Title: A probabilistic infection model for efficient trace-prediction of disease outbreaks in contact networks
We propose a novel method which we call the Probabilistic Infection Model (PIM). Instead of stochastically assigning exactly one state to each agent at a time, PIM tracks the likelihood of each agent being in a particular state. Thus, a particular agent can exist in multiple disease states concurrently. Our model gives an improved resolution of transitions between states, and allows for a more comprehensive view of outbreak dynamics at the individual level. Moreover, by using a probabilistic approach, our model gives a representative understanding of the overall trajectories of simulated outbreaks without the need for numerous (order of hundreds) of repeated Monte Carlo simulations.
We simulate our model over a contact network constructed using registration data of university students. We model three diseases; measles and two strains of influenza. We compare the results obtained by PIM with those obtained by simulating stochastic SEIR models over the same the contact network. The results demonstrate that the PIM can successfully replicate the averaged results from numerous simulations of a stochastic model in a single deterministic simulation.
Keywords: Computational epidemics, Outbreak simulation, SEIR model more »« less
Getz, Wayne M.; Salter, Richard; Vissat, Ludovica Luisa(
, BMC Medical Education)
AbstractBackground
An understanding of epidemiological dynamics, once confined to mathematical epidemiologists and applied mathematicians, can be disseminated to a non-mathematical community of health care professionals and applied biologists through simple-to-use simulation applications. We used Numerus Model Builder RAMPⓇ(Runtime Alterable Model Platform) technology, to construct deterministic and stochastic versions of compartmental SIR (Susceptible, Infectious, Recovered with immunity) models as simple-to-use, freely available, epidemic simulation application programs.
Results
We take the reader through simulations used to demonstrate the following concepts: 1) disease prevalence curves of unmitigated outbreaks have a single peak and result in epidemics that ‘burn’ through the population to become extinguished when the proportion of the susceptible population drops below a critical level; 2) if immunity in recovered individuals wanes sufficiently fast then the disease persists indefinitely as an endemic state, with possible dampening oscillations following the initial outbreak phase; 3) the steepness and initial peak of the prevalence curve are influenced by the basic reproductive valueR0, which must exceed 1 for an epidemic to occur; 4) the probability that a single infectious individual in a closed population (i.e. no migration) gives rise to an epidemic increases with the value ofR0>1; 5) behavior that adaptively decreases the contact rate among individuals with increasing prevalence has major effects on the prevalence curve including dramatic flattening of the prevalence curve along with the generation of multiple prevalence peaks; 6) the impacts of treatment are complicated to model because they effect multiple processes including transmission, recovery and mortality; 7) the impacts of vaccination policies, constrained by a fixed number of vaccination regimens and by the rate and timing of delivery, are crucially important to maximizing the ability of vaccination programs to reduce mortality.
Conclusion
Our presentation makes transparent the key assumptions underlying SIR epidemic models. Our RAMP simulators are meant to augment rather than replace classroom material when teaching epidemiological dynamics. They are sufficiently versatile to be used by students to address a range of research questions for term papers and even dissertations.
Evensen, Geir; Amezcua, Javier; Bocquet, Marc; Carrassi, Alberto; Farchi, Alban; Fowler, Alison; Houtekamer, Pieter L.; Jones, Christopher K.; de Moraes, Rafael J.; Pulido, Manuel; et al(
, Foundations of Data Science)
This work demonstrates the efficiency of using iterative ensemble smoothers to estimate the parameters of an SEIR model. We have extended a standard SEIR model with age-classes and compartments of sick, hospitalized, and dead. The data conditioned on are the daily numbers of accumulated deaths and the number of hospitalized. Also, it is possible to condition the model on the number of cases obtained from testing. We start from a wide prior distribution for the model parameters; then, the ensemble conditioning leads to a posterior ensemble of estimated parameters yielding model predictions in close agreement with the observations. The updated ensemble of model simulations has predictive capabilities and include uncertainty estimates. In particular, we estimate the effective reproductive number as a function of time, and we can assess the impact of different intervention measures. By starting from the updated set of model parameters, we can make accurate short-term predictions of the epidemic development assuming knowledge of the future effective reproductive number. Also, the model system allows for the computation of long-term scenarios of the epidemic under different assumptions. We have applied the model system on data sets from several countries, i.e., the four European countries Norway, England, The Netherlands, and France; the province of Quebec in Canada; the South American countries Argentina and Brazil; and the four US states Alabama, North Carolina, California, and New York. These countries and states all have vastly different developments of the epidemic, and we could accurately model the SARS-CoV-2 outbreak in all of them. We realize that more complex models, e.g., with regional compartments, may be desirable, and we suggest that the approach used here should be applicable also for these models.
