Global Properties of a Delay-Distributed HIV Dynamics Model Including Impairment of B-Cell Functions

Agha

2019

Adv Differ Equ

This paper studies the global dynamics of a general diffusive hepatitis B virus (HBV) infection model. The model includes both enveloped viruses and DNA containing capsids. Two immune responses are recruited to attack the virus and infected hepatocytes. These are the cytotoxic T-lymphocytes (CTL) which kill the infected liver cells, and B cells which send antibodies to attack the virus. The non-negativity and boundedness of the solutions are discussed. The existence of spatially homogeneous equilibrium points is examined. The global stability of all possible equilibrium points is proved by choosing suitable Lyapunov functionals. Some numerical simulations are performed to enhance the theoretical results and present the behavior of solutions in space and time.

Section: Resultsmentioning

confidence: 99%

Global dynamics of a general diffusive HBV infection model with capsids and adaptive immune response

Agha

2019

Adv Differ Equ

“…In this section, we prove the global asymptotic stability of all equilibria by constructing Lyapunov functional following the method presented in [46][47][48][49]. Define…”

Section: Global Stability Analysismentioning

confidence: 99%

Stability of a general CTL-mediated immunity HIV infection model with silent infected cell-to-cell spread

AlShamrani

2020

Adv Differ Equ

This paper proposes and analyzes a CTL-mediated HIV infection model. The model describes the interaction between healthy CD4 + T cells, silent infected cells, active infected cells, free HIV particles, and cytotoxic T lymphocytes (CTLs). The healthy CD4 + T cells can be infected when contacted by one of the following: (i) free HIV particles, (ii) silent infected cells, and (iii) active infected cells. The incidence rates of the healthy CD4 + T cells with free HIV particles, silent infected cells, and active infected cells are given by general functions. Moreover, the production/proliferation and removal/death rates of all compartments are represented by general functions. The model is an improvement of the existing HIV infection models which have neglected the incidence between the silent infected cells and healthy CD4 + T cells. We first show that the model is well posed. The proposed model has three equilibria and their existence is governed by derived two threshold parameters: the basic HIV reproduction number 0 and the HIV-specific CTL-mediated immunity reproduction number 1. Under a set of conditions on the general functions and the parameters 0 and 1 , we have proven the global asymptotic stability of all equilibria by using Lyapunov method. We have illustrated the theoretical results via numerical simulations. We have studied the effect of cell-to-cell (CTC) transmission on the dynamical behavior of the system. We have shown that inclusion of CTC transmission decreases the concentration of healthy CD4 + T cells and increases the concentrations of infected cells and free HIV particles.

“…Mathematical modeling has been used to understand the dynamics of malaria parasites during infection and to design more effective antimalarial drugs. Malaria models were built using similar ideas to those used in virus dynamics models [8][9][10][11][12][13][14][15][16]. The basic model for the within-host dynamics of malaria infection was proposed by Anderson et al [17].…”

Section: Introductionmentioning

confidence: 99%

Global Analysis of a Reaction-Diffusion Within-Host Malaria Infection Model with Adaptive Immune Response

Agha

2020

Mathematics

Malaria is one of the most dangerous global diseases. This paper studies a reaction-diffusion model for the within-host dynamics of malaria infection with both antibody and cell-mediated immune responses. The model explores the interactions between uninfected red blood cells (erythrocytes), three types of infected red blood cells, free merozoites, CTLs and antibodies. It contains some parameters to measure the effect of antimalarial drugs and isoleucine starvation on the blood cycle of malaria infection. The basic properties of the model are discussed. All possible equilibrium points and the threshold conditions required for their existence are addressed. The global stability of all equilibria are proved by selecting suitable Lyapunov functionals and using LaSalle’s invariance principle. The characteristic equations are used to study the local instability conditions of the equilibria. Some numerical simulations are conducted to support the theoretical results. The results indicate that antimalarial drugs with high efficacy can clear the infection and take the system towards the disease-free state. Increasing the efficacy of isoleucine starvation has a similar effect as antimalarial drugs and can eliminate the disease. The presence of immune responses with low efficacy of treatments does not provide a complete protection against the disease. However, the immune responses reduce the concentrations of all types of infected cells and limit the production of malaria parasites.