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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.
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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.
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Non-linear Dynamics of Two-Patch Model Incorporating Secondary Dengue Infection.

Arti Mishra1, Sunita Gakkhar1

  • 1Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand India.

International Journal of Applied and Computational Mathematics
|April 15, 2020
PubMed
Summary
This summary is machine-generated.

Human migration significantly impacts dengue epidemics. Migrants can introduce different dengue serotypes, increasing disease spread and severity, as seen in Brazil.

Keywords:
Basic reproduction numberDengueEstimationHuman migrationSecondary infectionStability

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Area of Science:

  • Epidemiology
  • Mathematical Modeling
  • Infectious Disease Dynamics

Background:

  • Dengue fever is a significant global health concern.
  • Human migration patterns can influence the spread of infectious diseases.
  • Understanding the interplay between migration and dengue is crucial for public health interventions.

Purpose of the Study:

  • To investigate the impact of human migration on dengue epidemic dynamics.
  • To analyze how migration affects disease transmission in a multi-patch model.
  • To evaluate the role of different dengue serotypes in migration-driven outbreaks.

Main Methods:

  • Developed a vector-host model with two patches, each with a distinct dengue serotype.
  • Incorporated constant migration rates for susceptible and recovered individuals between patches.
  • Computed and analyzed the basic reproduction number (R0) concerning migration parameters.
  • Performed stability analysis of equilibrium states and sensitivity analysis of R0.

Main Results:

  • Immigration into a patch increases its basic reproduction number, while emigration decreases it.
  • Migration dynamics significantly influence the overall dengue epidemic's trajectory.
  • Model simulations and analysis of Brazilian states indicate migration's role in severe outbreaks.

Conclusions:

  • Human migration is a critical factor in shaping dengue epidemic dynamics and severity.
  • Migration patterns can exacerbate dengue outbreaks, especially when different serotypes are involved.
  • The findings highlight the need to integrate migration data into dengue surveillance and control strategies.