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Related Experiment Video

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Mathematical Modelling of Dengue Transmission with Intervention Strategies Using Fractional Derivatives.

Nur 'Izzati Hamdan1, Adem Kilicman2

  • 1School of Mathematical Sciences, College of Computing, Informatics and Media, Universiti Teknologi MARA, 40450, Shah Alam, Selangor, Malaysia. izzatihamdan@uitm.edu.my.

Bulletin of Mathematical Biology
|October 26, 2022
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This study models dengue transmission using fractional-order differential equations (FODEs). Vector control combined with personal protection is most effective for controlling dengue spread.

Keywords:
DengueDengue controlFractional derivativeGlobal stabilityLyapunov function

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Area of Science:

  • Mathematical Biology
  • Epidemiology
  • Fractional Calculus

Background:

  • Dengue remains a significant public health concern globally.
  • Effective mathematical models are crucial for understanding and controlling dengue outbreaks.
  • Fractional-order differential equations (FODEs) offer a more nuanced approach to modeling complex biological systems.

Purpose of the Study:

  • To develop and analyze a deterministic mathematical model for dengue transmission using fractional-order differential equations (FODEs).
  • To evaluate the efficacy of various dengue control strategies relevant to Malaysia, including adulticides, larvicides, breeding site destruction, and individual protection.
  • To assess the performance of the FODE model against traditional integer-order models for dengue data fitting.

Main Methods:

  • Formulation of a deterministic mathematical model based on a system of fractional-order differential equations (FODEs).
  • Analysis of global stability for disease-free and endemic equilibria using Lyapunov function theory.
  • Numerical simulations to verify theoretical findings and assess intervention impacts.
  • Real-data fitting to compare the FODE model with an integer-order model.

Main Results:

  • Vector control strategies (adulticides, larvicides, breeding site destruction) are highly effective in combating dengue spread.
  • Combining vector control with individual protection significantly enhances disease control.
  • Individual protection alone can substantially reduce dengue cases, while mechanical control alone is insufficient for suppression.
  • The FODE model demonstrated a slight performance advantage over the integer-order model in fitting real dengue data.

Conclusions:

  • The FODE approach provides a valuable framework for modeling infectious diseases like dengue.
  • Integrated control strategies, particularly those involving vector control and personal protection, are essential for effective dengue management.
  • Mathematical modeling using fractional calculus can offer deeper insights into disease dynamics and intervention effectiveness.