index – Disease modeling for public health

Your epidemic model API is live. Without authentication, anyone who discovers the URL can call /simulate without limit, read your clients’ outbreak data, and flood the…

Securing Your API with JWT Authentication and Role-Based Access

business skills

security

authentication

JWT

FastAPI

You sign a contract with a health department for $2,000/month. A year in, you realise one client is running 5× more EnKF jobs than any other — and consuming 60% of your…

Usage-Based Billing: Metering API Calls and Compute

business skills

billing

pricing

Stripe

SaaS

An analyst opens your dashboard and selects “Run scenario: 30% transmission reduction for district_a”. Your system runs the surrogate model, queries TimescaleDB, formats the…

Caching Surrogate Model Outputs for Sub-Second API Responses

business skills

caching

Redis

performance

A client’s health department runs your epidemic model every morning to inform a 9 AM briefing. On Tuesday, a routine parameter update silently changes the outbreak peak by…

Automated Testing and CI/CD Pipelines for Epidemic Models

business skills

CI/CD

testing

GitHub Actions

The Health Insurance Portability and Accountability Act (1) governs Protected Health Information (PHI) in the United States. If your digital twin processes surveillance data…

HIPAA-Aware Architecture Patterns for Health Data on AWS

business skills

HIPAA

compliance

AWS

security

health data

A real-time epidemic digital twin ingests from multiple sources simultaneously:

A Lightweight Data Lake for Epidemic Surveillance Ingestion

business skills

data engineering

Parquet

DuckDB

Arrow

The EnKF from Post 4 receives daily case counts and updates its state estimate. What happens when the surveillance system sends a negative count (database export error), a…

Data Validation: Catching Bad Surveillance Data Before It Corrupts Your Model

business skills

data validation

data quality

surveillance

Your digital twin has been running in production for two months. You want to add a severity_level column to the model_states table — a field that did not exist when the…

Database Schema Migrations for Production TimescaleDB

business skills

database

migrations

Alembic

PostgreSQL

DevOps

A client health department’s jurisdiction contains 20 districts. Two are doing fine; three are accelerating rapidly; one has already peaked. A single aggregate model hides…

Spatial Epidemiology: Mapping Disease Burden and Transmission Corridors

business skills

spatial epidemiology

GIS

mapping

You spend two days clicking through the AWS console to configure an EC2 instance, install Docker, set up TimescaleDB, and configure the load balancer. It works perfectly.…

Infrastructure as Code: Reproducible AWS Environments with Terraform

business skills

infrastructure as code

Terraform

AWS

DevOps

Mechanistic SEIR models are powerful at long horizons (4–12 weeks) because they encode biological constraints: the epidemic cannot grow faster than $R_0$ allows, and it…

Hybrid Forecasting: Combining Mechanistic Models with Machine Learning

business skills

forecasting

machine learning

ensemble

Your EnKF runner is scheduled for 2 AM. At 6 AM your client’s epidemiologist logs in and the dashboard shows stale data. Was it a database connection failure? A malformed…

Observability for Digital Twin Services: Logging, Metrics, and Alerting

business skills

monitoring

logging

observability

operations

Your first client is running on a dedicated instance — one database, one API container. You sign a second client. Do you:

Multi-Tenant Architecture: Serving Multiple Health Departments on One Platform

business skills

multi-tenancy

database

architecture

software engineering

An analyst submits a request to run a 500-particle EnKF over 90 days with 50 scenario iterations. Your FastAPI handler calls the R model and waits. After 90 seconds, the…

Async Task Queues for Long-Running Simulation Jobs

business skills

task queue

async

Celery

software engineering

Every Monday morning, your client’s epidemiologist needs a briefing document: current outbreak status, 14-day forecast, and comparison to last week. You could spend 90…

Automated Parameterized Reports for Epidemic Scenario Outputs

business skills

reporting

Quarto

R Markdown

automation

Your FastAPI service works. A district epidemiologist wants to use it from their weekly R script. Without an SDK they write:

Publishing an R Client SDK for Your Digital Twin API

business skills

R package

SDK

httr2

API client

A developer pushes a database connection string to a public GitHub repository by accident. Within 15 minutes, a bot discovers it and begins exfiltrating patient data. This…

Secrets Management: Keeping Credentials Out of Your Code

business skills

security

secrets management

AWS

DevOps

A health department client asks: “You say $R_0 = 1.8$, but how sensitive is your 14-day forecast to that estimate? What if it’s actually 2.2?” Without sensitivity analysis…

