In this paper, we construct an Human immunodeficiency virus (HIV) dynamics model with impairment of B-cell functions and the general incidence rate. We incorporate three types of infected cells, (i) latently-infected cells, which contain the virus, but do not generate HIV particles, (ii) short-lived productively-infected cells, which live for a short time and generate large numbers of HIV particles, and (iii) long-lived productively-infected cells, which live for a long time and generate small numbers of HIV particles. The model considers five distributed time delays to characterize the time between the HIV contact of an uninfected CD4 + T-cell and the creation of mature HIV. The nonnegativity and boundedness of the solutions are proven. The model admits two equilibria, infection-free equilibrium E P 0 and endemic equilibrium E P 1 . We derive the basic reproduction number R 0 , which determines the existence and stability of the two equilibria. The global stability of each equilibrium is proven by utilizing the Lyapunov function and LaSalle’s invariance principle. We prove that if R 0 < 1 , then E P 0 is globally asymptotically stable, and if R 0 > 1 , then E P 1 is globally asymptotically stable. These theoretical results are illustrated by numerical simulations. The effect of impairment of B-cell functions, time delays, and antiviral treatment on the HIV dynamics are studied. We show that if the functions of B-cells are impaired, then the concentration of HIV is increased in the plasma. Moreover, we observe that the time delay has a similar effect to drug efficacy. This gives some impression for developing a new class of treatments to increase the delay period and then suppress the HIV replication.

This paper formulates a virus dynamics model with impairment of B-cell functions. The model incorporates two modes of viral transmission: cell-free and cell-to-cell. The cell-free and cell-cell incidence rates are modeled by general functions. The model incorporates both, latently and actively, infected cells as well as three distributed time delays. Nonnegativity and boundedness properties of the solutions are proven to show the well-posedness of the model. The model admits two equilibria that are determined by the basic reproduction number R 0 . The global stability of each equilibrium is proven by utilizing Lyapunov function and LaSalle's invariance principle. The theoretical results are illustrated by numerical simulations. The effect of impairment of B-cell functions and time delays on the virus dynamics are studied. We have shown that if the functions of B-cell is impaired, then the concentration of viruses is increased in the plasma.Moreover, we have observed that increasing the time delay will suppress the viral replication.

Coronavirus disease 2019 (COVID-19) is a respiratory disease caused by SARS-CoV-2. It appeared in China in late 2019 and rapidly spread to most countries of the world. Cancer patients infected with SARS-CoV-2 are at higher risk of developing severe infection and death. This risk increases further in the presence of lymphopenia affecting the lymphocytes count. Here, we develop a delayed within-host SARS-CoV-2/cancer model. The model describes the occurrence of SARS-CoV-2 infection in cancer patients and its effect on the functionality of immune responses. The model considers the time delays that affect the growth rates of healthy epithelial cells and cancer cells. We provide a detailed analysis of the model by proving the nonnegativity and boundedness of the solutions, finding steady states, and showing the global stability of the different steady states. We perform numerical simulations to highlight some important observations. The results indicate that increasing the time delay in the growth rate of cancer cells reduced the size of tumors and decreased the likelihood of deterioration in the condition of SARS-CoV-2/cancer patients. On the other hand, lymphopenia increased the concentrations of SARS-CoV-2 particles and cancer cells, which worsened the condition of the patient.