Related Experiment Video
Updated: Jul 4, 2026
11:52
Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps
Published on: February 9, 2017
Spatial patterns in a discrete-time SIS patch model
L J S Allen1, Y Lou, A L Nevai
1Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA.
Journal of Mathematical Biology
|June 13, 2008
Summary
Infectious disease spread depends on habitat risk, connectivity, and movement. High-risk areas always sustain disease, while low-risk areas may become disease-free with reduced movement.
Area of Science:
- Epidemiology
- Mathematical Biology
- Spatial Ecology
Background:
- Infectious disease dynamics are influenced by spatial factors.
- Understanding how habitat characteristics and population movement affect disease spread is crucial.
Purpose of the Study:
- To investigate the combined effects of spatial heterogeneity, habitat connectivity, and movement rates on infectious disease spatial patterns.
- To analyze a discrete-time SIS patch model to understand disease persistence and spatial distribution.
Main Methods:
- Formulation and analysis of a discrete-time SIS patch model.
- Characterization of patches as low-risk or high-risk based on local disease parameters.
- Analysis of endemic equilibrium (EE) and disease-free equilibrium (DFE) under varying mobility rates.
Main Results:
- Disease persistence differs between low-risk and high-risk habitats.
- In low-risk habitats, disease persists below a mobility threshold; in high-risk habitats, it always persists.
- The endemic equilibrium approaches a spatially inhomogeneous disease-free equilibrium as susceptible mobility decreases.
Conclusions:
- Habitat risk (low vs. high) significantly impacts disease persistence and spatial patterns.
- Sufficient conditions for disease eradication in high-risk patches can be determined by transmission, recovery, connectivity, and infected movement rates.
- The model provides insights into disease dynamics in heterogeneous environments.
Related Concept Videos
01:27State Space Representation
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
Consider an RLC circuit, a...
01:21Partial Differential Equations
A stone dropped into a still pond generates waves that propagate outward in circular patterns, creating a dynamic surface whose elevation depends on both position and time. At any given location, the water level oscillates as the wave passes, while at any fixed moment, the surface exhibits smooth, curved structures extending across space. This dual dependence requires a mathematical description that accounts for variation in multiple variables simultaneously.At a fixed point on the water...
00:54Distribution and Dispersion
Ecology is the study of how organisms interact with their environment and with one another. An important aspect of ecology is understanding where species are found and how individuals are distributed within those areas. The geographic range of a species refers to the total area where its members are located, while dispersion describes the pattern of spacing of individuals within that range.Geographic Range and Dispersion PatternsWithin a species’ geographic range, individuals may be distributed...
01:16Basic Discrete Time Signals
The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is the...
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is the...
01:21State Space to Transfer Function
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
01:29Real-World Applications of Space Curves
Modern aerospace navigation depends on the accurate prediction of motion in three-dimensional space. In defense applications, radar systems continuously track both interceptors and moving aerial targets to find whether their flight paths will result in a collision. These motions are modeled mathematically as space curves, which represent paths that change continuously with time. Each object’s position is described by a vector function that specifies its location in terms of time-dependent...