Global Sensitivity Analysis as a Billable Model Audit Service

business skills

sensitivity analysis

Sobol

epidemic modeling

A standard HTTP request has a request–response cycle: client asks, server computes, server replies. If the computation takes 30 seconds, the client waits with a blank…

Real-Time Simulation Progress Streaming with WebSockets

business skills

WebSockets

real-time

FastAPI

API

“Attention Is All You Need” by Vaswani et al. (1) is likely the most cited paper in the field of deep learning. It introduced the transformer architecture, which rendered…

Self-Attention and Transformers: The Architecture Behind LLMs

machine learning

transformers

attention

deep learning

Every machine learning algorithm — from linear regression to GPT-4 — is doing the same thing: finding parameter values that minimize a loss function. The loss measures how…

9 min

Gradient Descent: The Optimization Engine Behind Every ML Model

machine learning

optimization

epidemic modeling

Your digital twin produces R-effective estimates, 30-day case forecasts, and intervention scenarios — but the output is a dataframe. The epidemiologist at a health…

Using LLMs in Production: Automated Epidemic Intelligence Reports

machine learning

LLM

prompt engineering

API

public health

Neural networks are the backbone of modern ML — image classifiers, language models, and surrogate epidemic simulators all use the same underlying mechanism. Most tutorials…

Neural Networks from Scratch: Build and Train One in Pure R

machine learning

neural networks

deep learning

Epidemic risk scoring — flagging districts that are likely to see an outbreak — is a classification problem on tabular data: vaccination coverage, population density, age…

Random Forests: Ensemble Learning for Outbreak Risk Scoring

machine learning

random forests

ensemble methods

public health

The previous posts in this series trained a network to map time directly to compartment values, penalising ODE violations through the physics loss. There is a fundamentally…

Neural ODEs and Universal Differential Equations

PINN

Neural ODE

UDE

Python

deep learning

The Docker container from Post 3 runs on your laptop. The TimescaleDB instance from Post 6 persists data locally. Neither is accessible to a partner organisation in another…

17 min

Deploying a Digital Twin to the Cloud

digital twin

software engineering

AWS

cloud

deployment

DevOps

The digital twin stack built across Posts 1–7 now runs entirely on AWS:

Building a Real-Time Dashboard with Streamlit

digital twin

dashboard

Streamlit

Python

visualisation

After Post 4 (EnKF) and Post 5 (GP surrogate), your digital twin produces several types of time-stamped output every day:

Time-Series Data Storage with TimescaleDB

digital twin

database

TimescaleDB

PostgreSQL

data engineering

In Post 2 we built an epidemic model API. It runs on your laptop with uvicorn sir_api.main:app. To share it with a colleague you send them your code and they spend an…

Containerising Your Model Service with Docker

digital twin

software engineering

Docker

deployment

reproducibility

An epidemic model fed fixed parameters produces a single trajectory. A digital twin does something more: it continuously updates its internal state as real data arrive, so…

Real-Time State Estimation with the Ensemble Kalman Filter

digital twin

Kalman filter

data assimilation

epidemic modeling

In Post 1 we built a validated, testable SIR model function. That function can be called from R or Python by anyone who installs your package. But “install my package” is a…

Exposing Your Epidemic Model as a REST API

digital twin

software engineering

Python

FastAPI

REST API

You have built an epidemic model that works. It fits data, recovers parameters, and produces credible forecasts. You have written it carefully in R or Python, and the…

The Production Gap: From Research Code to Software Product

digital twin

software engineering

Python

reproducibility

The Ensemble Kalman Filter in Post 4 ran 300 particles through an SEIR model 90 times — around 27,000 model evaluations. For a compartmental ODE with five states, each…

Surrogate Models: Replacing Slow Simulations with Fast Emulators

digital twin

Gaussian process

surrogate model

emulator

The previous post showed that attention is a learned weighted average over a context window. That is the mechanism inside every LLM — GPT, Claude, Gemini — and it also…

Transformer-Based LLM Architectures for Epidemic Time Series Forecasting

machine learning

transformers

time series

forecasting

The SIR PINN tutorial recovered a constant transmission rate $\beta$ from noisy prevalence data. Real outbreaks are messier in two important ways.

