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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]

Malaria is one of the most dangerous diseases that threatens people's lives around the world. In this paper, we study a reaction-diffusion model for the within-host dynamics of malaria infection with an antibody immune response. The model is given by a system of partial differential equations (PDEs) to describe the blood-stage of malaria life cycle. It addresses the interactions between uninfected red blood cells, antibodies, and three types of infected red blood cells, namely ring-infected red blood cells, trophozoite-infected red blood cells and schizont-infected red blood cells. Moreover, the model contains a parameter to measure the efficacy of isoleucine starvation and its effect on the growth of malaria parasites. We show the basic properties of the model. We compute all equilibria and derive the thresholds from the conditions of existence of malaria equilibrium points. We prove the global stability of all equilibrium points based on choosing suitable Lyapunov functionals. We use the characteristic equations to verify the local instability of equilibrium points. We finally execute numerical simulations to validate the theoretical results and highlight some important observations. The results indicate that isoleucine starvation can have a critical impact on the stability of equilibrium points. When the efficacy of isoleucine starvation is high, it switches the system from the infection state to the malaria-free state. The presence of an antibody immune response does not lead to the elimination of malaria infection, but it suppresses the growth of malaria parasites and increases the amount of healthy red blood cells. [ABSTRACT FROM AUTHOR]

This paper investigates the stochastic HTLV-I infection model with CTL immune response, and the corresponding deterministic model has two basic reproduction numbers. We consider the nonlinear CTL immune response for the interaction between the virus and the CTL immune cells. Firstly, for the theoretical needs of system dynamical behavior, we prove that the stochastic model solution is positive and global. In addition, we obtain the existence of ergodic stationary distribution by stochastic Lyapunov functions. Meanwhile, sufficient condition for the extinction of the stochastic system is acquired. Reasonably, the dynamical behavior of deterministic model is included in our result of stochastic model when the white noise disappears. [ABSTRACT FROM AUTHOR]

In this paper, a human immunodeficiency virus (HIV) infection model with both the types of immune responses, the antibody and the killer cell immune responses has been introduced. The model has been made more logical by including two delays in the activation of both the immune responses, along with the combination drug therapy. The inclusion of both the delayed immune responses provides a greater understanding of long-term dynamics of the disease. The dependence of the stability of the steady states of the model on the reproduction number R 0 has been explored through stability theory. Moreover, the global stability analysis of the infection-free steady state and the infected steady state has been proved with respect to R 0 . The bifurcation analysis of the infected steady state with respect to both delays has been performed. Numerical simulations have been carried out to justify the results proved. This model is capable of explaining the long-term dynamics of HIV infection to a greater extent than that of the existing model as it captures some basic parameters involved in the system such as immunological delay and immune response. Similarly, the model also explains the basic understanding of the disease dynamics as a result of activation of the immune response toward the virus. [ABSTRACT FROM AUTHOR]

This paper studies the dynamical behavior of an HIV-1 infection model with saturated virus-target and infected-target incidences with Cytotoxic T Lymphocyte (CTL) immune response. The model is incorporated by two types of intracellular distributed time delays. The model generalizes all the existing HIV-1 infection models with cell-to-cell transmission presented in the literature by considering saturated incidence rate and the effect of CTL immune response. The existence and global stability of all steady states of the model are determined by two parameters, the basic reproduction number () and the CTL immune response activation number (). By using suitable Lyapunov functionals, we show that if , then the infection-free steady state is globally asymptotically stable; if , then the CTL-inactivated infection steady state is globally asymptotically stable; if , then the CTL-activated infection steady state is globally asymptotically stable. Using MATLAB we conduct some numerical simulations to confirm our results. The effect of the saturated incidence of the HIV-1 dynamics is shown. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model for bacterial growth, mutations, horizontal transfer and development of antibiotic resistance. The model is based on the so-called kinetic theory for active particles that is able to capture the main complexity features of the system. Bacterial and immune cells are viewed as active particles whose microscopic state is described by a scalar variable. Particles interact among them and the temporal evolution of the system is described by a generalized distribution function over the microscopic state. The model is derived and tested in a couple of case studies in order to confirm its ability to describe one of the most fundamental problems of modern medicine, namely bacterial resistance to antibiotics. [ABSTRACT FROM AUTHOR]

In this paper, a hepatitis B viral infection model with a density-dependent proliferation rate of cytotoxic T lymphocyte (CTL) cells and immune response delay is investigated. By analyzing the model, we show that the virus-free equilibrium is globally asymptotically stable, if the basic reproductive ratio is less than one and an endemic equilibrium exists if the basic reproductive ratio is greater than one. By using the stability switches criterion in the delay-differential system with delay-dependent parameters, we present that the stability of endemic equilibrium changes and eventually become stable as time delay increases. This means majority of hepatitis B infection would eventually become a chronic infection due to the immune response time delay is fairly long. Numerical simulations are carried out to explain the mathematical conclusions and biological implications. [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]

