Project description:Existing compartmental mathematical modelling methods for epidemics, such as SEIR models, cannot accurately represent effects of contact tracing. This makes them inappropriate for evaluating testing and contact tracing strategies to contain an outbreak. An alternative used in practice is the application of agent- or individual-based models (ABM). However ABMs are complex, less well-understood and much more computationally expensive. This paper presents a new method for accurately including the effects of Testing, contact-Tracing and Isolation (TTI) strategies in standard compartmental models. We derive our method using a careful probabilistic argument to show how contact tracing at the individual level is reflected in aggregate on the population level. We show that the resultant SEIR-TTI model accurately approximates the behaviour of a mechanistic agent-based model at far less computational cost. The computational efficiency is such that it can be easily and cheaply used for exploratory modelling to quantify the required levels of testing and tracing, alone and with other interventions, to assist adaptive planning for managing disease outbreaks.
Project description:Human hematopoiesis is surprisingly resilient to disruptions, providing suitable responses to severe bleeding, long-lasting immune activation, and even bone marrow transplants. Still, many blood disorders exist which push the system past its natural plasticity, resulting in abnormalities in the circulating blood. While proper treatment of such diseases can benefit from understanding the underlying cell dynamics, these are non-trivial to predict due to the hematopoietic system's hierarchical nature and complex feedback networks. To characterize the dynamics following different types of perturbations, we investigate a model representing hematopoiesis as a sequence of compartments covering all maturation stages-from stem to mature cells-where feedback regulates cell production to ongoing necessities. We find that a stable response to perturbations requires the simultaneous adaptation of cell differentiation and self-renewal rates, and show that under conditions of continuous disruption-as found in chronic hemolytic states-compartment cell numbers evolve to novel stable states.
Project description: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.
Project description:During autumn 2020, Italy faced a second important SARS-CoV-2 epidemic wave. We explored the time pattern of the instantaneous reproductive number, R 0(t), and estimated the prevalence of infections by region from August to December calibrating SIRD models on COVID-19-related deaths, fixing at values from literature Infection Fatality Rate (IFR) and average infection duration. A Global Sensitivity Analysis (GSA) was performed on the regional SIRD models. Then, we used Bayesian meta-analysis and meta-regression to combine and compare the regional results and investigate their heterogeneity. The meta-analytic R 0(t) curves were similar in the Northern and Central regions, while a less peaked curve was estimated for the South. The maximum R 0(t) ranged from 2.15 (South) to 2.61 (North) with an increase following school reopening and a decline at the end of October. The predictive performance of the regional models, assessed through cross validation, was good, with a Mean Absolute Percentage Error of 7.2% and 10.9% when considering prediction horizons of 7 and 14 days, respectively. Average temperature, urbanization, characteristics of family medicine and healthcare system, economic dynamism, and use of public transport could partly explain the regional heterogeneity. The GSA indicated the robustness of the regional R 0(t) curves to different assumptions on IFR. The infectious period turned out to have a key role in determining the model results, but without compromising between-region comparisons.
Project description:Compartmental models have provided a framework for understanding disease transmission dynamics for over 100 years. The predictions from these models are often policy relevant and need to be robust to model assumptions, parameter values and model structure. A selection of compartmental models with the same parameter values but different model structures (ranging from simple structures to complex ones) were compared in the absence and presence of several policy interventions to assess sensitivity to model structure. Models were fitted to data to assess if this might reduce this sensitivity. The compartmental models produced wide-ranging estimates of outcome measures but when fitted to data, the estimates obtained were robust to model structure. This finding suggests that there may be an argument for selecting simple models over complex ones, but the complexity of the model should be determined by the purpose of the model and the use to which it will be put.
Project description:Economic evaluations of infectious disease control interventions frequently use dynamic compartmental epidemic models. Such models capture heterogeneity in risk of infection by stratifying the population into discrete risk groups, thus approximating what is typically continuous variation in risk. An important open question is whether and how different risk stratification choices influence model predictions of intervention effects. We develop equivalent Susceptible-Infected-Susceptible (SIS) dynamic transmission models: an unstratified model, a model stratified into a high-risk and low-risk group, and a model with an arbitrary number of risk groups. Absent intervention, the models produce the same overall prevalence of infected individuals in steady state. We consider an intervention that either reduces the contact rate or increases the disease clearance rate. We develop analytical and numerical results characterizing the models and the effects of the intervention. We find that there exist multiple feasible choices of risk stratification, contact distribution, and within- and between-group contact rates for models that stratify risk. We show analytically and empirically that these choices can generate different estimates of intervention effectiveness, and that these differences can be significant enough to alter conclusions from cost-effectiveness analyses and change policy recommendations. We conclude that the choice of how to discretize risk in compartmental epidemic models can influence predicted effectiveness of interventions. Therefore, analysts should examine multiple alternatives and report the range of results.