PINNs for SEIR: Learning Time-Varying Transmission

PINN

SEIR

epidemiology

Python

deep learning

Over five technical posts we built a complete digital-twin pipeline for vaccine clinical trials:

The Business of Digital Twins in Drug Development

digital twin

vaccine

clinical trial

business

market

pharma

Post 1 built a within-host ODE model that predicts the antibody titre trajectory $\text{Ab}(t)$ for a vaccinated individual. We can run that model for any individual whose…

Correlates of Protection

digital twin

vaccine

correlate of protection

immunology

The outcome of a vaccine trial depends on processes that span at least three orders of magnitude in time and space: molecular events inside a single cell, the kinetics of an…

18 min

Multiscale Modelling for Digital Twins in Vaccine Trials

digital twin

multiscale

ODE

vaccine

infectious disease

Skeletal muscle is one of the most tractable organs for digital-twin modelling. Its adaptation to mechanical loading follows dose–response kinetics that can be written down…

Muscle Digital Twins: Science, Opportunity, and Directions

digital twin

muscle

ODE

sarcopenia

business

Clinical trials use randomisation to ensure that, on average, the treatment and placebo groups are comparable at baseline. This is a powerful guarantee: if subjects are…

Synthetic Control Arms

digital twin

vaccine

synthetic control

clinical trial

Bayesian

Trial design has always involved simulation. The classical approach uses algebraic power formulas: given assumed effect size, variance, and type I and II error rates, solve…

Adaptive Trial Design with Digital Twins

digital twin

vaccine

adaptive design

trial simulation

power analysis

Post 1 built an ODE model of vaccine-induced immunity for a single individual. Post 2 showed how to convert an antibody trajectory into a protection probability at each…

19 min

Building Virtual Patient Cohorts

digital twin

vaccine

virtual patients

Latin hypercube sampling

Sobol

quasi-Monte Carlo

The previous post introduced digital twins for clinical trials at a high level. A vaccine digital twin is, at its core, a model that takes one patient’s characteristics as…

32 min

Within-Host Dynamics of Vaccine-Induced Immunity

digital twin

vaccine

immunology

ODE

The term digital twin was coined by Michael Grieves around 2002 in a manufacturing context: a real artefact, a virtual replica that mirrors it, and a bidirectional data…

Digital Twins in Clinical Trials

digital twin

clinical trial

vaccine

infectious disease

Apr 21, 2026

In my previous post on Physics-Informed Neural Networks, the SIR residual was computed with a single line:

Understanding Automatic Differentiation

automatic differentiation

deep learning

PINN

backpropagation

Python

Apr 20, 2026

24 min

Minimax: Planning for the Worst-Case Epidemic

game theory

minimax

robust decision

vaccination

cholera

The vaccination game was a game between people. Each individual weighed the cost of vaccination against the risk of infection, and the Nash equilibrium emerged from their…

Apr 20, 2026

Part 1 of a 5-part series on game theory for theoretical epidemiologists. The goal is not a comprehensive textbook but a working vocabulary, a few canonical examples, and a…

Game Theory for Infectious Disease Modeling

game theory

vaccination

SIR

epidemiology

evolutionary games

Apr 20, 2026

Reinforcement learning (RL) addresses a deceptively simple problem: an agent interacts with an environment by selecting actions, observing the resulting state, and receiving…

Reinforcement Learning for Epidemic Control

reinforcement learning

DQN

SIR

epidemiology

Python

deep learning

Apr 14, 2026

17 min

Bayesian Physics-Informed Neural Networks

PINN

SIR

Bayesian

PyTorch

deep learning

The SIR PINN tutorial recovered point estimates of $\beta$ and $\gamma$. Here we exlore the distribution of $\beta$ consistent with these data.

Apr 11, 2026

29 min

Physics-Informed Neural Networks for Epidemic Modeling

PINN

SIR

epidemiology

Python

deep learning

The idea of using neural networks to solve differential equations predates deep learning. Lagaris et al. (1) showed in 1998 that a simple feedforward network, trained to…

Apr 9, 2026

In the previous post we saw that lag effects in daily stock returns are generally weak — a finding consistent with the efficient market hypothesis. But zoom in to 1–5 minute…

High-Frequency Lead-Lag Effects in Stock Markets

statistics

stock market

Python

cross-correlation

time series

high-frequency

Mar 15, 2026

When we study multiple stock prices together, one of the first questions is: do they move together, and if so, by how much and with what delay? Cross-correlation answers…

Cross-Correlation in Stock Market Data

statistics

stock market

Python

cross-correlation

time series

Mar 14, 2026

When a newly infected person successfully isolates, how many downstream infections does that prevent? The answer depends on the structure of transmission — not just the…

How many infections does one isolation prevent?

epidemiology

branching process

isolation

overdetermination

Mar 10, 2026

18세기 유럽은 천연두(smallpox)의 그림자 아래 살고 있었다. 이 무서운 질병은 매년 수십만 명의 목숨을 앗아갔으며, 생존자들에게는 평생 지울 수 없는 흉터를 남겼다 (Razzell, 1977). 이런 상황에서 한 수학자가 수학적 사고를 통해 이 질병에 맞서고자 했다. 그의 이름은 다니엘…

다니엘 베르누이의 천연두 연구: 최초의 감염병 수리모형

감염병

수리모형

역학

역사

May 6, 2025

수학은 세상을 설명하는 언어다. 바이러스는 숫자를 모른다. 바이러스 어떤 수식을 계산해서 다음 날 환자수를 결정하지는 않을 것이다. 그런데 우리는 바이러스의 전파 과정을 숫자로 설명한다. 왜 그럴까?

