In the past few years, approaches such as physics informed neural networks (PINNs) have been applied to a variety of applications that can be modeled by linear and nonlinear ordinary and partial differential equations. Specifically, this work builds on the application of PINNs to a SIRD (susceptible, infectious, recovered, and dead) compartmental model and enhances it to build new mathematicalmodels that incorporate transportation between populations and their impact on the dynamics of infectious diseases. Our work employs neural networks capable of learning how diseases spread, forecasting their progression, and finding their unique parameters. We show how these approaches are capable of predicting the behavior of a disease described by governing differential equations that include parameters and variables associated with the movement of the population between neighboring cities. We show that our model validates real data and also how such PINNs based methodspredict optimal parameters for given datasets.
Accurate numerical and physical models play an important role in modeling the spread of infectious disease as well as informing policy decisions. Vaccination programs rely on the estimation of disease parameters from limited, error-prone reported data. Using physics-informed neural networks (PINNs) as universal function approximators of the susceptible-infected-recovered (SIR) compartmentalized differential equation model, we create a data-driven framework that uses reported data to estimate disease spread and approximate corresponding disease parameters. We apply this to datafrom a London boarding school, demonstrating the framework's ability to produce accurate disease and parameter estimations despite noisy data. However, real-world populations contain sub-populations, each exhibiting different levels of risk and activity. Thus, we expand our framework to model meta-populations of preferentially-mixed subgroups with various contact rates, introducing a new substitution to decrease the number of parameters. Optimal parameters are estimated throughPINNs which are then used in a negative gradient approach to calculate an optimal vaccine distribution plan for informed policy decisions. We also manipulate a new hyperparameter in the loss function of the PINNs network to expedite training. Together, our work creates a data-driven tool for future infectious disease vaccination efforts in heterogeneously mixed populations.
more » « less- Award ID(s):
- 2230117
- NSF-PAR ID:
- 10535752
- Publisher / Repository:
- Begell House
- Date Published:
- Journal Name:
- Journal of Machine Learning for Modeling and Computing
- Volume:
- 4
- Issue:
- 3
- ISSN:
- 2689-3967
- Page Range / eLocation ID:
- 83 to 99
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
more » « less
-
Abstract In this work, the dynamics of the spread of COVID-19 is considered in the presence of both human-to-human transmission as well as environment-to-human transmission. Specifically, we expand and modify traditional epidemiological model for COVID-19 by incorporating a compartment to study the dynamics of pathogen concentration in the environmental reservoir, for instance concentration of droplets in closed spaces. We perform a mathematical analysis for the model proposed including an endemic equilibrium analysis as well as a next-generation approach both of which help to derive the basic reproduction number. We also study the e˚cacy of wearing a facemask through this model. Another important contribution of this work is the introduction to physics informed deep learning methods (PINNs) to study the dynamics. We propose this as an alternative to traditional numerical methods for solving system of differential equations used to describe dynamics of infectious diseases. Our results show that the proposed PINNs approach is a reliable candidate for both solving such systems and for helping identify important parameters that control the disease dynamics.more » « less
-
During large scale outbreaks of infectious diseases, it is imperative that media report about the potential risks. Because media reporting plays a vital role in disseminating crucial information about diseases and its associated risk, understanding how media reports could influence individuals’ behavior and its potential impact on disease transmission dynamics is important. A mathematical model within an optimal control framework of a generic disease, accounting for treatment and media reporting of disease-induced deaths is formulated. Due to the complexity of choosing the best media function, our goal is to attempt to address the following research question: what is the effect of the media-induced functional response on mitigating the spread of the disease? Connecting the functional forms to the control problem is an approach that is not very developed in the literature. Thus, this study analyses the effect of different incidence functions on disease transmission, and the qualitative nature of epidemic dynamics by carrying out optimal control analysis using three different contact rates and a media function that is dependent on the number of deaths. Theoretical analyses show that the functional forms of the effective contact rate have no effect on initial disease transmission. Time-dependent controls for treatment and vaccination with a constant effective contact rate are incorporated to determine optimal control strategies. Numerical simulations show the short-term impact of media coverage on mitigating the spread of the disease, and it is observed that with three incidence functions used, the qualitative nature of the controls remains the same. The effective contact rates are graphically shown to have a population-level effect on the disease dynamics as the number of treated and recovered individuals could be significantly different. Finally, it is shown that treatment of infectives should be at its maximum rate for a longer period compared to vaccination, while concurrent implementation of vaccination and treatment is more impactful in mitigating the spread of the disease. Thus, it is imperative that media reports and health policy decision making on infectious diseases are contextualized.more » « less
-
more » « less
Summary A key component in controlling the spread of an epidemic is deciding where, when and to whom to apply an intervention. We develop a framework for using data to inform these decisions in realtime. We formalize a treatment allocation strategy as a sequence of functions, one per treatment period, that map up-to-date information on the spread of an infectious disease to a subset of locations where treatment should be allocated. An optimal allocation strategy optimizes some cumulative outcome, e.g. the number of uninfected locations, the geographic footprint of the disease or the cost of the epidemic. Estimation of an optimal allocation strategy for an emerging infectious disease is challenging because spatial proximity induces interference between locations, the number of possible allocations is exponential in the number of locations, and because disease dynamics and intervention effectiveness are unknown at outbreak. We derive a Bayesian on-line estimator of the optimal allocation strategy that combines simulation–optimization with Thompson sampling. The estimator proposed performs favourably in simulation experiments. This work is motivated by and illustrated using data on the spread of white nose syndrome, which is a highly fatal infectious disease devastating bat populations in North America.
-
more » « less
Summary Malaria is an infectious disease affecting a large population across the world, and interventions need to be efficiently applied to reduce the burden of malaria. We develop a framework to help policy-makers decide how to allocate limited resources in realtime for malaria control. We formalize a policy for the resource allocation as a sequence of decisions, one per intervention decision, that map up-to-date disease related information to a resource allocation. An optimal policy must control the spread of the disease while being interpretable and viewed as equitable to stakeholders. We construct an interpretable class of resource allocation policies that can accommodate allocation of resources residing in a continuous domain and combine a hierarchical Bayesian spatiotemporal model for disease transmission with a policy-search algorithm to estimate an optimal policy for resource allocation within the pre-specified class. The estimated optimal policy under the proposed framework improves the cumulative long-term outcome compared with naive approaches in both simulation experiments and application to malaria interventions in the Democratic Republic of the Congo.
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1615/JMachLearnModelComput.2023047642
