Related Experiment Video
Updated: May 28, 2026
07:42
A Data-Driven Approach to Quantifying Immune States in Sepsis
Published on: February 7, 2025
The SIS and SIR stochastic epidemic models: a maximum entropy approach
J R Artalejo1, M J Lopez-Herrero
1Department of Statistics and Operations Research, Faculty of Mathematics, Complutense University of Madrid, 28040 Madrid, Spain. jesus_artalejo@mat.ucm.es
Theoretical Population Biology
|October 25, 2011
Summary
This study introduces maximum entropy (ME) solutions for susceptible-infected-susceptible (SIS) and susceptible-infected-removed (SIR) models to analyze infectious disease dynamics. ME formalism offers insights into epidemic spread, recovery, and extinction times, with an ESBL outbreak application.
Area of Science:
- Epidemiology and mathematical modeling of infectious diseases.
Background:
- Stochastic models like SIS and SIR are crucial for understanding disease transmission dynamics.
- The maximum entropy (ME) principle offers a framework for deriving statistical models from limited information.
Purpose of the Study:
- To formulate and analyze maximum entropy (ME) solutions for stochastic susceptible-infected-susceptible (SIS) and susceptible-infected-removed (SIR) epidemic models.
- To explore the utility of the ME formalism in providing insights into epidemic dynamics and outbreak behavior.
Main Methods:
- Derivation of ME solutions for SIS and SIR stochastic models.
- Analysis of model dynamics using descriptors such as the number of recovered individuals and time to extinction.
- Application of the ME formalism to real-world infectious disease data.
Main Results:
- Identified specific scenarios where the ME formalism provides valuable insights into epidemic modeling.
- Demonstrated the effectiveness of ME results in characterizing disease spread dynamics.
- Illustrated the application of ME formalism to analyze extended spectrum beta lactamase (ESBL) outbreaks in a hospital setting.
Conclusions:
- The maximum entropy (ME) principle is a powerful tool for developing and analyzing stochastic epidemic models.
- ME formalism offers a robust approach to understanding disease dynamics, including recovery and extinction.
- The study validates the practical application of ME-based epidemic models using real outbreak data.
Related Concept Videos
01:25Modeling with Differential Equations
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
01:18Steps in Outbreak Investigation
In the ever-evolving field of public health, statistical analysis serves as a cornerstone for understanding and managing disease outbreaks. By leveraging various statistical tools, health professionals can predict potential outbreaks, analyze ongoing situations, and devise effective responses to mitigate impact. For that to happen, there are a few possible stages of the analysis:
02:39Entropy
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
01:18Entropy
The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
01:23Mechanistic Models: Compartment Models in Individual and Population Analysis
Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...