왜 수학으로 감염병을 설명하는가?

Apr 18, 2025

The mathematical modeling of infectious diseases has become an indispensable tool in modern epidemiology, guiding intervention strategies and policy decisions. While…

The Ross-Macdonald Framework: Foundational Mathematical Models in Vector-Borne Disease Epidemiology

Apr 17, 2025

10 min

The Birth of Epidemic Modeling: Daniel Bernoulli and the Smallpox Inoculation Controversy

Mathematical modeling of infectious diseases is now a cornerstone of public health decision-making. During COVID-19, we all became familiar with concepts like “flattening…

Apr 14, 2025

Regularization is a fundamental technique in statistical modeling that helps prevent overfitting and improves model generalization. This blog post explores different…

Regularization in statistical models

Feb 2, 2025

Understanding relationships between variables is a fundamental aspect of statistical analysis. Three key concepts in this domain are correlation, covariation, and least…

Understanding correlation, covariation, and least squares regression

Jan 30, 2025

When working with data from different sources or distributions, we often need to transform one distribution to match another. In this post, we’ll explore various methods for…

Distribution Matching Methods: From Theory to Practice

Oct 31, 2024

This post is my attempt to follow along a Bayesian Workflow by Gelman et al and create examples for better understanding. While my ultimate goal is to study infectious…

Bayesian workflow: fake social contact data example

Bayesian workflow

negative binomial

social contact

Jul 21, 2024

감염병의 전파 양상을 연구하는 감염병 역학 (Epidemiology of Infectious Diseases ; EID)에서는 감염병의 발생 양샹을 세 가지 요소로 해석하고자 한다. 하나는 병을 일으키는 감염원 (infectious agent)이고, 다른 하나는 사람이 살아가고 있는 주변 환경…

Modeling human behavior: Infectious disease transmission modeling perspective

Bayesian workflow

negative binomial

social contact

Jul 21, 2024

Arroyo-Marioli et al used a Kalman filter approach to estimate. I tried to reproduce in R. Let’s use a SIR model as was used in my previous post to generate growth rate time…

Kalman filter to estimate R using the FKF package

kalman filter

Jul 11, 2024

Neural networks can approximate any function according to the Universal Approximation Theorem. A more precise statement of the theorem is that neural networks with a single…

Learning ChatGPT 4: Universal Approximation Theorem

Universal Approximation Theorem

Neural network

Arbitrary-Width

Arbitrary-Depth

Jun 24, 2024

I find that parallel, doParallel and foreach packages provide the easiest approach for parallel computing in R. The doParallel vignette provides a great overview. library(doP…

Parallel simulation in R

parallelism

foreach

doParallel

Jun 14, 2024

A recent article (1) published in Mathematics discusses an approach to calculating $\mathcal{R}_0$. Since I have previously written a post about calculating \(\mathcal{R}_0…

Basic reproduction number: An algorithmic approach

Basic reproduction number

Mathematica

algorithmic approach

next generation matrix

Jun 2, 2024

Claude 3

LLM

Claude

Testing Claude 3 with R

May 30, 2024

The blog post by Stephen Wolfram discusses a neural network for approximating some sort of a step function. This post is my attempt to reproduce it. A YouTube video and a boo…

Learning ChatGPT 2: Approximating a tower function using a neural net

Neural network

Adam

matrix

May 28, 2024

I am documenting my learning of a neural network. The contents are mostly based on the e-book by Keydana (1). Neural networks have become the foundation of modern deep…

A very basic implementation of a neural network

GPT-2

ChatGPT

Wolfram

May 27, 2024

When building statistical models, one of the most critical steps is variable selection. This process involves choosing the appropriate predictors or features that will be…

Variables selection in statistical models

variable selection

generalized linear model

May 18, 2024

Inspired by the blog post by Stephen Wolfram about the workings of the GPT-2 system, I decided to learn a bit about ChatGPT myself. Luckily, GPT-2 is now available for R. My…

