Inference, prediction and optimization of non-pharmaceutical interventions using compartment models: the PyRoss library

Adhikari, R.; Bolitho, Austen; Caballero, Fernando; Cates, Michael E.; Doležal, Jaromír; Ekeh, Timothy; Guioth, Jules; Jack, Robert L.; Kappler, Julian; Kikuchi, Lukas; Kobayashi, Hideki; Li, Yuting I.; Peterson, Joseph D.; Pietzonka, Patrick; Remez, Benjamin; Rohrbach, Paul; Singh, Rajesh; Turk, Günther

doi:10.48550/arxiv.2005.09625

Cited by 6 publications

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“…With a description of fluctuations around a model in hand, one only needs a description of the way chosen data relates to the realization of the model, to be able to go on to construct a likelihood function for the estimation of model parameters and for model comparisons (see also [7]). Such data might consist of test results, hospitalization and death numbers at various times, with parameters (that could be sampled over and solved for) determining their relation to the underlying epidemic accounting for time delays, incompleteness and so on.…”

Section: Discussionmentioning

confidence: 99%

“…[3,4,5,6]. The work of [7] also discusses fluctuations around SIR-type models, from an alternative viewpoint, and provides references to the literature on infectious disease modelling and inference.…”

Section: Introductionmentioning

confidence: 99%

“…Section (6) presents a comparison of these results with numerical simulations, and a discussion and conclusions are given in Sec. (7).…”

Section: Introductionmentioning

confidence: 99%

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Path Integral Approach to Uncertainties in SIR-type Systems

Gratton¹

2020

Preprint

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In this paper I show how path integral techniques can be used to put measures on histories in "susceptible-infectious-recovered" (SIR)-type systems. The standard SIR solution emerges as the classical saddle point of the action describing the measure. One can then expand perturbatively around the background solution, and this paper goes on to work out the covariance of fluctuations around the background solution. Using a Green's function type approach, one simply needs to solve additional ordinary differential equations; an explicit matrix inversion is not required. The computed covariance matrix should be useful in the construction of fast likelihoods for fitting the parameters of SIR-type models to data. A comparison of the predictions of the approach to an ensemble of simulations is presented.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Path Integral Approach to Uncertainties in SIR-type Systems

Gratton¹

2020

Preprint

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“…The model describes the dynamics of N agents moving randomly in continuous space in a box of size L×L with periodic boundary conditions. The agents represent groups of individuals and have an internal state variable, which is inspired by the SIR model [35][36][37] and its variants [38][39][40][41][42]. We use colors (see legend in Fig.…”

Section: Modelmentioning

confidence: 99%

Strategic Spatiotemporal Vaccine Distribution Increases the Survival Rate in an Infectious Disease like Covid-19

Grauer¹,

Löwen²,

Liebchen³

2020

Preprint

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Covid-19 has caused hundred of thousands of deaths and an economic damage amounting to trillions of dollars, creating a desire for the rapid development of vaccine. Once available, vaccine is gradually produced, evoking the question on how to distribute it best. While official vaccination guidelines largely focus on the question to whom vaccines should be provided first (e.g. to risk groups), here we propose a strategy for their distribution in time and space, which sequentially prioritizes regions with a high local infection growth rate. To demonstrate this strategy, we develop a simple statistical model describing the time-evolution of infection patterns and their response to vaccination, for infectious diseases like Covid-19. For inhomogeneous infection patterns, locally well-mixed populations and basic reproduction numbers R0 ∼ 1.5 − 4 the proposed strategy at least halves the number of deaths in our simulations compared to the standard practice of distributing vaccines proportionally to the population density. For R0 ∼ 1 we still find a significant increase of the survival rate. The proposed vaccine distribution strategy can be further tested in detailed modelling works and could excite discussions on the importance of the spatiotemporal distribution of vaccines for official guidelines.

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“…The advantages of a TSI model for disease dynamics do not eliminate the need to resolve discrete compartments. For example, in modeling the transmission of SARS-CoV-2, in addition to knowing the total number of infected at any point in time, one must also make predictions for the total number of hospitalizations if there is a risk that the healthcare system might become overwhelmed [13,15]. In this report, we present a very simple and flexible strategy for decoupling the residence time distributions at each stage from the overall dynamics for transmission.…”

Section: Background and Introductionmentioning

confidence: 99%

Efficient and flexible methods for time since infection models

Peterson,

Adhikari

2020

Preprint

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Epidemic models are useful tools in the fight against infectious diseases, as they allow policy makers to test and compare various strategies to limit disease transmission while mitigating collateral damage on the economy. Epidemic models that are more faithful to the microscopic details of disease transmission can offer more reliable projections, which in turn can lead to more reliable control strategies. For example, many epidemic models describe disease progression via a series of artificial 'stages' or 'compartments' (e.g. exposed, activated, infectious, etc.) but an epidemic model that explicitly tracks time since infection (TSI) can provide a more precise description. At present, epidemic models with 'compartments' are more common than TSI models , largely due to higher computational cost and complexity typically associated with TSI models. Here, however, we show that with the right discretization scheme a TSI model is not much more difficult to solve than a comparment model with three or four 'stages' for the infected class. We also provide a new perspective for adding 'stages' to a TSI model in a way that decouples the disease transmission dynamics from the residence time distributions at each stage. These results are also generalized for age-structured TSI models in an appendix. Finally, as proof-of-principle for the efficiency of the proposed numerical methods, we provide calculations for optimal epidemic control by nonpharmaceutical intervention. Many of the tools described in this report are available through the software package 'pyross'

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Inference, prediction and optimization of non-pharmaceutical interventions using compartment models: the PyRoss library

Cited by 6 publications

References 0 publications

Path Integral Approach to Uncertainties in SIR-type Systems

Path Integral Approach to Uncertainties in SIR-type Systems

Strategic Spatiotemporal Vaccine Distribution Increases the Survival Rate in an Infectious Disease like Covid-19

Efficient and flexible methods for time since infection models

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