Project description:Several factors have played a strong role in influencing the dynamics of COVID-19 in the U.S. One being the economy, where a tug of war has existed between lockdown measures to control disease versus loosening of restrictions to address economic hardship. A more recent effect has been availability of vaccines and the mass vaccination efforts of 2021. In order to address the challenges in analyzing this complex process, we developed a competing risk compartmental model framework with and without vaccination compartment. This framework separates instantaneous risk of removal for an infectious case into competing risks of cure and death, and when vaccinations are present, the vaccinated individual can also achieve immunity before infection. Computations are performed using a simple discrete time algorithm that utilizes a data driven contact rate. Using population level pre-vaccination data, we are able to identify and characterize three wave patterns in the U.S. Estimated mortality rates for second and third waves are 1.7%, which is a notable decrease from 8.5% of a first wave observed at onset of disease. This analysis reveals the importance cure time has on infectious duration and disease transmission. Using vaccination data from 2021, we find a fourth wave, however the effect of this wave is suppressed due to vaccine effectiveness. Parameters playing a crucial role in this modeling were a lower cure time and a signficantly lower mortality rate for the vaccinated.
Project description:Theoretical models of infection spread on networks predict that targeting vaccination at individuals with a very large number of contacts (superspreaders) can reduce infection incidence by a significant margin. These models generally assume that superspreaders will always agree to be vaccinated. Hence, they cannot capture unintended consequences such as policy resistance, where the behavioral response induced by a new vaccine policy tends to reduce the expected benefits of the policy. Here, we couple a model of influenza transmission on an empirically-based contact network with a psychologically structured model of influenza vaccinating behavior, where individual vaccinating decisions depend on social learning and past experiences of perceived infections, vaccine complications and vaccine failures. We find that policy resistance almost completely undermines the effectiveness of superspreader strategies: the most commonly explored approaches that target a randomly chosen neighbor of an individual, or that preferentially choose neighbors with many contacts, provide at best a 2% relative improvement over their non-targeted counterpart as compared to 12% when behavioral feedbacks are ignored. Increased vaccine coverage in super spreaders is offset by decreased coverage in non-superspreaders, and superspreaders also have a higher rate of perceived vaccine failures on account of being infected more often. Including incentives for vaccination provides modest improvements in outcomes. We conclude that the design of influenza vaccine strategies involving widespread incentive use and/or targeting of superspreaders should account for policy resistance, and mitigate it whenever possible.
Project description:The recent coronavirus disease (COVID-19) outbreak has dramatically increased the public awareness and appreciation of the utility of dynamic models. At the same time, the dissemination of contradictory model predictions has highlighted their limitations. If some parameters and/or state variables of a model cannot be determined from output measurements, its ability to yield correct insights – as well as the possibility of controlling the system – may be compromised. Epidemic dynamics are commonly analysed using compartmental models, and many variations of such models have been used for analysing and predicting the evolution of the COVID-19 pandemic. In this paper we survey the different models proposed in the literature, assembling a list of 36 model structures and assessing their ability to provide reliable information. We address the problem using the control theoretic concepts of structural identifiability and observability. Since some parameters can vary during the course of an epidemic, we consider both the constant and time-varying parameter assumptions. We analyse the structural identifiability and observability of all of the models, considering all plausible choices of outputs and time-varying parameters, which leads us to analyse 255 different model versions. We classify the models according to their structural identifiability and observability under the different assumptions and discuss the implications of the results. We also illustrate with an example several alternative ways of remedying the lack of observability of a model. Our analyses provide guidelines for choosing the most informative model for each purpose, taking into account the available knowledge and measurements. Highlights • Structural identifiability and observability are desirable model properties.• They describe a model’s ability to inform about unmeasured parameters and states.• We collect and analyse hundreds of compartmental models of the COVID-19 pandemics.• We show which parameters and states can be determined from output measurements.• We discuss how to choose the most informative model for the available knowledge.
Project description:The pathophysiological mechanisms underlying the seasonal dynamic and epidemic occurrence of bacterial meningitis in the African meningitis belt remain unknown. Regular seasonality (seasonal hyperendemicity) is observed for both meningococcal and pneumococcal meningitis and understanding this is critical for better prevention and modelling. The two principal hypotheses for hyperendemicity during the dry season imply (1) an increased risk of invasive disease given asymptomatic carriage of meningococci and pneumococci; or (2) an increased transmission of these bacteria from carriers and ill individuals. In this study, we formulated three compartmental deterministic models of seasonal hyperendemicity, featuring one (model1-'inv' or model2-'transm'), or a combination (model3-'inv-transm') of the two hypotheses. We parameterised the models based on current knowledge on meningococcal and pneumococcal biology and pathophysiology. We compared the three models' performance in reproducing weekly incidences of suspected cases of acute bacterial meningitis reported by health centres in Burkina Faso during 2004-2010, through the meningitis surveillance system. The three models performed well (coefficient of determination R2, 0.72, 0.86 and 0.87, respectively). Model2-'transm' and model3-'inv-transm' better captured the amplitude of the seasonal incidence. However, model2-'transm' required a higher constant invasion rate for a similar average baseline transmission rate. The results suggest that a combination of seasonal changes of the risk of invasive disease and carriage transmission is involved in the hyperendemic seasonality of bacterial meningitis in the African meningitis belt. Consequently, both interventions reducing the risk of nasopharyngeal invasion and the bacteria transmission, especially during the dry season are believed to be needed to limit the recurrent seasonality of bacterial meningitis in the meningitis belt.