Learning ChatGPT 1: Probabilities for the next word

GPT-2

ChatGPT

Wolfram

May 1, 2024

The logistic function, represented as: \[ f(x) = \frac{L}{1+e^{-k(x-x_0)}} \] , where $x_{0}, L$, and $k$ represent tht value of the function’s midpoint, the supremum of…

Logistic function in R

Logistic function

indirect vaccine effectiveness

oral cholera vaccine

Apr 19, 2024

In this article, I examined the process of modifying the disease transmission model (for instance, the $SEIR$ model) to include vaccination and the waning of…

Waning vaccine efficacy on susceptibility

Vaccine

waning

SEIR

Erlang distribution

Apr 8, 2024

The $SEIR$ model structures each stage as a distinct compartment, with transitions between compartments dictated by specific rate constants, except for the transition…

SEIR model with varying number of compartments

SEIR

Erlang distribution

Apr 5, 2024

The protection derived from vaccination often wanes over time and require the second or the third doses (so-called booster doses). For example, the study showed the efficacy…

Waning of vaccine effectiveness

vaccine efficacy

clinical trial

SEIR

Apr 4, 2024

In this post, I compared the numerical solutions obtained using deSolve::ode with the algebraic solutions derived from Mathematica for the steady states of a SEIR model. The…

Solutions for the steady states of the SEIR model

SEIR model

steady states

ODE

deSolve

Mathematica

Mar 28, 2024

10 min

Vaccine effectiveness

SEIR

vaccine efficacy

direct

indirect

total

overall

Vaccine efficacy and effectiveness (VE) is generally estimated as one minus some measure of relative risk (RR) in the vaccinated group compared to the unvaccinated group Hall…

Mar 26, 2024

An article by Heesterbeek et al. (1) provides a few examples on the counterintuitive behavior of a dynamical system of disease transmission. The first example was about the…

Counterintuitive effects in disease transmission dynamics

Infectious diseases

nonlinearity

transmission dynamics

Mar 20, 2024

In the following, I implemented a simple model of disease incidence and recovery. Susceptibles are infected at a constant rate, go through the natural history of infection…

Prevalence vs. incidence for the SIR model

prevalence

incidence

deSolve

Mar 12, 2024

감염병 인류 라는 책을 재미있게 읽는 중이다. 136페이지에는 기초감염재생산지수와 대유행의 가능성에 대한 간단한 수식이 나온다. \[\text{대유행의 가능성} = 1 - \frac{1}{R_0}\]

감염병의 대유행 가능성

probability of a large outbreak

reproduction number

Mar 4, 2024

The use of ordinary differential equation (ODE) models to simulate disease spread and evaluate vaccine impact is growing. Waning of vaccine-derived immunity often follows an…

Modeling the waning of the vaccine-derived immunity in the ODE model

vaccine-derived immunity

waning

cholera

ODE

exponential

Gamma

Feb 27, 2024

10 min

Incremental Cost-Effectiveness Ratio (ICER)

cholera

sub-Saharan Africa

The Incremental Cost-Effectiveness Ratio (ICER) is a crucial metric in health economics, offering insights into the value of medical interventions by comparing their costs…

Feb 25, 2024

In the realm of infectious disease modeling, accurately simulating the incubation period–the time between exposure to a pathogen and the onset of symptoms–is crucial for…

Implementing incubation period of cholera in the ODE model

incubation period

ODE

cholera

exponential

Erlang

Feb 22, 2024

In models of transmission of directly transmitted pathogens, e.g., COVID-19, the transmission is assumed to occur via so-called mass action principle. It means the rate of…

Mass-action assumption: density- vs. frequency-dependent transmission

mass action

frequency-dependent

density-dependent

Feb 19, 2024

The LabelledArrays package makes it easy to use the ODE model in Julia. It offers a method to manage variables via keys instead of indices. Variables can be constructed…

LabelledArrays and NamedTupleTools make it easy to use the ODE model in Julia

julia

ODE

LabelledArrays

NamedTupleTools

SEIR

Jan 26, 2024

This post benchmarks three approaches to solving ODE-based SIR models: the deSolve package (1) in R, the odin package (2), and diffeqr which calls Julia…

SIR model benchmarks: deSolve, odin, and diffeqr

ODE

deSolve

odin

diffeqr

C++

Julia

Jan 19, 2024

Julia DifferentialEquations.jl provides an impressive collection of differential equation solvers. The DE solvers available in the package are reliable and a lot faster than…

diffeqr: R interface to the Julia’s DifferentialEquations.jl

differential equation

julia

DifferentialEquations.jl

diffeqr

Jan 15, 2024

The UDE refers to an approach to embed the machine learning into differential equations. The resulting UDE has some parts of the equation replaced by universal approximators …

Universal differential equation using Julia

universal differential equation

julia

sub-exponential growth

Jan 12, 2024

This post is my attempt to learn machine learning in Julia. The contents of this page came from the Flux. Flux is a machine learning package written in Julia.

