An evaluation of Hamiltonian Monte Carlo performance to calibrate age-structured compartmental SEIR models to incidence data

Anchoring the mean generation time in the SEIR to mitigate biases in ℜ0 estimates due to uncertainty in the distribution of the epidemiological delays

The basic reproduction number, ℜ 0 , is of paramount importance in the study of infectious disease dynamics. Primarily, ℜ 0 serves as an indicator of the transmission potential of an emerging infectious disease and the effort required to control the invading pathogen. However, its estimates from compartmental models are strongly conditioned by assumptions in the model structure, such as the distributions of the latent and infectious periods (epidemiological delays). To further complicate matters, models with dissimilar delay structures produce equivalent incidence dynamics. Following a simulation study, we reveal that the nature of such equivalency stems from a linear relationship between ℜ 0 and the mean generation time, along with adjustments to other parameters in the model. Leveraging this knowledge, we propose and successfully test an alternative parametrization of the SEIR model that produces accurate ℜ 0 estimates regardless of the distribution of the epidemiological delays, at the expense of biases in other quantities deemed of lesser importance. We further explore this approach's robustness by testing various transmissibility levels, generation times and data fidelity (overdispersion). Finally, we apply the proposed approach to data from the 1918 influenza pandemic. We anticipate that this work will mitigate biases in estimating ℜ 0 .

Optimal interventional policy based on discrete-time fuzzy rules equivalent model utilizing with COVID-19 pandemic data

In this paper, a mathematical model of the COVID-19 pandemic is formulated by fitting it to actual data collected during the fifth wave of the COVID-19 pandemic in Coahuila, Mexico, from June 2022 to October 2022. The data sets used are recorded on a daily basis and presented in a discrete-time sequence. To obtain the equivalent data model, fuzzy rules emulated networks are utilized to derive a class of discrete-time systems based on the daily hospitalized individuals' data. The aim of this study is to investigate the optimal control problem to determine the most effective interventional policy including precautionary and awareness measures, the detection of asymptomatic and symptomatic individuals, and vaccination. A main theorem is developed to guarantee the closed-loop system performance by utilizing approximate functions of the equivalent model. The numerical results indicate that the proposed interventional policy can eradicate the pandemic within 1-8 weeks. Additionally, the results show that if the policy is implemented within the first 3 weeks, the number of hospitalized individuals remains below the hospital's capacity.

Validating and Testing an Agent-Based Model for the Spread of COVID-19 in Ireland

Agent-based models can be used to better understand the impacts of lifting restrictions or implementing interventions during a pandemic. However, agent-based models are computationally expensive, and running a model of a large population can result in a simulation taking too long to run for the model to be a useful analysis tool during a public health crisis. To reduce computing time and power while running a detailed agent-based model for the spread of COVID-19 in the Republic of Ireland, we introduce a scaling factor that equates 1 agent to 100 people in the population. We present the results from model validation and show that the scaling factor increases the variability in the model output, but the average model results are similar in scaled and un-scaled models of the same population, and the scaled model is able to accurately simulate the number of cases per day in Ireland during the autumn of 2020. We then test the usability of the model by using the model to explore the likely impacts of increasing community mixing when schools reopen after summer holidays.

Inferring the effective reproductive number from deterministic and semi-deterministic compartmental models using incidence and mobility data

The effective reproduction number (ℜt) is a theoretical indicator of the course of an infectious disease that allows policymakers to evaluate whether current or previous control efforts have been successful or whether additional interventions are necessary. This metric, however, cannot be directly observed and must be inferred from available data. One approach to obtaining such estimates is fitting compartmental models to incidence data. We can envision these dynamic models as the ensemble of structures that describe the disease’s natural history and individuals’ behavioural patterns. In the context of the response to the COVID-19 pandemic, the assumption of a constant transmission rate is rendered unrealistic, and it is critical to identify a mathematical formulation that accounts for changes in contact patterns. In this work, we leverage existing approaches to propose three complementary formulations that yield similar estimates for ℜt based on data from Ireland’s first COVID-19 wave. We describe these Data Generating Processes (DGP) in terms of State-Space models. Two (DGP1 and DGP2) correspond to stochastic process models whose transmission rate is modelled as Brownian motion processes (Geometric and Cox-Ingersoll-Ross). These DGPs share a measurement model that accounts for incidence and transmission rates, where mobility data is assumed as a proxy of the transmission rate. We perform inference on these structures using Iterated Filtering and the Particle Filter. The final DGP (DGP3) is built from a pool of deterministic models that describe the transmission rate as information delays. We calibrate this pool of models to incidence reports using Hamiltonian Monte Carlo. By following this complementary approach, we assess the tradeoffs associated with each formulation and reflect on the benefits/risks of incorporating proxy data into the inference process. We anticipate this work will help evaluate the implications of choosing a particular formulation for the dynamics and observation of the time-varying transmission rate.

Calibrating COVID-19 susceptible-exposed-infected-removed models with time-varying effectivecontact rates

We describe the population-based susceptible-exposed-infected-removed (SEIR) model developed by the Irish Epidemiological Modelling Advisory Group (IEMAG), which advises the Irish government on COVID-19 responses. The model assumes a time-varying effective contact rate (equivalently, a time-varying reproduction number) to model the effect of non-pharmaceutical interventions. A crucial technical challenge in applying such models is their accurate calibration to observed data, e.g. to the daily number of confirmed new cases, as the history of the disease strongly affects predictions of future scenarios. We demonstrate an approach based on inversion of the SEIR equations in conjunction with statistical modelling and spline-fitting of the data to produce a robust methodology for calibration of a wide class of models of this type. This article is part of the theme issue 'Data science approaches to infectious disease surveillance'.

