Related Experiment Video
Updated: Jan 28, 2026
09:05
Meal Duration as a Measure of Orofacial Nociceptive Responses in Rodents
Published on: January 10, 2014
8.0K
Duration of a minor epidemic
William Tritch1, Linda J S Allen1
1Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA.
Infectious Disease Modelling
|March 7, 2019
Summary
This study provides new formulas for understanding minor disease outbreaks in epidemic models. These findings help predict epidemic duration and case counts, crucial for public health interventions.
Area of Science:
- Epidemiology
- Mathematical Biology
- Stochastic Processes
Background:
- Stochastic SIR epidemic models classify outbreaks as minor or major.
- Whittle's 1955 work established probabilities for minor/major epidemics.
- Minor epidemics are characterized by shorter durations and fewer cases than major ones.
Purpose of the Study:
- To derive analytical formulas approximating the probability density, mean, and higher-order moments for the duration of minor epidemics.
- To extend these findings to various stochastic epidemic models.
- To provide a foundation for numerical computation in complex models.
Main Methods:
- Derivation of analytical formulas for minor epidemic duration moments.
- Application to single-infected class SIR, SIS, and SIRS models.
- Numerical computation using multitype branching processes and backward Kolmogorov equations for complex models.
Main Results:
- Analytical approximations for minor epidemic duration probability density, mean, and moments.
- Demonstrated applicability across SIR, SIS, and SIRS models.
- Identified that minor epidemics become more common and longer when the transmission rate approaches one.
Conclusions:
- The derived formulas offer valuable insights into the duration of minor epidemics.
- These results are applicable to a range of stochastic epidemic models.
- Understanding minor epidemic dynamics is essential for effective disease control strategies.
Related Concept Videos
01:25Minor Losses in Pipes
1.9K
In pipe systems, minor losses refer to energy losses arising from components such as valves, bends, fittings, expansions, and other features that disrupt the steady flow of fluid. These disturbances cause energy dissipation through turbulence and resistance, which engineers quantify to manage system efficiency effectively.
Valves play a significant role in generating minor losses by obstructing or redirecting the fluid flow. When a valve is closed or partially closed, it restricts the flow...
Valves play a significant role in generating minor losses by obstructing or redirecting the fluid flow. When a valve is closed or partially closed, it restricts the flow...
1.9K
02:16Solution Formation
37.4K
There is no one solvent that can dissolve every type of solute. Some substances that readily dissolve in a certain solvent might be insoluble in a different solvent. A simple way to predict which substances dissolve in which solvent is the phrase "like dissolves like". This means that polar substances, such as salt and sugar, dissolve in a polar substance like water. In contrast, non-polar substances are more soluble in non-polar solvents such as carbon tetrachloride.
This selective...
This selective...
37.4K
02:02Cis-regulatory Sequences
11.7K
Cis-regulatory sequences are short fragments of non-coding DNA that are present on the same chromosomes as the genes that they regulate. These fragments serve as binding sites for transcriptional regulators, proteins that are responsible for controlling gene transcription and differential gene expression across cell types in eukaryotes. Cis-regulatory sequences can be close to the gene of interest or thousands of bases away in the DNA sequence; however, those sequences that are further away are...
11.7K
03:24Hybridization of Atomic Orbitals I
66.6K
The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
66.6K
01:48Classification of Skeletal Muscle Fibers
59.5K
Skeletal muscles continuously produce ATP to provide the energy that enables muscle contractions. Skeletal muscle fibers can be categorized into three types based on differences in their contraction speed and how they produce ATP, as well as physical differences related to these factors. Most human muscles contain all three muscle fiber types, albeit in varying proportions.
Slow-Twitch Muscle Fibers
Slow oxidative, muscle fibers appear red due to large numbers of capillaries and high levels of...
Slow-Twitch Muscle Fibers
Slow oxidative, muscle fibers appear red due to large numbers of capillaries and high levels of...
59.5K
02:39The Integrated Rate Law: The Dependence of Concentration on Time
41.3K
While the differential rate law relates the rate and concentrations of reactants, a second form of rate law called the integrated rate law relates concentrations of reactants and time. Integrated rate laws can be used to determine the amount of reactant or product present after a period of time or to estimate the time required for a reaction to proceed to a certain extent. For example, an integrated rate law helps determine the length of time a radioactive material must be stored for its...
41.3K