Fitting a straight line in Julia: Flux machine learning

julia

Flux

linear model

Jan 4, 2024

The following article by Fine provides a great introduction to the critical vaccination threshold.

Critical vaccination threshold

vaccine

population immunity

critical vaccination threshold

Dec 14, 2023

Although not published, I wrote a correspondence to Lancet to commenting the article. In the article, the authors stated that the generation interval is the sum of the…

Generation interval

generation interval

reproduction number

Dec 7, 2023

Wallinga and Lipsitch wrote a highly cited paper about the reproduction number. It discusses how to derive reproduction number, $R$, given the growth rate, $r$, and the…

Generation interval, growth rate, reproduction number

generation interval

growth rate

reproduction number

Dec 6, 2023

The following content was adapted from Grant Sanderson’s YouTube video and the Wikipedia article.

Convolution

particle filter

Dec 5, 2023

Debates in the population ecology have been categorized by Bjørnstad and Grenfell (1).

Idiosyncrasies and generalities

ecology

idiosyncransy

generality

COVID-19

Dec 4, 2023

I developed a SIR model (1) and solved it using an Euler method, then generated fake data as a sequence of noisy observations of daily incidence. Stan (2) is used for…

SIR model in Stan: Euler method

Stan

Euler method

SIR model

Nov 28, 2023

This post extends the right-truncation approach from the previous post (see Seaman et al. (1)) by implementing the likelihood in Stan (2), a probabilistic programming…

Estimating a time-to-event distribution in Stan

news

code

analysis

Nov 24, 2023

Seaman et al. (1) write: Data on time to an event are said to be right truncated if they come from a set of individuals who have been randomly sampled from a population…

Estimating a time-to-event distribution from right-truncated data

right truncation

exponential growth

Poisson process

Nov 23, 2023

We start simple. Our task is to estimate parameters of a probability density function used to model the serial interval. Suppose dates of onsets of infectors, $A$, and…

Estimating serial interval: doubly interval-censored data

serial interval

interval censoring

Nov 17, 2023

When estimating serial intervals or other time-to-event distributions from epidemic data, right truncation is a key consideration: individuals are observed only if their…

Estimating serial interval for a growing epidemic

serial interval

interval censoring

Nov 17, 2023

Suppose dates of onsets of infectors, $t^{A}$, and infectees, $t^{B}$, are given as specific dates. Then the likelihood function for the serial interval may be written…

Estimating serial interval: interval cenoring

serial interval

interval censoring

MLE

Nov 15, 2023

In the branching process model, the number of secondary infections is realized as a random number (e.g., Poission or Negative binomial).

Branching process model 2

branching process

final epidemic size

Nov 14, 2023

Miller (1) shows that the final size of an epidemic for a well-mixed population can be derived in the following way. We divide the population into susceptible, infected, and…

Final epidemic size: uniroot vs. optimize

epidemic

size

uniroot

optimize

Nov 10, 2023

SEIR 모형은 잠복기가 어느 정도 긴 감염병 (예를 들어 코로나19)의 전파를 모형하는 데 사용한다. 이번 포스트에서는 SEIR 모형을 만드는 방법을 알아본다. 결정론적 (deterministic) 그리고 확률론적 (stochastic) 방법으로 SEIR 모형을 R언어로 만들어 본다.

SEIR model

SEIR

deterministic

stochastic

Gillespie's algorithm

Nov 9, 2023

In the branching process model, the number of secondary infections is realized as a random number (e.g., Poission or Negative binomial).

Branching process model

branching process

final epidemic size

Nov 8, 2023

This post describes my attempt to reproduce Table 1 of Mossong et al. (1), a landmark study on social contact patterns relevant to infectious disease transmission. Data were…

Negative binomial regression with censored data: POLYMOD data

regression

contact

censor

Nov 2, 2023

9 min

Apartment transactions in Korea via API provided by the Ministry of Land, Infrastructure, and Transport

API

apartment

I will plot the price

Nov 1, 2023

수리 모형을 이용하여 연구를 하게되면 관찰값을 이용하여 모형의 모수를 보정하는 과정을 거치게 된다. 이 과정을 소위 결과 (관찰값)로 부터 원인 (모형)을 알아내는 과정이라 하여 inverse problem 이라 부르기도 한다. 이 글에서는 $SEIR$ 모형과 중국 우한 에서의 초기 코로나-19 발열자…

Confidence interval using profile likelihood

SEIR

profile likelihood

likelihood ratio

Oct 19, 2023

I attempted to replicate some of the simple analytical results presented in the book, Mathematical Epidemiology by Brauer et al.

