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On existence of traveling wave of an HBV infection dynamics model: A novel approach

Rupchand Sutradhar, D C Dalal

TL;DR

In this work, a hepatitis B virus infection dynamics model is proposed including the spatial dependence of viruses, and it is observed that due to diffusion, viruses spread rapidly throughout the liver.

Abstract

In this work, a hepatitis B virus infection dynamics model is proposed including the spatial dependence of viruses. The existence of traveling waves for the proposed model is established through the application of the celebrated Gersgorin theorem. The procedure followed to establish the existence of a traveling wave solution is innovative and probably the first attempt of this particular approach. The elasticity of basic reproduction number with respect to some model parameters are also shown. Furthermore, the effects of spatial diffusivity of the viruses on infection are studied, and it is noticed that due to the diffusion, viruses spread rapidly throughout the liver.

On existence of traveling wave of an HBV infection dynamics model: A novel approach

TL;DR

In this work, a hepatitis B virus infection dynamics model is proposed including the spatial dependence of viruses, and it is observed that due to diffusion, viruses spread rapidly throughout the liver.

Abstract

In this work, a hepatitis B virus infection dynamics model is proposed including the spatial dependence of viruses. The existence of traveling waves for the proposed model is established through the application of the celebrated Gersgorin theorem. The procedure followed to establish the existence of a traveling wave solution is innovative and probably the first attempt of this particular approach. The elasticity of basic reproduction number with respect to some model parameters are also shown. Furthermore, the effects of spatial diffusivity of the viruses on infection are studied, and it is noticed that due to the diffusion, viruses spread rapidly throughout the liver.
Paper Structure (11 sections, 2 theorems, 23 equations, 6 figures, 1 table)

This paper contains 11 sections, 2 theorems, 23 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Initial and boundary conditions
  4. Initial conditions:
  5. Boundary conditions
  6. Elasticities of basic reproduction number with respect to parameters
  7. Existence of Traveling wave solution
  8. Quantitative Analysis
  9. Traveling wave solution:
  10. The effects of diffusion of the viruses:
  11. Conclusions

Key Result

Theorem 2.1

2012_horn_matrix Consider a matrix $A=[a_{ij}]\in M_n$, set of all $n\times n$ matrices. Let denote the deleted absolute row sums of the given matrix $A$. Consider $n$$Ger\hat{s}gorin$ discs, defined as Then, the eigenvalues of the matrix $A$ lie in the union of $Ger\hat{s}gorin$ discs Additionally, if, out of $n$ discs, $k$ discs form the set $G_k(A)$ that remains disjoint from the remaining $

Figures (6)

  • Figure 1: The diagrammatic representation of the system \ref{['Eqn:PDE']}.
  • Figure 2: Elasticities of basic reproduction number with respect to parameters $\alpha$, $\gamma$ and $\beta$.
  • Figure 3: Four distinct $Ger\hat{s}gorin$ dices of the matrix $A$.
  • Figure 4: Traveling wave solution of uninfected hepatocytes for different values of wave speed $c$.
  • Figure 5: Solution of system \ref{['Eqn: PDE-simple form rho-1 to rho-5']} starting from initial conditions \ref{['eq:initial condition']} without diffusion.
  • ...and 1 more figures

Theorems & Definitions (5)

  • Theorem 2.1
  • Definition 2.2
  • Theorem 5.1
  • proof
  • Remark 5.2