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Modelling and optimal control for Chikungunya disease.

Miled El Hajji1,2

  • 1Department of Mathematics, Faculty of Sciences, University of Jeddah, Jeddah, Saudi Arabia. miled.elhajji@enit.rnu.tn.

Theory in Biosciences = Theorie in Den Biowissenschaften
|October 31, 2020
PubMed
Summary

This study models Chikungunya virus (CHIKV) infection dynamics and uses optimal control strategies to manage viral load. Mathematical modeling demonstrates stability conditions and antibody flow rate optimization for better patient outcomes.

Keywords:
Antibodies’ flow rateCHIKVLaSalle’s invariance principleLyapunov theoryNonlinear incidence rateOptimal controlStabilityViral and cellular infections

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Area of Science:

  • Mathematical Biology
  • Virology
  • Control Theory

Background:

  • Chikungunya virus (CHIKV) infection poses a significant public health challenge.
  • Understanding intra-host viral dynamics is crucial for developing effective treatment strategies.
  • Mathematical modeling provides a framework for analyzing complex biological systems.

Purpose of the Study:

  • To develop a generalized mathematical model for intra-host CHIKV infection.
  • To analyze the stability of CHIKV-free and infected steady states.
  • To determine an optimal control strategy using antibody flow rate to manage infection.

Main Methods:

  • Utilized the next-generation matrix method to calculate the basic reproduction number.
  • Employed Lyapunov stability analysis to determine the global asymptotic stability of steady states.
  • Formulated and solved a nonlinear optimal control problem using adjoint variables and a competitive Gauss-Seidel-like implicit difference method.

Main Results:

  • Established conditions for the global asymptotic stability of both CHIKV-free and infected steady states based on the basic reproduction number.
  • Identified an optimal antibody flow rate strategy to minimize the infected compartment and maximize the uninfected compartment.
  • Numerical simulations confirmed the theoretical findings of the optimal control strategy.

Conclusions:

  • The proposed mathematical model accurately describes intra-host CHIKV infection dynamics.
  • Optimal control strategies targeting antibody flow rate can effectively manage CHIKV infection.
  • This research provides a theoretical basis for developing novel therapeutic interventions against CHIKV.