Numbers of close contacts of individuals infected with SARS-CoV-2 and their association with government intervention strategies

Background

Contact tracing is conducted with the primary purpose of interrupting transmission from individuals who are likely to be infectious to others. Secondary analyses of data on the numbers of close contacts of confirmed cases could also: provide an early signal of increases in contact patterns that might precede larger than expected case numbers; evaluate the impact of government interventions on the number of contacts of confirmed cases; or provide data information on contact rates between age cohorts for the purpose of epidemiological modelling. We analysed data from 140,204 close contacts of 39,861 cases in Ireland from 1st May to 1st December 2020.

Results

Negative binomial regression models highlighted greater numbers of contacts within specific population demographics, after correcting for temporal associations. Separate segmented regression models of the number of cases over time and the average number of contacts per case indicated that a breakpoint indicating a rapid decrease in the number of contacts per case in October 2020 preceded a breakpoint indicating a reduction in the number of cases by 11 days.

Conclusions

We found that the number of contacts per infected case was overdispersed, the mean varied considerable over time and was temporally associated with government interventions. Analysis of the reported number of contacts per individual in contact tracing data may be a useful early indicator of changes in behaviour in response to, or indeed despite, government restrictions. This study provides useful information for triangulating assumptions regarding the contact mixing rates between different age cohorts for epidemiological modelling.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12889-021-12318-y.

Reproducible parallel inference and simulation of stochastic state space models using odin, dust, and mcstate

State space models, including compartmental models, are used to model physical, biological and social phenomena in a broad range of scientific fields. A common way of representing the underlying processes in these models is as a system of stochastic processes which can be simulated forwards in time. Inference of model parameters based on observed time-series data can then be performed using sequential Monte Carlo techniques. However, using these methods for routine inference problems can be made difficult due to various engineering considerations: allowing model design to change in response to new data and ideas, writing model code which is highly performant, and incorporating all of this with up-to-date statistical techniques. Here, we describe a suite of packages in the R programming language designed to streamline the design and deployment of state space models, targeted at infectious disease modellers but suitable for other domains. Users describe their model in a familiar domain-specific language, which is converted into parallelised C++ code. A fast, parallel, reproducible random number generator is then used to run large numbers of model simulations in an efficient manner. We also provide standard inference and prediction routines, though the model simulator can be used directly if these do not meet the user’s needs. These packages provide guarantees on reproducibility and performance, allowing the user to focus on the model itself, rather than the underlying computation. The ability to automatically generate high-performance code that would be tedious and time-consuming to write and verify manually, particularly when adding further structure to compartments, is crucial for infectious disease modellers. Our packages have been critical to the development cycle of our ongoing real-time modelling efforts in the COVID-19 pandemic, and have the potential to do the same for models used in a number of different domains.

Epidemic model dynamics and fuzzy neural-network optimal control with impulsive traveling and migrating: Case study of COVID-19 vaccination

To suppress the epidemics caused by a virus such as COVID-19, three effective strategies listing vaccination, quarantine and medical treatments, are employed under suitable policies. Quarantine motions may affect the economic systems and pharmaceutical medications may be recently in the developing phase. Thus, vaccination seems the best hope of the current situation to control COVID-19 epidemics. In this work, the dynamic model of COVID-19 epidemic is developed when the quarantine factor and the antiviral factor are established as free variables. Moreover, the impulsive populations are comprehended for traveling and migrating of individuals. The proposed dynamics with impulsive distractions are employed to generate the online data. Thereafter, the equivalent model is developed by using only the daily data of symptomatic infectious individuals and the optimal vaccination policy is derived by utilizing the closed-loop control topology. The theoretical framework of the proposed schemes validates the reduction of symptomatic infectious individuals by using fewer doses of vaccines comparing with the scheduling vaccination.

Reproducible parallel inference and simulation of stochastic state space models using odin, dust, and mcstate

State space models, including compartmental models, are used to model physical, biological and social phenomena in a broad range of scientific fields. A common way of representing the underlying processes in these models is as a system of stochastic processes which can be simulated forwards in time. Inference of model parameters based on observed time-series data can then be performed using sequential Monte Carlo techniques. However, using these methods for routine inference problems can be made difficult due to various engineering considerations: allowing model design to change in response to new data and ideas, writing model code which is highly performant, and incorporating all of this with up-to-date statistical techniques. Here, we describe a suite of packages in the R programming language designed to streamline the design and deployment of state space models, targeted at infectious disease modellers but suitable for other domains. Users describe their model in a familiar domain-specific language, which is converted into parallelised C++ code. A fast, parallel, reproducible random number generator is then used to run large numbers of model simulations in an efficient manner. We also provide standard inference and prediction routines, though the model simulator can be used directly if these do not meet the user’s needs. These packages provide guarantees on reproducibility and performance, allowing the user to focus on the model itself, rather than the underlying computation. The ability to automatically generate high-performance code that would be tedious and time-consuming to write and verify manually, particularly when adding further structure to compartments, is crucial for infectious disease modellers. Our packages have been critical to the development cycle of our ongoing real-time modelling efforts in the COVID-19 pandemic, and have the potential to do the same for models used in a number of different domains.