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Pulmonary Tuberculosis II01:28

Pulmonary Tuberculosis II

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Tuberculosis, or TB, is a bacterial infectious disease caused by Mycobacterium tuberculosis. While its primary impact is on the lungs, leading to pulmonary tuberculosis, it can also affect various other organs, a condition referred to as extrapulmonary tuberculosis.
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Tuberculosis, often called TB, is a contagious illness primarily caused by Mycobacterium tuberculosis. It mainly affects the lung parenchyma but can also impact other body parts.
Causative Organism
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Tuberculosis (TB) is a contagious infection primarily affecting the lung parenchyma but which can also affect other body parts. TB can be classified based on disease development, presentation, and the affected anatomical site.
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Medical management of tuberculosis (TB) patients involves a comprehensive approach that includes diagnosis, treatment, and monitoring. The specific strategies can vary depending on the type of tuberculosis (latent or active), the patient's overall health status, and other considerations.
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Bacterial generation time, the period required for a bacterial population to double during its exponential growth phase, serves as a critical measure of microbial growth dynamics under optimal conditions. This parameter varies significantly across bacterial species and can be influenced by factors such as temperature, pH, and the availability of nutrients. For example, Escherichia coli can achieve a generation time of approximately 20 minutes, while Mycobacterium tuberculosis exhibits a much...
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A noninteger order SEITR dynamical model for TB.

Jitendra Panchal1, Falguni Acharya1, Kanan Joshi1

  • 1Department of Applied Sciences and Humanities, Parul Institute of Engineering and Technology, Parul University, Vadodara, Gujarat India.

Advances in Continuous and Discrete Models
|April 22, 2022
PubMed
Summary

This study introduces a fractional-order SEITR model for tuberculosis (TB) dynamics, offering a more realistic representation than traditional models. The model accurately fits Indian TB data and provides key insights into disease transmission.

Keywords:
Dynamical systemMathematical modelMycobacterium tuberculosis bacteriaNoninteger order derivativeNumerical simulation

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Dynamical Systems

Background:

  • Tuberculosis (TB) remains a significant global health challenge.
  • Existing mathematical models may not fully capture the complex dynamics of TB transmission.
  • Fractional calculus offers advanced tools for modeling intricate biological processes.

Purpose of the Study:

  • To design and validate a novel noninteger-order SEITR (Susceptible-Exposed-Infected-Treated-Recovered) dynamical model for tuberculosis (TB).
  • To enhance the understanding of TB infection dynamics by incorporating detailed compartments, including unrecognized infections and treatment delays.
  • To assess the model's accuracy and applicability using real-world TB data from India.

Main Methods:

  • Development of a fractional-order SEITR model using the Caputo fractional derivative.
  • Parameter estimation via least squares curve fitting to match TB confirmed cases in India (2000-2020).
  • Calculation of the basic reproduction number (R0 ≈ 1.73) using the next-generation matrix method.
  • Validation of the model's approximate solutions using the generalized Adams-Bashforth-Moulton numerical method.

Main Results:

  • The proposed fractional-order SEITR model demonstrates a strong fit to confirmed TB cases in India.
  • The estimated basic reproduction number (R0 ≈ 1.73) suggests TB transmission potential within the studied period.
  • Numerical simulations and graphical representations confirm the model's validity and effectiveness.

Conclusions:

  • Fractional-order models provide a more realistic and detailed representation of TB disease dynamics compared to classical integer-order models.
  • The developed SEITR model offers valuable insights for understanding and potentially controlling TB transmission.
  • This research highlights the utility of fractional calculus in epidemiological modeling for infectious diseases.