SIR model using SymPy

SIR

SymPy

Oct 16, 2023

The following example was adapted from the Tobit model in Model Estimation by Example. The dataset contains 200 observations. The academic aptitude variable is apt, the…

Regression with censored data: AER::tobit and optim

regression

censor

tobit

Oct 15, 2023

This post describes my attempt to reproduce Table 1 of the POLYMOD study (1), which is a large European study on social contacts and mixing patterns relevant to the spread…

Mulitple regression: POLYMOD data

regression

contact

Oct 12, 2023

I will use the cars data with give the speed of cars and the distances taken to stop.

Regression using optim

optim

regression

Oct 11, 2023

raster 이미지의 일부를 추출해보자. 특히, shapefile에 담겨져 있는 polygon에 해당하는 raster 를 추출해보자. raster 패키지의 crop 과 mask 함수를 이용할 수 있다.

Extract raster based on a polygon

raster

shapefile

crop

mask

Sep 23, 2023

이번 Vaccine Impact Modeling Consortium (VIMC) 연례회의에서 odin (1) 이라는 패키지에 대해 알게 되었다. deSolve (2) 의 업그레이드 버전이라고 보면 될까? R 코드를 C언어로 컴파일하기 때문에 최종 모형의 구동속도가 빠르다. 따라서 모형을 여러번 돌려야 하는…

odin package

ODE

odin

Sep 15, 2023

PubMed search, ChatGPT summary, and sending an email in Python

ChatGPT

xml

httr

Sep 1, 2023

Search the PubMed database Use the entrez_search function from the rentrez package to search the PubMed database

PubMed search, ChatGPT summary, and sending an email in R

ChatGPT

xml

httr

Sep 1, 2023

shapefile에 담겨져 있는 polygon의 면적을 구해보자 raster 패키지의 area 혹은 sf 패키지의 st_area 함수를 이용할 수 있다.

Polygon 면적 구하기: sf 와 raster 패키지

shapefile

ggplot2

raster

RColorBrewer

ggplot2를 이용하여 지도 그리기를 해보자. 지도는 shapefile에 담겨져 있다고 가정하자. shapefile을 읽는 방법은 여러가지가 있을 수 있는데 sf 패키지의 st_read 혹은 read_sf 함수를 이용한 후 ggplot2의 geom_sf를 이용하여 그리는 것이 가장 쉬운 것 같다.

ggplot2로 지도 그리기

map

ggplot2

RColorBrewer

연구자의 업무 중에 연구 만큼 중요한 것이 글쓰기, 특히 논문 쓰기이다. 논문으로 쓰여지지 못한 연구는 타인에게는 존재하지 않는 것이나 다름 없는 것이다.. Whitesides의 논문 (1) 에 논문 쓰기에 유용한 팁이 있어 여기에 기록으로 남긴다. 한 마디로 요약하면 outline (개요)을 이용하는…

Writing a paper: Start with an outline

writing

paper

Importance sampling is a Monte Carlo method for evaluating properties of a particular distribution, while only having samples generated from a different distribution than…

Importance sampling

importance sampling

How to Avoid a Climate Disaster: The Solutions We Have and the Breakthroughs We Need by Bill Gates is a comprehensive and accessible guide on how to tackle the urgent issue…

Important figures from the book, How to avoid a climate diaster? by Bill Gates

parameter estimation

maximum likelihood

profile likelihood

Aug 28, 2023

In his lecture, Joseph Blitzstein talks about two basic statistical phenomena: Regression toward to the mean (RTTM) and survivor bias (or conditioning more broadly). The…

Regression toward the mean

parameter estimation

maximum likelihood

profile likelihood

Aug 25, 2023

In his lecture titled “The Soul of statistics” Joseph Blitzstein talks about a survivor bias (or conditioning more broadly) Dr. Derek Muller also talks about various…

Survivor bias

parameter estimation

maximum likelihood

profile likelihood

Aug 25, 2023

파티클 필터 (particle filter) 를 이용하여 잠재 변수 (latent variable)를 추정하는 과정을 지난 글에서 다루었다. 관찰값들이 코로나 19 일별 감염자일때 감염병 수리 모형을 이용하여 일별 감염재생산지수 ($(R_t$) 를 추정한다. 아래 글은 Kucharski et al. (1) …

