Related Experiment Video

Updated: Oct 15, 2025

A Mouse Model for the Transition of Streptococcus pneumoniae from Colonizer to Pathogen upon Viral Co-Infection Recapitulates Age-Exacerbated Illness
12:21

A Mouse Model for the Transition of Streptococcus pneumoniae from Colonizer to Pathogen upon Viral Co-Infection Recapitulates Age-Exacerbated Illness

Published on: September 28, 2022

2.7K

Modeling the transmission dynamics of delayed pneumonia-like diseases with a sensitivity of parameters

Muhammad Naveed1, Dumitru Baleanu2,3,4, Ali Raza5,6

  • 1Department of Mathematics, Air University, PAF Complex E-9, Islamabad, Pakistan.

Advances in Difference Equations
|October 25, 2021
PubMed

Insights

Pneumonia significantly impacts child mortality globally, particularly in South Asia and sub-Saharan Africa. Mathematical modeling reveals disease dynamics, confirming theoretical predictions through numerical simulations.

Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Public Health

Background:

  • Pneumonia is a leading cause of death in children under five, with high transmission rates.
  • The World Health Organization (WHO) identifies South Asia and sub-Saharan Africa as heavily impacted regions.
  • In 2017, pneumonia caused 0.88 million deaths in children under five.

Purpose of the Study:

  • To analyze the transmission dynamics of pneumonia using a delayed mathematical modeling technique.
  • To investigate the stability of equilibrium points in the pneumonia epidemiological model.
  • To validate theoretical findings through numerical simulations.

Main Methods:

  • Development of a mathematical model incorporating susceptible, carrier, infected, and recovered subpopulations.
  • Analysis of nonlinear interactions between different subpopulations.
  • Rigorous mathematical proof of positivity and boundedness for nonnegative initial data.
  • Stability analysis of pneumonia-free and pneumonia-existing equilibrium points.

Main Results:

  • The mathematical model demonstrates the epidemiological system's dynamics.
  • Positivity and boundedness of the model are mathematically proven.
  • Stability of both pneumonia-free and pneumonia-existing equilibrium points is rigorously established.
  • Numerical simulations confirm the theoretical results derived from the model.

Conclusions:

  • The delayed mathematical modeling approach provides valuable insights into pneumonia transmission dynamics.
  • The study confirms the existence and stability of critical disease states.
  • Numerical simulations validate the theoretical framework, supporting its applicability in public health analysis.

Keywords:
Delayed modelNumerical simulationsPneumonia diseaseStability analysis

More Related Videos

A Robust Pneumonia Model in Immunocompetent Rodents to Evaluate Antibacterial Efficacy against S. pneumoniae, H. influenzae, K. pneumoniae, P. aeruginosa or A. baumannii09:17

A Robust Pneumonia Model in Immunocompetent Rodents to Evaluate Antibacterial Efficacy against S. pneumoniae, H. influenzae, K. pneumoniae, P. aeruginosa or A. baumannii

Published on: January 2, 2017

14.8K
Following in Real Time the Impact of Pneumococcal Virulence Factors in an Acute Mouse Pneumonia Model Using Bioluminescent Bacteria11:32

Following in Real Time the Impact of Pneumococcal Virulence Factors in an Acute Mouse Pneumonia Model Using Bioluminescent Bacteria

Published on: February 23, 2014

15.2K

Related Concept Videos

Steps in Outbreak Investigation01:18

Steps 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:
253
Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
703
Pneumonia II: Pathophysiology01:29

Pneumonia II: Pathophysiology

The pathophysiology of pneumonia involves the following steps:
960
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
148
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic 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...
109
Pharmacokinetic Models: Comparison and Selection Criterion01:26

Pharmacokinetic Models: Comparison and Selection Criterion

Physiological and compartmental models are valuable tools used in studying biological systems. These models rely on differential equations to maintain mass balance within the system, ensuring an accurate representation of the dynamic processes at play.
Physiological models take a detailed approach by considering specific molecular processes. They can predict drug distribution, metabolism, and elimination changes, providing a comprehensive understanding of how drugs interact with the body.
174