Threshold dynamics of a general delayed within-host viral infection model with humoral immunity and two modes of virus transmission

Zhikun She; Xin Jiang

doi:10.3934/dcdsb.2020259

Article Contents

2021, Volume 26, Issue 7: 3835-3861. Doi: 10.3934/dcdsb.2020259

This issue Previous Article Convergence of quasilinear parabolic equations to semilinear equations Next Article Weak pullback mean random attractors for non-autonomous

$ p $

-Laplacian equations

Threshold dynamics of a general delayed within-host viral infection model with humoral immunity and two modes of virus transmission

Zhikun She^1, , and
Xin Jiang^1,2,

1.
School of Mathematical Sciences, Beihang University, Beijing 100191, China
2.
College of Science, North China University of Technology, Beijing 100144, China

^* Corresponding author: Zhikun She
^* Corresponding author: Zhikun She

Received: November 30, 2019

Revised: June 30, 2020

Early access: August 2020

Published: July 2021

The first author is supported by Beijing Natural Science Foundation (Z180005) and National Natural Science Foundation of China (11422111)

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Abstract

In this paper, a general viral infection model with humoral immunity is investigated. The model describes the interaction of uninfected target cells, infected cells, free viruses and humoral immune response, incorporating two virus transmission modes and intracellular delay. Some reasonable hypothesises are made for the general incidence rates. Through stability analysis of equilibria under these hypothesises, the model exhibits threshold dynamics with respect to the immune-inactivated reproduction rate $ \mathfrak{R}_0 $ and the immune-activated reproduction rate $ \mathfrak{R}_1 $. The theoretical results and corresponding numerical simulations show that the intracellular latency, both of virus-to-cell infection and cell-to-cell infection have direct effects on the global dynamics of the general viral infection model. Our results improve and generalize some known results on within-host virus dynamics.

Keywords:

Mathematics Subject Classification: 92D25, 34K20, 34K25.

Citation:

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Figure 1. Graph trajectories of system (23) with respect to different values of $ \Lambda $. The time delay $ \tau $ is increased from $ \tau = 4\; days $ $ (\mathfrak{R}_0 = 1.3558,\; \mathfrak{R}_1 = 1.2030) $ to $ \tau = 4.5\; days $ $ (\mathfrak{R}_0 = 1.1101,\; \mathfrak{R}_1 = 0.9790) $ and finally to $ \tau = 6\; days $ $ (\mathfrak{R}_0 = 0.7441,\; \mathfrak{R}_1 = 0.6453) $

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Figure 2. Graph trajectories of system (23) with respect to different values of $ \beta_1 $. $ \beta_1 $ is decreased from $ \beta_1 = 0.0000004\; ml\cdot day^{-1} $ $ (\mathfrak{R}_0 = 2.4913,\; \mathfrak{R}_1 = 1.0639) $ to $ \beta_1 = 0.00000015\; ml\cdot day^{-1} $ $ (\mathfrak{R}_0 = 1.5027,\; \mathfrak{R}_1 = 0.9469) $ and finally to $ \beta_1 = 0.00000001\; ml\cdot day^{-1} $ $ (\mathfrak{R}_0 = 0.9491,\; \mathfrak{R}_1 = 0.8814) $

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Figure 3. Graph trajectories of system (23) with respect to different values of $ \beta_2 $. $ \beta_2 $ is decreased from $ \beta_2 = 0.0000015\; ml\cdot day^{-1} $ $ (\mathfrak{R}_0 = 2.3134,\; \mathfrak{R}_1 = 1.4273) $ to $ \beta_2 = 0.000001\; ml\cdot day^{-1} $ $ (\mathfrak{R}_0 = 1.8586,\; \mathfrak{R}_1 = 0.9890) $ and finally to $ \beta_2 = 0.00000001\; ml\cdot day^{-1} $ $ (\mathfrak{R}_0 = 0.9582,\; \mathfrak{R}_1 = 0.1211) $

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