Estimating the instantaneous reproduction number using the particle filter

particle filter

COVID-19

Aug 19, 2023

통계학은 많은 부분 확률모형의 모수를 추정하는 (inferential statistics) 과정이고 모수 추정방법으로 가장 많이 사용되는 방법이 maximum likelihood (ML)이다. 이번 포스트는 2014년 출간된 Cole et al.의 Maximum Likelihood, Profile…

Maximum Likelihood and Profile Likelihood for the SEIR model

parameter estimation

maximum likelihood

profile likelihood

Aug 14, 2023

감염병의 전파를 이해하는 데 있어 가장 기본적인 개념이 재감염지수, 특히 기초재감염지수 ($\mathcal{R}_0$) 이다. 재감염지수는 한 명의 감염자로부터 생산되는 평균 후속 감염자의 수를 일컫는데 기초재감염지수는 코로나19의 경우 처럼 인구 집단에 면역력을 가진 사람이 없어 모든 사람이 감염될 수…

Basic reproduction number using SymPy

Basic reproduction number

SymPy

Aug 11, 2023

최근에 파티클필터링 (particle filtering; PF) 방법을 이용하여 $\mathcal{R}_t$ 추정하는 과정에 대한 논문을 썼다. 그런데, 항상 의문이었던 것은 PF를 조금만 변형하면 감염병 모형의 감염속도 $\beta=\mathcal{R}_0 \gamma$ 와 같은…

Population Monte Carlo 파퓰레이션 몬테카를로

Monte Carlo

parameter estimation

code

analysis

Aug 10, 2023

Robert M. May Nature Vol. 261 June 10, 1976

Simple mathematical models with very complicated dynamics

code

analysis

Aug 8, 2023

대부분의 SIR 모형은 감염병 확산의 메커니즘을 아래와 같은 식으로 표현한다.

Sub-exponential growth

news

code

analysis

Aug 7, 2023

Stan은 통계 모형 뿐 아니라 ODE 모형을 시물레이션하고 모수를 추정하는 데에도 유용하다. 이 포스팅에서는 일별 감염자 자료가 주어졌을 경우 Stan을 이용하여 SIR 모형의 두 개의 모수 ($\beta, \gamma$)를 추정하는 과정을 기술하겠다. 먼저 deSolve 패키지 양식을 따라 SIR…

ODE-based SIR models in Stan

Stan

ODE

SIR

Aug 6, 2023

코로나19에 효과적으로 대응하고자 방역 당국과 연구자들이 코로나19의 전파 양상을 분석한 결과가 뉴스에 종종 보도 되었는데 그 내용 중에 빠지지 않는 것이 감염재생산지수이다. 영어로는 reproduction number ($\mathcal{R}$) 로 불리는 데 한 명의 감염자로부터 야기된 후속 감염자의…

감염재생산지수 계산하기

modeling

reproduction number

Aug 4, 2023

The following example was adapted from the post in RPubs.

Particle filter using R

particle filter

Jul 19, 2023

When implementing a model of stochastic disease transmission, one has to deal with a situation in which multiple events are possible. For example, susceptible people may…

Multinomial distribution

multinomial

Rcpp

pomp

Jun 19, 2023

감염병 수리 모형을 개발하는 데 있어 가장 근본적인 질문 중 하나는 주어진 관찰값 (시계열)하에서 어떤 모형을 선택하고 그 모수의 값을 어떻게 결정하는가이다. 모형을 선택하는 과정은 따로 다루기로 하고 여기서는 일반적으로 사용되는 감염병 수리 모형 (i.e., SIR)을 사용할 때 모수를 추정하는 과정에…

SEIR model using the Nimble pacakge

nimble

MCMC

posterior predictive check

trace plot

Jun 19, 2023

수학 모델로 감염병 확산을 예측한다. 현실과 얼마나 맞을까? 코로나19는 이 질문의 정답을 알려줬다.

모델과 현실: 수학으로 감염병 확산을 읽다

Apr 18, 2023

14 min

The Model and Reality: Bridging Mathematical Frameworks with Real-World Infectious Disease Dynamics

As infectious disease modelers, we face a fundamental epistemological question: How can abstract mathematical constructs help us understand and predict the complex dynamics…

Apr 18, 2023

Major human infecious disease are believed to have arisen after agriculture revolutionOrigins of major human infectious diseases. By the way, this emergence of infectious…

Origins of major human infectious diseases

infectious disease

emergence

density

Mar 4, 2023