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Single-Cell Characterization of Calcium Influx and HIV-1 Infection using a Multiparameter Optofluidic Platform

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A fast Fibonacci wavelet-based numerical algorithm for the solution of HIV-infected cells model.

Vivek¹, Manoj Kumar¹, Suyash Narayan Mishra¹

¹Applied Sciences and Humanities Department, Institute of Engineering and Technology, An Autonomous Constituent Institute of Dr. A.P.J. Abdul Kalam Technical University, Lucknow, UP 226021 India.

European Physical Journal Plus

|May 30, 2023

Summary

This study introduces an efficient Fibonacci wavelet method to solve mathematical models of HIV infection, offering enhanced accuracy for complex biological systems.

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Area of Science:

Biomathematics
Computational Biology
Numerical Analysis

Background:

Mathematical models are crucial for understanding HIV infection dynamics.
Nonlinear ordinary differential equations (ODEs) often represent these complex biological systems.
Developing efficient numerical methods is essential for accurate HIV model simulations.

Purpose of the Study:

To present a novel, computationally efficient approach for solving the mathematical model of HIV infection.
To utilize the Fibonacci wavelet and collocation technique for approximating solutions to nonlinear ODEs.
To demonstrate the method's applicability to various medical and engineering differential equations.

Main Methods:

Approximation of unknown functions and their derivatives using Fibonacci wavelets.
Transformation of the nonlinear ODE system into a set of algebraic equations.
Simplification of algebraic equations using a suitable numerical method.
Implementation and computation performed using MATLAB software.

Main Results:

The proposed Fibonacci wavelet method provides computationally efficient solutions.
Enhanced accuracy is demonstrated through tables and graphs for various problems.
The method effectively solves the nonlinear ODEs representing the HIV infection model.

Conclusions:

The Fibonacci wavelet and collocation technique offers a powerful and accurate tool for solving HIV infection models.
This approach is suitable for a broad range of nonlinear differential equations in medical science and engineering.
The method shows significant potential for applications in oncology and drug targeting systems.