Zhou, Di; Whitmore, Michael P.; Griffin, Kevin P.; Bae, Hyunji Jane(
, American Institute of Aeronautics and Astronautics)
We develop a wall model for large-eddy simulation (LES) that takes into account various pressure-gradient effects using multi-agent reinforcement learning. The model is trained using low-Reynolds-number flow over periodic hills with agents distributed on the wall at various computational grid points. It utilizes a wall eddy-viscosity formulation as the boundary condition to apply the modeled wall shear stress. Each agent receives states based on local instantaneous flow quantities at an off-wall location, computes a reward based on the estimated wall-shear stress, and provides an action to update the wall eddy viscosity at each time step. The trained wall model is validated in wall-modeled LES of flow over periodic hills at higher Reynolds numbers, and the results show the effectiveness of the model on flow with pressure gradients. The analysis of the trained model indicates that the model is capable of distinguishing between the various pressure gradient regimes present in the flow. To further assess the robustness of the developed wall model, simulations of flow over the Boeing Gaussian bump are conducted at a Reynolds number of 2 million, based on the free-stream velocity and the bump width. The results of mean skin friction and pressure on the bump surface, as well as the velocity statistics of the flow field, are compared to those obtained from equilibrium wall model (EQWM) simulations and published experimental data sets. The developed wall model is found to successfully capture the acceleration and deceleration of the turbulent boundary layer on the bump surface, providing better predictions of skin friction near the bump peak and exhibiting comparable performance to the EQWM with respect to the wall pressure and velocity field. We also conclude that the subgrid-scale model is crucial to the accurate prediction of the flow field, in particular the prediction of separation.
Cross-linked actin networks are the primary component of the cell cytoskeleton and have been the subject of numerous experimental and modeling studies. While these studies have demonstrated that the networks are viscoelastic materials, evolving from elastic solids on short timescales to viscous fluids on long ones, questions remain about the duration of each asymptotic regime, the role of the surrounding fluid, and the behavior of the networks on intermediate timescales. Here we perform detailed simulations of passively cross-linked non-Brownian actin networks to quantify the principal timescales involved in the elastoviscous behavior, study the role of nonlocal hydrodynamic interactions, and parameterize continuum models from discrete stochastic simulations. To do this, we extend our recent computational framework for semiflexible filament suspensions, which is based on nonlocal slender body theory, to actin networks with dynamic cross linkers and finite filament lifetime. We introduce a model where the cross linkers are elastic springs with sticky ends stochastically binding to and unbinding from the elastic filaments, which randomly turn over at a characteristic rate. We show that, depending on the parameters, the network evolves to a steady state morphology that is either an isotropic actin mesh or a mesh with embedded actin bundles. For different degrees of bundling, we numerically apply small-amplitude oscillatory shear deformation to extract three timescales from networks of hundreds of filaments and cross linkers. We analyze the dependence of these timescales, which range from the order of hundredths of a second to the actin turnover time of several seconds, on the dynamic nature of the links, solvent viscosity, and filament bending stiffness. We show that the network is mostly elastic on the short time scale, with the elasticity coming mainly from the cross links, and viscous on the long time scale, with the effective viscosity originating primarily from stretching and breaking of the cross links. We show that the influence of nonlocal hydrodynamic interactions depends on the network morphology: for homogeneous meshworks, nonlocal hydrodynamics gives only a small correction to the viscous behavior, but for bundled networks it both hinders the formation of bundles and significantly lowers the resistance to shear once bundles are formed. We use our results to construct three-timescale generalized Maxwell models of the networks.
