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Related Concept Videos

Infection01:20

Infection

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When a pathogen enters the body and reproduces, it can cause an infection, damage body cells, and cause illness symptoms that eventually lead to disease. Therefore, its prevention requires breaking the chain of infection.
The chain begins with pathogens: bacteria, viruses, fungi, prions, or parasites such as protozoa helminths. These can be present on the skin as transient or resident flora, or they can be acquired from the environment. Identifying and treating the type of infection and...
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Exponential Equations for Modeling Growth02:33

Exponential Equations for Modeling Growth

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Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is...
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Viral Replication: Lysogenic Cycle01:16

Viral Replication: Lysogenic Cycle

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The lysogenic cycle is a crucial viral replication strategy that allows bacteriophages to persist within host cells without immediately destroying them. This process is primarily observed in temperate phages, such as bacteriophage lambda (λ), which infects Escherichia coli. The cycle allows the viral genome to persist across bacterial generations while keeping host cells viable.Integration of the Viral GenomeUpon infection, bacteriophage lambda attaches to the bacterial surface and injects...
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Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model01:13

Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model

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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.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
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Nonlinear Pharmacokinetics: Causes of Nonlinearity01:22

Nonlinear Pharmacokinetics: Causes of Nonlinearity

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Nonlinearity in drug pharmacokinetics is caused by various factors influencing how a drug is absorbed, distributed, metabolized, and excreted. Understanding these nonlinear processes is crucial for predicting drug behavior in the body and optimizing drug dosing regimens.
Nonlinear drug absorption can occur when the process is rate-limited by solubility, carrier-mediated transport systems, or saturation of the presystemic gut wall or hepatic metabolism. For instance, high doses of riboflavin...
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Stages of Infection01:26

Stages of Infection

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Stages of infection describe what happens to a susceptible host once a pathogen invades the human body. The stages of infection are incubation, prodromal, illness, stage of decline, and convalescence. The incubation stage is the period from exposure to a pathogen until symptoms start. The infected person is unaware of impending illness as the pathogens grow and multiply within the body. The duration may vary depending on the type of infection. The incubation period of measles averages ten to...
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Related Experiment Video

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A Mouse Model for the Transition of Streptococcus pneumoniae from Colonizer to Pathogen upon Viral Co-Infection Recapitulates Age-Exacerbated Illness
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Global stability of a delayed and diffusive virus model with nonlinear infection function.

Yan Geng1, Jinhu Xu2

  • 1School of Science, Xi'an Polytechnic University, Xi'an, People's Republic of China.

Journal of Biological Dynamics
|May 4, 2021
PubMed
Summary

This study analyzes a delayed viral infection model. The research demonstrates that the basic reproduction number determines the global stability of either the infection-free or the infection equilibrium.

Keywords:
DiffusionLyapunov methoddelayglobal stabilitynonlinear incidence

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Area of Science:

  • Mathematical epidemiology
  • Virology
  • Dynamical systems

Background:

  • Viral infections pose significant public health challenges.
  • Mathematical models are crucial for understanding disease dynamics.
  • Delayed viral infection models with diffusion and general incidence rates require robust analytical methods.

Purpose of the Study:

  • To develop and analyze a discrete-time delayed viral infection model.
  • To investigate the impact of diffusion and general incidence rates on disease spread.
  • To determine the conditions for global asymptotic stability of equilibria.

Main Methods:

  • Derivation of a discrete-time model using a nonstandard finite difference scheme.
  • Analysis of solution positivity and boundedness.
  • Application of Lyapunov methods to establish global stability of equilibria.
  • Numerical simulations to validate theoretical findings.

Main Results:

  • The model's solutions are proven to be positive and bounded.
  • Global stability of equilibria is determined by the basic reproduction number ().
  • If < 1, the infection-free equilibrium () is globally asymptotically stable.
  • If > 1, the infection equilibrium () is globally asymptotically stable.

Conclusions:

  • The basic reproduction number is a critical threshold parameter for this viral infection model.
  • The model accurately predicts disease persistence or eradication based on .
  • Numerical experiments confirm the theoretical stability results.