System identifiability in a time-evolving agent-based model

Mathematical models are a valuable tool for studying and predicting the spread of infectious agents. The accuracy of model simulations and predictions invariably depends on the specification of model parameters. Estimation of these parameters is therefore extremely important; however, while some parameters can be derived from observational studies, the values of others are difficult to measure. Instead, models can be coupled with inference algorithms (i.e., data assimilation methods, or statistical filters), which fit model simulations to existing observations and estimate unobserved model state variables and parameters. Ideally, these inference algorithms should find the best fitting solution for a given model and set of observations; however, as those estimated quantities are unobserved, it is typically uncertain whether the correct parameters have been identified. Further, it is unclear what 'correct' really means for abstract parameters defined based on specific model forms. In this work, we explored the problem of non-identifiability in a stochastic system which, when overlooked, can significantly impede model prediction. We used a network, agent-based model to simulate the transmission of Methicillin-resistant staphylococcus aureus (MRSA) within hospital settings and attempted to infer key model parameters using the Ensemble Adjustment Kalman Filter, an efficient Bayesian inference algorithm. We show that even though the inference method converged and that simulations using the estimated parameters produced an agreement with observations, the true parameters are not fully identifiable. While the model-inference system can exclude a substantial area of parameter space that is unlikely to contain the true parameters, the estimated parameter range still included multiple parameter combinations that can fit observations equally well. We show that analyzing synthetic trajectories can support or contradict claims of identifiability. While we perform this on a specific model system, this approach can be generalized for a variety of stochastic representations of partially observable systems. We also suggest data manipulations intended to improve identifiability that might be applicable in many systems of interest.

Real-time updating of dynamic social networks for COVID-19 vaccination strategies

Vaccination strategy is crucial in fighting the COVID-19 pandemic. Since the supply is still limited in many countries, contact network-based interventions can be most powerful to set an efficient strategy by identifying high-risk individuals or communities. However, due to the high dimension, only partial and noisy network information can be available in practice, especially for dynamic systems where contact networks are highly time-variant. Furthermore, the numerous mutations of SARS-CoV-2 have a significant impact on the infectious probability, requiring real-time network updating algorithms. In this study, we propose a sequential network updating approach based on data assimilation techniques to combine different sources of temporal information. We then prioritise the individuals with high-degree or high-centrality, obtained from assimilated networks, for vaccination. The assimilation-based approach is compared with the standard method (based on partially observed networks) and a random selection strategy in terms of vaccination effectiveness in a SIR model. The numerical comparison is first carried out using real-world face-to-face dynamic networks collected in a high school, followed by sequential multi-layer networks generated relying on the Barabasi-Albert model emulating large-scale social networks with several communities.

Real-time estimation of the epidemic reproduction number: Scoping review of the applications and challenges

The time-varying reproduction number (Rt) is an important measure of transmissibility during outbreaks. Estimating whether and how rapidly an outbreak is growing (Rt > 1) or declining (Rt < 1) can inform the design, monitoring and adjustment of control measures in real-time. We use a popular R package for Rt estimation, EpiEstim, as a case study to evaluate the contexts in which Rt estimation methods have been used and identify unmet needs which would enable broader applicability of these methods in real-time. A scoping review, complemented by a small EpiEstim user survey, highlight issues with the current approaches, including the quality of input incidence data, the inability to account for geographical factors, and other methodological issues. We summarise the methods and software developed to tackle the problems identified, but conclude that significant gaps remain which should be addressed to enable easier, more robust and applicable estimation of Rt during epidemics.

Mathematical Analysis of Two Waves of COVID-19 Disease with Impact of Vaccination as Optimal Control

This paper is devoted to answering some questions using a mathematical model by analyzing India’s first and second phases of the COVID-19 pandemic. A new mathematical model is introduced with a nonmonotonic incidence rate to incorporate the psychological effect of COVID-19 in society. The paper also discusses the local stability and global stability of an endemic equilibrium and a disease-free equilibrium. The basic reproduction number is evaluated using the proposed COVID-19 model for disease spread in India based on the actual data sets. The study of nonperiodic solutions at a positive equilibrium point is also analyzed. The model is rigorously studied using MATLAB to alert the decision-making bodies to hinder the emergence of any other pandemic outbreaks or the arrival of subsequent pandemic waves. This paper shows the excellent prediction of the first wave and very commanding for the second wave. The exciting results of the paper are as follows: (i) psychological effect on the human population has an impact on propagation; (ii) lockdown is a suitable technique mathematically to control the COVID spread; (iii) different variants produce different waves; (iv) the peak value always crosses its past value.

