Global analysis of a diffusive viral model with cell‐to‐cell infection and incubation period

Meng

Math Methods in App Sciences

2020

Impulsive reaction–diffusion system is a novel assemblage of tools for better understanding ecological dynamics. This paper is devoted to mathematical and biological analysis of an impulsive tritrophic periodic plankton–fish system with diffusion and Beddington–DeAngelis functional response in lakes. On the basis of comparison theory and method of upper and lower solution, we have rigorously analyzed ultimate boundedness and permanence of the reaction–diffusion system under impulsive effects. Significantly, the existence and globally asymptotic stability of a unique positive periodic solution are verified by Brouwer's fixed point theorem and auxiliary function method. Additionally, two particular scenarios are chosen to illustrate our results. It is found that impulsive effects can influence lake ecological dynamics and regulate lake biological structure.

Section: Discussionmentioning

confidence: 99%

Dynamics for a tritrophic impulsive periodic plankton–fish system with diffusion in lakes

Meng

Math Methods in App Sciences

2020

“…In the literature, the viral infection models with CTC transmission and silent infected cells have assumed that the CTC transmission only occurs due to the active infected cells. In a very recent work, Wang et al [41] formulated a viral infection model by assuming that both silent and active infected cells can participate in CTC infection. However, in [41], the immune response has not been considered.…”

Section: Introductionmentioning

confidence: 99%

“…In a very recent work, Wang et al [41] formulated a viral infection model by assuming that both silent and active infected cells can participate in CTC infection. However, in [41], the immune response has not been considered.…”

Section: Introductionmentioning

confidence: 99%

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

Ełaiw

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.

“…We note that the mathematical models of HIV dynamics with CTC transmission presented in the literature assumed that the CTC transmission is only due to the active infected CD4 + T cells. In (2020), Wang et al [54], have formulated a viral infection model by assuming that both silent and active infected cells can share in CTC infection. However, in [54], the role of the immune response has been neglected.…”

mentioning

confidence: 99%

“…In (2020), Wang et al [54], have formulated a viral infection model by assuming that both silent and active infected cells can share in CTC infection. However, in [54], the role of the immune response has been neglected. Elaiw and Alshamrani [12] have investigated an HIV mon-infection model with silent and active CTC transmissions and CTL immune response.…”

mentioning

confidence: 99%

Global stability of HIV/HTLV co-infection model with CTL-mediated immunity

Ełaiw¹,

AlShamrani²

2022

DCDS-B

Mathematical modeling of human immunodeficiency virus (HIV) and human T-lymphotropic virus type I (HTLV-I) mono-infections has received considerable attention during the last decades. These two viruses share the same way of transmission between individuals; through direct contact with certain contaminated body fluids. Therefore, a person can be co-infected with both viruses. In the present paper, we construct and analyze a new HIV/HTLV-I co-infection model under the effect of Cytotoxic T lymphocytes (CTLs) immune response. The model describes the interaction between susceptible CD4 + T cells, silent HIV-infected cells, active HIV-infected cells, silent HTLV-infected cells, Tax-expressing (active) HTLV-infected cells, free HIV particles, HIV-specific CTLs and HTLV-specific CTLs. The HIV can spread by two routes of transmission, virus-to-cell (VTC) and cell-to-cell (CTC). Both active and silent HIV-infected cells can infect the susceptible CD4 + T cells by CTC mechanism. On the other side, HTLV-I has only one mode of transmission via direct cell-to-cell contact. The well-posedness of the model is established by showing that the solutions of the model are nonnegative and bounded. We calculate all possible equilibria and define the key threshold parameters which govern the existence and stability of all equilibria of the model. We explore the global asymptotic stability of all equilibria by utilizing Lyapunov function and LaSalle's invariance principle. We have discussed the influence of CTL immune response on the co-infection dynamics. We have presented numerical simulations to justify the applicability and effectiveness of the theoretical results. In addition, we evaluate the effect of HTLV-I infection on the HIV dynamics and vice versa.