In this paper, we propose a nonlinear virus dynamics model that describes the interactions of the virus, uninfected target cells, multiple stages of infected cells and B cells and includes multiple discrete delays. We assume that the incidence rate of infection and removal rate of infected cells are given by general nonlinear functions. The model can be seen as a generalization of several humoral immunity viral infection model presented in the literature. We derive two threshold parameters and establish a set of conditions on the general functions which are sufficient to establish the existence and global stability of the three equilibria of the model. We study the global asymptotic stability of the equilibria by using Lyapunov method. We perform some numerical simulations for the model with specific forms of the general functions and show that the numerical results are consistent with the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the tumor-immune dynamics are simulated by solving a nonlinear system of differential equations. The fractional-order mathematical model incorporated with three Michaelis-Menten terms to indicate the saturated effect of immune response, the limited immune response to the tumor and to account the self-limiting production of cytokine interleukin-2. Two types of treatments were considered in the mathematical model to demonstrate the importance of immunotherapy. The limiting values of these treatments were considered, satisfying the stability criteria for fractional differential system. A graphical analysis is made to highlight the effects of antigenicity of the tumor and the fractional-order derivative on the tumor mass. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behaviors for a five-dimensional virus infection model with Latently Infected Cells and Beddington–DeAngelis incidence are investigated. In the model, four delays which denote the latently infected delay, the intracellular delay, virus production period and CTL response delay are considered. We define the basic reproductive number and the CTL immune reproductive number. By using Lyapunov functionals, LaSalle's invariance principle and linearization method, the threshold conditions on the stability of each equilibrium are established. It is proved that when the basic reproductive number is less than or equal to unity, the infection-free equilibrium is globally asymptotically stable; when the CTL immune reproductive number is less than or equal to unity and the basic reproductive number is greater than unity, the immune-free infection equilibrium is globally asymptotically stable; when the CTL immune reproductive number is greater than unity and immune response delay is equal to zero, the immune infection equilibrium is globally asymptotically stable. The results show that immune response delay may destabilize the steady state of infection and lead to Hopf bifurcation. The existence of the Hopf bifurcation is discussed by using immune response delay as a bifurcation parameter. Numerical simulations are carried out to justify the analytical results. [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]

A new mathematical model of chronic hepatitis C virus (HCV) infection incorporating humoral and cell-mediated immune responses, distinct cell proliferation rates for both uninfected and infected hepatocytes, and antiviral treatment all at once, is formulated and analyzed meticulously. Analysis of the model elucidates the existence of multiple equilibrium states. Moreover, the model has a locally asymptotically stable disease-free equilibrium (DFE) whenever the basic reproduction number is less than unity. Local sensitivity analysis (LSA) result exhibits that the most influential (negatively sensitive) parameters on the epidemic threshold are the drug efficacy of blocking virus production and the drug efficacy of removing infection. However, LSA does not accurately assess uncertainty and sensitivity in the system and may mislead us since by default this technique holds all other parameters fixed at baseline values. To overcome this pitfall, one of the most robust and efficient global sensitivity analysis (GSA) methods, which is Latin hypercube sampling-partial rank correlation coefficient technique, elucidates that the proliferation rate of infected hepatocytes and the drug efficacy of killing infected hepatocytes are highly sensitive parameters that affect the transmission dynamics of HCV in any population. Our study suggests that cell proliferation of the infected hepatocytes can be very crucial in controlling disease outbreak. Thus, a future HCV drug that boosts cell-mediated immune response is expected to be quite effective in controlling disease outbreak. [ABSTRACT FROM AUTHOR]

In this investigation, we propose and analyze a virus dynamics model with multi-stages of infected cells. The model incorporates the effect of both humoral and cell-mediated immune responses. We consider two modes of transmissions, virus-to-cell and cell-to-cell. Multiple intracellular discrete-time delays have been integrated into the model. The incidence rate of infection as well as the generation and removal rates of all compartments are described by general nonlinear functions. We derive five threshold parameters which determine the existence of the equilibria of the model under consideration. A set of conditions on the general functions has been established which is sufficient to investigate the global stability of the five equilibria of the model. The global asymptotic stability of all equilibria is proven by utilizing Lyapunov function and LaSalle's invariance principle. The theoretical results are illustrated by numerical simulations of the model with specific forms of the general functions. [ABSTRACT FROM AUTHOR]