control the pandemic. Recently, we created a method in forecasting the daily number of confirmed cases of infectious diseases by combining a mechanistic ordinary differential equation (ODE) model for infectious classes and a generalized boosting machine learning model (GBM) for predicting how public health policies and mobility data affect the transmission rate in the ODE model (Wang et al. in Bull Math Biol 84:57, 2022). In this paper, we extend the method to the post-vaccination period, accordingly obtain a retrospective forecast of COVID-19 daily confirmed cases in the US, and identify the relative influence of the policies used as the predictor variables. In particular, our ODE model contains both partially and fully vaccinated compartments and accounts for the breakthrough cases, that is, vaccinated individuals can still get infected. Our results indicate that the inclusion of data on non-pharmaceutical interventions can significantly improve the accuracy of the predictions. With the use of policy data, the model predicts the number of daily infected cases up to 35 days in the future, with an average mean absolute percentage error of [Formula: see text], which is further improved to [Formula: see text] if combined with human mobility data. Moreover, the most influential predictor variables are the policies of restrictions on gatherings, testing and school closing. The modeling approach used in this work can help policymakers design control measures as variant strains threaten public health in the future.

A Hybrid Epidemic Model to Explore Stochasticity in COVID-19 Dynamics.

The dynamic nature of the COVID-19 pandemic has demanded a public health response that is constantly evolving due to the novelty of the virus. Many jurisdictions in the USA, Canada, and across the world have adopted social distancing and recommended the use of face masks. Considering these measures, it is prudent to understand the contributions of subpopulations-such as "silent spreaders"-to disease transmission dynamics in order to inform public health strategies in a jurisdiction-dependent manner. Additionally, we and others have shown that demographic and environmental stochasticity in transmission rates can play an important role in shaping disease dynamics. Here, we create a model for the COVID-19 pandemic by including two classes of individuals: silent spreaders, who either never experience a symptomatic phase or remain undetected throughout their disease course; and symptomatic spreaders, who experience symptoms and are detected. We fit the model to real-time COVID-19 confirmed cases and deaths to derive the transmission rates, death rates, and other relevant parameters for multiple phases of outbreaks in British Columbia (BC), Canada. We determine the extent to which SilS contributed to BC's early wave of disease transmission as well as the impact of public health interventions on reducing transmission from both SilS and SymS. To do this, we validate our model against an existing COVID-19 parameterized framework and then fit our model to clinical data to estimate key parameter values for different stages of BC's disease dynamics. We then use these parameters to construct a hybrid stochastic model that leverages the strengths of both a time-nonhomogeneous discrete process and a stochastic differential equation model. By combining these previously established approaches, we explore the impact of demographic and environmental variability on disease dynamics by simulating various scenarios in which a COVID-19 outbreak is initiated. Our results demonstrate that variability in disease transmission rate impacts the probability and severity of COVID-19 outbreaks differently in high- versus low-transmission scenarios.

An Epidemic Model with Time-Distributed Recovery and Death Rates.

A compartmental epidemiological model with distributed recovery and death rates is proposed. In some particular cases, the model can be reduced to the conventional SIR model. However, in general, the dynamics of epidemic progression in this model is different. Distributed recovery and death rates are evaluated from COVID-19 data. The model is validated by the epidemiological data for different countries, and it shows better agreement with the data than the SIR model. The time-dependent disease transmission rate is estimated.

Balancing Quarantine and Self-Distancing Measures in Adaptive Epidemic Networks.

We study the relative importance of two key control measures for epidemic spreading: endogenous social self-distancing and exogenous imposed quarantine. We use the framework of adaptive networks, moment-closure, and ordinary differential equations to introduce new model types of susceptible-infected-recovered (SIR) dynamics. First, we compare computationally expensive, adaptive network simulations with their corresponding computationally efficient ODE equivalents and find excellent agreement. Second, we discover that there exists a critical curve in parameter space for the epidemic threshold, which suggests a mutual compensation effect between the two mitigation strategies: as long as social distancing and quarantine measures are both sufficiently strong, large outbreaks are prevented. Third, we study the total number of infected and the maximum peak during large outbreaks using a combination of analytical estimates and numerical simulations. Also for large outbreaks we find a similar compensation mechanism as for the epidemic threshold. This means that if there is little incentive for social distancing in a population, drastic quarantining is required, and vice versa. Both pure scenarios are unrealistic in practice. The new models show that only a combination of measures is likely to succeed to control epidemic spreading. Fourth, we analytically compute an upper bound for the total number of infected on adaptive networks, using integral estimates in combination with a moment-closure approximation on the level of an observable. Our method allows us to elegantly and quickly check and cross-validate various conjectures about the relevance of different network control measures. In this sense it becomes possible to adapt also other models rapidly to new epidemic challenges.

Delays, Masks, the Elderly, and Schools: First Covid-19 Wave in the Czech Republic.

Running across the globe for nearly 2 years, the Covid-19 pandemic keeps demonstrating its strength. Despite a lot of understanding, uncertainty regarding the efficiency of interventions still persists. We developed an age-structured epidemic model parameterized with epidemiological and sociological data for the first Covid-19 wave in the Czech Republic and found that (1) starting the spring 2020 lockdown 4 days earlier might prevent half of the confirmed cases by the end of lockdown period, (2) personal protective measures such as face masks appear more effective than just a realized reduction in social contacts, (3) the strategy of sheltering just the elderly is not at all effective, and (4) leaving schools open is a risky strategy. Despite vaccination programs, evidence-based choice and timing of non-pharmaceutical interventions remains an effective weapon against the Covid-19 pandemic.