Forecasting Virus Outbreaks With Social Media Data Via Neural Ordinary Differential Equations

ODEs

mathematics

forecasting

infectious disease modeling

epidemiology

Notes for the 2023 paper Forecasting Virus Outbreaks With Social Media Data Via Neural Ordinary Differential Equations by Nunez.

Published

January 1, 2025

Modified

June 14, 2026

[A] PAPER for Nunez_FVOWSMDVNODE_2023.

1 Abstract

[R] Claims: social media data as early predictor of epidemic waves (1); online polls can be used as predictor (2); neural ODE can capture the dynamics and estimate new infections well (3); consequences of change in infections can be predicted with neural ODEs (4).

[T] Define COVID-19, neural ODE, social media, forecast, prediction, …

2 Introduction

[R] Pandemic → parameter estimates, not the other way around.

[R] That is a nice quote that was included.

[>] “You tell me what numbers to put in my equations, and I’ll give you the answer …But you can’t tell me the numbers, because nobody knows them…”

[Q] How is forecasting vital for health during epidemics and pandemics?

[Q] What health surveillance systems have been established across the globe?

[Q] What are example information sources in health surveillance?

[T] Add the other two entries from PAPER pg. 1

[T] Define weight adjustment and sample bias.

[R] What I am getting is that digital surveillance (old) and “late indicators” together as predictors outperform either predictor alone.

[T] Add Mermaid model for part with “M” on pg. 2. This describes the data available.

[T] Describe the tasks with “T” as a Mermaid model as well.

[T] Describe parts in [ ] using mathematics. What is “this object”?

[Q] How do “these phase space methods” (why is it called this) allow “the prediction of potential future … region.”

3 COVID-19 Symptom Survey Through Facebook

[Q] What are ll the numerical indicators?

[R] The most meaningful part here is (1) how do the sruvey responses yield the numerical indicators and (2) what are the numerical indicators? (pg. 2)

[R] From Facebook (with public health officials) as the data providers. (pg. 2)

[Q] Why is this study a “non-formal” investigation of the indicators’ recall? (pg. 3)

4 Models: First Principls And Data Driven

[R] Need a model that “relates the rate of variation if the different indicators to the model’s state variables” and “relates the new cases as a function of the different signals extracted from the surveys.”

[R] Claim is need a data drive over parameter driven model?

[R] For a region, $\vec{y}(t)$ is a vector of indicators (and new cases); the model is a “function that approximates the vector’s temporal resolution”.

[Q] “Nowt clear how to characterize the link between them from first principles.” How much though went into this? “…absence of known functional form that links the variables.”

[R] Rate of variation in indicators / variables as $\frac{\triangle \vec{y}}{\triangle t}$ with sufficiently small $\triangle t$ as $\frac{d \vec{y}}{d t}$.

[T] Define parameterized function, NN, …

[Q] What other parametric / non-parametric options exist for the task, why a neural ODE?

[R] $\frac{d \vec{y}}{d t}= NN(\vec{y}, t, \theta)$ with $\theta$ as the weights; also, this depends on $t$; the forward pass solves the initial value problem, i.e. gets the value of $\vec{y}(t_0)$.

[R] So neural-ODEs are time continuous so non-uniform data and predictors are available (unlike RNNs and LSTMs).

[T] Claude to use forecasttools or forecasttools-py (first with adding data access options) to get the data then set up MLflow comparison for neural ODEs with LSTMs and RNNs.

--- title: Forecasting Virus Outbreaks With Social Media Data Via Neural Ordinary Differential Equations description: "Notes for the 2023 paper _Forecasting Virus Outbreaks With Social Media Data Via Neural Ordinary Differential Equations_ by Nunez." categories: ["ODEs", "mathematics", "forecasting", "infectious disease modeling", "epidemiology"] date: "2025-01-01" date-modified: "2026-06-14" slug: "Nunez_FVOWSMDVNODE_2023" --- [A] PAPER for Nunez_FVOWSMDVNODE_2023. ## Abstract [R] Claims: social media data as early predictor of epidemic waves (1); online polls can be used as predictor (2); neural ODE can capture the dynamics and estimate new infections well (3); consequences of change in infections can be predicted with neural ODEs (4). [T] Define COVID-19, neural ODE, social media, forecast, prediction, ... ## Introduction [R] Pandemic → parameter estimates, not the other way around. [R] That is a nice quote that was included. [>] "You tell me what numbers to put in my equations, and I’ll give you the answer ...But you can’t tell me the numbers, because nobody knows them..." [Q] How is forecasting vital for health during epidemics and pandemics? [Q] What health surveillance systems have been established across the globe? [Q] What are example information sources in health surveillance? [T] Add the other two entries from PAPER pg. 1 [T] Define weight adjustment and sample bias. [R] What I am getting is that digital surveillance (old) and "late indicators" together as predictors outperform either predictor alone. [T] Add Mermaid model for part with "M" on pg. 2. This describes the data available. [T] Describe the tasks with "T" as a Mermaid model as well. [T] Describe parts in [ ] using mathematics. What is "this object"? [Q] How do "these phase space methods" (why is it called this) allow "the prediction of potential future ... region." ## COVID-19 Symptom Survey Through Facebook [Q] What are ll the numerical indicators? [R] The most meaningful part here is (1) how do the sruvey responses yield the numerical indicators and (2) what are the numerical indicators? (pg. 2) [R] From Facebook (with public health officials) as the data providers. (pg. 2) [Q] Why is this study a "non-formal" investigation of the indicators' recall? (pg. 3) ## Models: First Principls And Data Driven [R] Need a model that "relates the rate of variation if the different indicators to the model's state variables" and "relates the new cases as a function of the different signals extracted from the surveys." [R] Claim is need a data drive over parameter driven model? [R] For a region, $\vec{y}(t)$ is a vector of indicators (and new cases); the model is a "function that approximates the vector's temporal resolution". [Q] "Nowt clear how to characterize the link between them from first principles." How much though went into this? "...absence of known functional form that links the variables." [R] Rate of variation in indicators / variables as $\frac{\triangle \vec{y}}{\triangle t}$ with sufficiently small $\triangle t$ as $\frac{d \vec{y}}{d t}$. [T] Define parameterized function, NN, ... [Q] What other parametric / non-parametric options exist for the task, why a neural ODE? [R] $\frac{d \vec{y}}{d t}= NN(\vec{y}, t, \theta)$ with $\theta$ as the weights; also, this depends on $t$; the forward pass solves the initial value problem, i.e. gets the value of $\vec{y}(t_0)$. [R] So neural-ODEs are time continuous so non-uniform data and predictors are available (unlike RNNs and LSTMs). [T] Claude to use `forecasttools` or `forecasttools-py` (first with adding data access options) to get the data then set up MLflow comparison for neural ODEs with LSTMs and RNNs.