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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:

One-Compartment Open Model for IV Bolus Administration: Estimation of Elimination Rate Constant, Half-Life and Volume of Distribution

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The one-compartment open model is a simplified approach used in pharmacokinetics to understand the distribution and elimination of a drug administered through an intravenous bolus. This model assumes rapid drug dispersal throughout the body and elimination using a first-order process. Key pharmacokinetic parameters, such as the elimination rate constant (k), half-life (t1/2), and the apparent volume of distribution (Vd), can be estimated from this model. The elimination rate is calculated...

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Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
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Two-Compartment Open Model: IV Bolus Administration

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The two-compartment model for intravenous (IV) bolus administration illustrates drug distribution in the body, subdividing it into central and peripheral compartments. This model operates on the concept of two-compartment kinetics. The drug's plasma concentration shows a bi-exponential decline following IV bolus administration, signaling the presence of two disposition processes: distribution and elimination.
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Related Experiment Video

Updated: Jun 18, 2025

Laboratory Techniques Used to Maintain and Differentiate Biotypes of Vibrio cholerae Clinical and Environmental Isolates

Laboratory Techniques Used to Maintain and Differentiate Biotypes of Vibrio cholerae Clinical and Environmental Isolates

Published on: May 30, 2017

Cholera disease dynamics with vaccination control using delay differential equation.

Jaskirat Pal Singh¹, Sachin Kumar², Ali Akgül^3,4

¹Department of Mathematics and Statistics, Central University of Punjab, Bathinda, 151401, India.

Scientific Reports

|July 29, 2024

Summary

This study introduces a fractional order delay differential model to combat rising cholera cases, demonstrating that water chlorination and vaccination are effective public health interventions against disease spread.

Keywords:

Bifurcation analysis Caputo derivative Cholera Predictor–corrector method Sensitivity analysis Stability analysis delay differential equation

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Area of Science:

Epidemiology
Mathematical Biology
Public Health

Background:

The COVID-19 pandemic disrupted global health initiatives, leading to increased cholera incidence in developing nations due to vaccination gaps.
Lack of timely interventions exacerbates cholera outbreaks, particularly in resource-limited settings.

Purpose of the Study:

To develop and analyze a novel fractional order delay differential model for cholera transmission.
To mathematically evaluate the efficacy of public health interventions, including water chlorination and vaccination, in controlling cholera.

Main Methods:

A fractional order delay differential equation model incorporating two distinct delays (latent period and disinfectant application delay) was formulated.
Sensitivity analysis of the basic reproduction number was performed to assess control measure effectiveness.
Stability analysis of equilibrium points and numerical simulations were conducted.

Main Results:

Mathematical evidence was provided for the effectiveness of water disinfection and vaccination in preventing cholera spread.
The study identified stability switching curves.
Numerical simulations illustrated the impact of delays on disease dynamics and the influence of fractional order on oscillations.

Conclusions:

The proposed model confirms that combining water chlorination and vaccination strategies is crucial for mitigating cholera outbreaks.
Delay parameters significantly influence disease dynamics, highlighting the importance of timely intervention.
Fractional calculus offers a valuable framework for modeling complex epidemiological phenomena.