Bayesian data assimilation for estimating instantaneous reproduction numbers during epidemics: Applications to COVID-19

Estimating the changes of epidemiological parameters, such as instantaneous reproduction number, Rt, is important for understanding the transmission dynamics of infectious diseases. Current estimates of time-varying epidemiological parameters often face problems such as lagging observations, averaging inference, and improper quantification of uncertainties. To address these problems, we propose a Bayesian data assimilation framework for time-varying parameter estimation. Specifically, this framework is applied to estimate the instantaneous reproduction number Rt during emerging epidemics, resulting in the state-of-the-art 'DARt' system. With DARt, time misalignment caused by lagging observations is tackled by incorporating observation delays into the joint inference of infections and Rt; the drawback of averaging is overcome by instantaneously updating upon new observations and developing a model selection mechanism that captures abrupt changes; the uncertainty is quantified and reduced by employing Bayesian smoothing. We validate the performance of DARt and demonstrate its power in describing the transmission dynamics of COVID-19. The proposed approach provides a promising solution for making accurate and timely estimation for transmission dynamics based on reported data.

Digital twins based on bidirectional LSTM and GAN for modelling the COVID-19 pandemic

The outbreak of the coronavirus disease 2019 (COVID-19) has now spread throughout the globe infecting over 150 million people and causing the death of over 3.2 million people. Thus, there is an urgent need to study the dynamics of epidemiological models to gain a better understanding of how such diseases spread. While epidemiological models can be computationally expensive, recent advances in machine learning techniques have given rise to neural networks with the ability to learn and predict complex dynamics at reduced computational costs. Here we introduce two digital twins of a SEIRS model applied to an idealised town. The SEIRS model has been modified to take account of spatial variation and, where possible, the model parameters are based on official virus spreading data from the UK. We compare predictions from one digital twin based on a data-corrected Bidirectional Long Short-Term Memory network with predictions from another digital twin based on a predictive Generative Adversarial Network. The predictions given by these two frameworks are accurate when compared to the original SEIRS model data. Additionally, these frameworks are data-agnostic and could be applied to towns, idealised or real, in the UK or in other countries. Also, more compartments could be included in the SEIRS model, in order to study more realistic epidemiological behaviour.

A Graph Clustering Approach to Localization for Adaptive Covariance Tuning in Data Assimilation Based on State-Observation Mapping

An original graph clustering approach for the efficient localization of error covariances is proposed within an ensemble-variational data assimilation framework. Here, the localization term is very generic and refers to the idea of breaking up a global assimilation into subproblems. This unsupervised localization technique based on a linearized state-observation measure is general and does not rely on any prior information such as relevant spatial scales, empirical cutoff radii or homogeneity assumptions. Localization is performed via graph theory, a branch of mathematics emerging as a powerful approach to capturing complex and highly interconnected Earth and environmental systems in computational geosciences. The novel approach automatically segregates the state and observation variables in an optimal number of clusters, and it is more amenable to scalable data assimilation. The application of this method does not require underlying block-diagonal structures of prior covariance matrices. To address intercluster connectivity, two alternative data adaptations are proposed. Once the localization is completed, a covariance diagnosis and tuning are performed within each cluster, whose contribution is sequentially integrated into the entire covariance matrix. Numerical twin experiment tests show the reduced cost and added flexibility of this approach compared to global covariance tuning, and more accurate results yielded for both observation- and background-error parameter tuning.

Modeling of suppression and mitigation interventions in the COVID-19 epidemics

Background

The global spread of the COVID-19 pandemic has become the most fundamental threat to human health. In the absence of vaccines and effective therapeutical solutions, non-pharmaceutic intervention has become a major way for controlling the epidemic. Gentle mitigation interventions are able to slow down the epidemic but not to halt it well. While strict suppression interventions are efficient for controlling the epidemic, long-term measures are likely to have negative impacts on economics and people’s daily live. Hence, dynamically balancing suppression and mitigation interventions plays a fundamental role in manipulating the epidemic curve.

Methods

We collected data of the number of infections for several countries during the COVID-19 pandemics and found a clear phenomenon of periodic waves of infection. Based on the observation, by connecting the infection level with the medical resources and a tolerance parameter, we propose a mathematical model to understand impacts of combining intervention measures on the epidemic dynamics.

Results

Depending on the parameters of the medical resources, tolerance level, and the starting time of interventions, the combined intervention measure dynamically changes with the infection level, resulting in a periodic wave of infections controlled below an accepted level. The study reveals that, (a) with an immediate, strict suppression, the numbers of infections and deaths are well controlled with a significant reduction in a very short time period; (b) an appropriate, dynamical combination of suppression and mitigation may find a feasible way in reducing the impacts of epidemic on people’s live and economics.

Conclusions

While the assumption of interventions deployed with a cycle of period in the model is limited and unrealistic, the phenomenon of periodic waves of infections in reality is captured by our model. These results provide helpful insights for policy-makers to dynamically deploy an appropriate intervention strategy to effectively battle against the COVID-19.