Fintzi, Jonathan; Wakefield, Jon; Minin, Vladimir N.(
, Biometrics)
Abstract
Stochastic epidemic models (SEMs) fit to incidence data are critical to elucidating outbreak dynamics, shaping response strategies, and preparing for future epidemics. SEMs typically represent counts of individuals in discrete infection states using Markov jump processes (MJPs), but are computationally challenging as imperfect surveillance, lack of subject‐level information, and temporal coarseness of the data obscure the true epidemic. Analytic integration over the latent epidemic process is impossible, and integration via Markov chain Monte Carlo (MCMC) is cumbersome due to the dimensionality and discreteness of the latent state space. Simulation‐based computational approaches can address the intractability of the MJP likelihood, but are numerically fragile and prohibitively expensive for complex models. A linear noise approximation (LNA) that approximates the MJP transition density with a Gaussian density has been explored for analyzing prevalence data in large‐population settings, but requires modification for analyzing incidence counts without assuming that the data are normally distributed. We demonstrate how to reparameterize SEMs to appropriately analyze incidence data, and fold the LNA into a data augmentation MCMC framework that outperforms deterministic methods, statistically, and simulation‐based methods, computationally. Our framework is computationally robust when the model dynamics are complex and applies to a broad class of SEMs. We evaluate our method in simulations that reflect Ebola, influenza, and SARS‐CoV‐2 dynamics, and apply our method to national surveillance counts from the 2013–2015 West Africa Ebola outbreak.
Qian, W., Bhowmick, S., O’Neill, M., Ramisetty-Mikler, S., and Mikler, A. R. A probabilistic infection model for efficient trace-prediction of disease outbreaks in contact networks. Retrieved from https://par.nsf.gov/biblio/10187220. International Conference on Computational Science ICCS2020 . Web. doi:10.1007/978-3-030-50371-0_50.
Qian, W., Bhowmick, S., O’Neill, M., Ramisetty-Mikler, S., & Mikler, A. R. A probabilistic infection model for efficient trace-prediction of disease outbreaks in contact networks. International Conference on Computational Science ICCS2020, (). Retrieved from https://par.nsf.gov/biblio/10187220. https://doi.org/10.1007/978-3-030-50371-0_50
Qian, W., Bhowmick, S., O’Neill, M., Ramisetty-Mikler, S., and Mikler, A. R.
"A probabilistic infection model for efficient trace-prediction of disease outbreaks in contact networks". International Conference on Computational Science ICCS2020 (). Country unknown/Code not available. https://doi.org/10.1007/978-3-030-50371-0_50.https://par.nsf.gov/biblio/10187220.
@article{osti_10187220,
place = {Country unknown/Code not available},
title = {A probabilistic infection model for efficient trace-prediction of disease outbreaks in contact networks},
url = {https://par.nsf.gov/biblio/10187220},
DOI = {10.1007/978-3-030-50371-0_50},
abstractNote = {We propose a novel method which we call the Probabilistic Infection Model (PIM). Instead of stochastically assigning exactly one state to each agent at a time, PIM tracks the likelihood of each agent being in a particular state. Thus, a particular agent can exist in multiple disease states concurrently. Our model gives an improved resolution of transitions between states, and allows for a more comprehensive view of outbreak dynamics at the individual level. Moreover, by using a probabilistic approach, our model gives a representative understanding of the overall trajectories of simulated outbreaks without the need for numerous (order of hundreds) of repeated Monte Carlo simulations. We simulate our model over a contact network constructed using registration data of university students. We model three diseases; measles and two strains of influenza. We compare the results obtained by PIM with those obtained by simulating stochastic SEIR models over the same the contact network. The results demonstrate that the PIM can successfully replicate the averaged results from numerous simulations of a stochastic model in a single deterministic simulation. Keywords: Computational epidemics, Outbreak simulation, SEIR model},
journal = {International Conference on Computational Science ICCS2020},
author = {Qian, W. and Bhowmick, S. and O’Neill, M. and Ramisetty-Mikler, S. and Mikler, A. R.},
}
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