Related Experiment Video
Updated: May 10, 2025
08:00
Measuring and Modeling Contractile Drying in Human Stratum Corneum
Published on: March 1, 2017
6.6K
Dynamical analysis of scabies delayed epidemic model with second-order global stability
Emad Fadhal1, Ali Raza2,3,4, Eugénio M Rocha4
1Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa, Saudi Arabia.
Plos One
|April 21, 2025
Summary
This study introduces a mathematical model using delay differential equations to understand scabies transmission dynamics. The findings enhance epidemic management strategies for this widespread skin disease.
Area of Science:
- Epidemiology
- Mathematical Biology
- Infectious Disease Modeling
Background:
- Scabies is a highly contagious skin disease affecting all ages, with significant impact in South Asia and sub-Saharan Africa.
- Mathematical modeling is crucial for understanding disease dynamics and informing public health interventions.
Purpose of the Study:
- To develop and analyze a mathematical model for scabies transmission dynamics.
- To investigate the impact of delays on scabies epidemiology.
- To provide insights for effective epidemic management.
Main Methods:
- Development of a delay differential equation (DDE) model with four subpopulations: unvaccinated, vaccinated, infected, and recovered.
- Rigorous mathematical analysis including positivity, boundedness, existence, uniqueness, equilibria, and reproduction number.
- Sensitivity analysis and local/global stability analysis of the model.
- Numerical simulations to validate theoretical findings.
Main Results:
- The mathematical model's fundamental properties (positivity, boundedness, existence, uniqueness) were proven.
- Equilibria, reproduction number, and stability (local and global) were rigorously analyzed.
- Numerical simulations confirmed the theoretical results, demonstrating the model's validity.
Conclusions:
- Delay-based modeling offers a valuable approach to studying scabies dynamics.
- Advanced stability analysis enhances understanding of epidemic spread and control.
- The model provides a framework for improved scabies management and intervention strategies.
Related Concept Videos
01:18Second Order systems II
62
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
62
01:18Steps in Outbreak Investigation
90
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:
90
01:25Multimachine Stability
101
Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
101
01:21Linear Approximation in Time Domain
56
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
56
01:20Second Order systems I
115
A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...
By reinterpreting the system, one can derive the closed-loop transfer function, which...
115
01:19Routh-Hurwitz Criterion II
157
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
157