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In this paper, a delayed cytokine-enhanced viral infection model incorporating nonlinear incidence and immune response is proposed and studied. The global stabilities of the equilibria of the model are characterized by constructing suitable Lyapunov functionals. The existence and properties of local Hopf bifurcation are discussed by regarding the immunity delay as the bifurcation parameter. Moreover, the global existence of Hopf bifurcation has been proved by regarding the immune delay as the bifurcation parameter. Numerical simulations are carried out to validate the obtained results. The results show that ignoring the cytokine-enhanced effect makes the infection risk underevaluated. The simulations show that increasing the immune delay destabilizes the model and generates a Hopf bifurcation and stability switches occurs. Moreover, it shows that immune delay may dominate the intracellular delays in such a viral infection model which means that the immune system of the host itself is complicated during virus infection. [ABSTRACT FROM AUTHOR]

In this paper, a new delayed within host model for dengue fever with immune response and Beddington–DeAngelis incidence is investigated. The basic reproduction number is computed. In addition, a detailed analysis on the local and global dynamics of the model is conducted. Finally, sensitivity analysis is carried out on basic reproduction number and numerical simulations are given to elucidate our theoretical results. [ABSTRACT FROM AUTHOR]

This paper develops a mathematical model to investigate the Human Immunodeficiency Virus (HIV) infection dynamics. The model includes two transmission modes (cell-to-cell and cell-free), two adaptive immune responses (cytotoxic T-lymphocyte (CTL) and antibody), a saturated CTL immune response, and latent HIV infection. The existence and local stability of equilibria are fully characterized by four reproduction numbers. Through sensitivity analyses, we assess the partial rank correlation coefficients of these reproduction numbers and identify that the infection rate via cell-to-cell transmission, the number of new viruses produced by each infected cell during its life cycle, the clearance rate of free virions, and immune parameters have the greatest impact on the reproduction numbers. Additionally, we compare the effects of immune stimulation and cell-to-cell spread on the model's dynamics. The findings highlight the significance of adaptive immune responses in increasing the population of uninfected cells and reducing the numbers of latent cells, infected cells, and viruses. Furthermore, cell-to-cell transmission is identified as a facilitator of HIV transmission. The analytical and numerical results presented in this study contribute to a better understanding of HIV dynamics and can potentially aid in improving HIV management strategies. [ABSTRACT FROM AUTHOR]

We propose a mathematical model studying a within-host infection dynamics of SARS-CoV-2 in pneumocytes. This model incorporates immune response, vaccination and antiviral drugs. The crucial properties of the model — the existence, positivity and boundary of solutions — are established. Equilibrium points and the basic reproduction number are calculated. The stability of each equilibrium point is analyzed. Optimal control is applied to the model by adding three control variables: vaccination, treatment by Favipiravir and treatment by Molnupiravir. Numerical results show that each individual control could reduce SARS-CoV-2 infection in some aspects; however, with a combination of three controls, we obtain the best results in reducing SARS-CoV-2 infection. This study has emphasized the importance of prevention by vaccine and the antiviral treatments. [ABSTRACT FROM AUTHOR]

To describe the interaction between viral infection and immune response, we establish a mathematical model with intracellular delay and investigate an optimal control problem to examine the effect of antiviral therapy. Dynamic analysis of the proposed model for the stability of equilibria and Hopf bifurcation is conducted. Theoretical results reveal that the dynamical properties are determined by both the immune-inactivated reproduction number and the immune-activated reproduction number. With the aim of minimizing the infected cells and viral load with consideration for the treatment costs, the optimal solution is discussed analytically. Numerical simulations are performed to suggest the optimal therapeutic strategy and compare the model-predicted consequences. [ABSTRACT FROM AUTHOR]

Coronavirus disease 2019 (COVID-19) is a new respiratory disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). It started in China and spread quickly to all continents. This virus has changed the life style and the education system in many countries. As for other viruses, mathematical models have been rated as a useful tool to support the research on COVID-19. In this work, we develop a reaction–diffusion model to describe the within-host dynamics of SARS-CoV-2 in cancer patients. This model studies the interactions between nutrient, healthy epithelial cells, cancer cells, SARS-CoV-2 particles, and immune cells. The model incorporates the spatial mobility of the cells and viruses. The model includes parameters for measuring the effect of lymphopenia on SARS-CoV-2/cancer patients. We verify the basic features of the model's solutions including the uniqueness, nonnegativity and boundedness. We list all equilibrium points of the proposed model. We show the global stability and the local instability of the most meaningful equilibria. We display some numerical simulations to enhance our theoretical results. The results indicate that diffusion can have a clear effect at the beginning of SARS-CoV-2 infection. Lymphopenia in SARS-CoV-2/cancer patients impairs the immune responses against cancer and SARS-CoV-2, and worsens the health state of patients. [ABSTRACT FROM AUTHOR]