Global stability of secondary DENV infection models with non-specific and strain-specific CTLs.

Dengue virus (DENV) is a highly perilous virus that is transmitted to humans through mosquito bites and causes dengue fever. Consequently, extensive efforts are being made to develop effective treatments and vaccines. Mathematical modeling plays a significant role in comprehending the dynamics of DENV within a host in the presence of cytotoxic T lymphocytes (CTL) immune response. This study examines two models for secondary DENV infections that elucidate the dynamics of DENV under the influence of two types of CTL responses, namely non-specific and strain-specific responses. The first model encompasses five compartments, which consist of uninfected monocytes, infected monocytes, free DENV particles, non-specific CTLs, and strain-specific CTLs. In the second model, latently infected cells are introduced into the model. We posit that the CTL responsiveness is determined by a combination of self-regulating CTL response and a predator-prey-like CTL response. The model's solutions are verified to be nonnegativity and bounded and the model possesses two equilibrium states: the uninfected equilibrium EQ0 and the infected equilibrium EQ⁎. Furthermore, we calculate the basic reproduction number R0, which determines the existence and stability of the model's equilibria. We examine the global stability by constructing suitable Lyapunov functions. Our analysis reveals that if R0≤1, then EQ0 is globally asymptotically stable (G.A.S), and if R0>1, then EQ0 is unstable while EQ⁎ is G.A.S. To illustrate our findings analytically, we conduct numerical simulations for each model. Additionally, we perform sensitivity analysis to demonstrate how the parameter values of the proposed model impact R0 given a set of data. Finally, we discuss the implications of including the CTL immune response and latently infected cells in the secondary DENV infection model. Our study demonstrates that incorporating the CTL immune response and latently infected cells diminishes R0 and enhances the system's stability around EQ0.

Stability of a delayed SARS-CoV-2 reactivation model with logistic growth and adaptive immune response.

This paper develops and analyzes a SARS-CoV-2 dynamics model with logistic growth of healthy epithelial cells, CTL immune and humoral (antibody) immune responses. The model is incorporated with four mixed (distributed/discrete) time delays, delay in the formation of latent infected epithelial cells, delay in the formation of active infected epithelial cells, delay in the activation of latent infected epithelial cells, and maturation delay of new SARS-CoV-2 particles. We establish that the model's solutions are non-negative and ultimately bounded. We deduce that the model has five steady states and their existence and stability are perfectly determined by four threshold parameters. We study the global stability of the model's steady states using Lyapunov method. The analytical results are enhanced by numerical simulations. The impact of intracellular time delays on the dynamical behavior of the SARS-CoV-2 is addressed. We noted that increasing the time delay period can suppress the viral replication and control the infection. This could be helpful to create new drugs that extend the delay time period.

Global dynamics of IAV/SARS-CoV-2 coinfection model with eclipse phase and antibody immunity.

Coronavirus disease 2019 (COVID-19) and influenza are two respiratory infectious diseases of high importance widely studied around the world. COVID-19 is caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), while influenza is caused by one of the influenza viruses, A, B, C, and D. Influenza A virus (IAV) can infect a wide range of species. Studies have reported several cases of respiratory virus coinfection in hospitalized patients. IAV mimics the SARS-CoV-2 with respect to the seasonal occurrence, transmission routes, clinical manifestations and related immune responses. The present paper aimed to develop and investigate a mathematical model to study the within-host dynamics of IAV/SARS-CoV-2 coinfection with the eclipse (or latent) phase. The eclipse phase is the period of time that elapses between the viral entry into the target cell and the release of virions produced by that newly infected cell. The role of the immune system in controlling and clearing the coinfection is modeled. The model simulates the interaction between nine compartments, uninfected epithelial cells, latent/active SARS-CoV-2-infected cells, latent/active IAV-infected cells, free SARS-CoV-2 particles, free IAV particles, SARS-CoV-2-specific antibodies and IAV-specific antibodies. The regrowth and death of the uninfected epithelial cells are considered. We study the basic qualitative properties of the model, calculate all equilibria, and prove the global stability of all equilibria. The global stability of equilibria is established using the Lyapunov method. The theoretical findings are demonstrated via numerical simulations. The importance of considering the antibody immunity in the coinfection dynamics model is discussed. It is found that without modeling the antibody immunity, the case of IAV and SARS-CoV-2 coexistence will not occur. Further, we discuss the effect of IAV infection on the dynamics of SARS-CoV-2 single infection and vice versa.

Global dynamics of SARS-CoV-2/malaria model with antibody immune response.

Coronavirus disease 2019 (COVID-19) is a new viral disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Malaria is a parasitic disease caused by Plasmodium parasites. In this paper, we explore a within-host model of SARS-CoV-2/malaria coinfection. This model consists of seven ordinary differential equations that study the interactions between uninfected red blood cells, infected red blood cells, free merozoites, uninfected epithelial cells, infected epithelial cells, free SARS-CoV-2 particles, and antibodies. We show that the model has bounded and nonnegative solutions. We compute all steady state points and derive their existence conditions. We use appropriate Lyapunov functions to confirm the global stability of all steady states. We enhance the reliability of the theoretical results by performing numerical simulations. The steady states reflect the monoinfection and coinfection with malaria and SARS-CoV-2. The shared immune response reduces the concentrations of malaria merozoites and SARS-CoV-2 particles in coinfected patients. This response reduces the severity of SARS-CoV-2 infection in this group of patients.

Global analysis of within-host SARS-CoV-2/HIV coinfection model with latency.

The coronavirus disease 2019 (COVID-19) is a respiratory disease caused by a virus called the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). In this paper, we analyze a within-host SARS-CoV-2/HIV coinfection model. The model is made up of eight ordinary differential equations. These equations describe the interactions between healthy epithelial cells, latently infected epithelial cells, productively infected epithelial cells, SARS-CoV-2 particles, healthy CD 4 + T cells, latently infected CD 4 + T cells, productively infected CD 4 + T cells, and HIV particles. We confirm that the solutions of the developed model are bounded and nonnegative. We calculate the different steady states of the model and derive their existence conditions. We choose appropriate Lyapunov functions to show the global stability of all steady states. We execute some numerical simulations to assist the theoretical contributions. Based on our results, weak CD 4 + T cell immunity in SARS-CoV-2/HIV coinfected patients causes an increase in the concentrations of productively infected epithelial cells and SARS-CoV-2 particles. This may lead to severe SARS-CoV-2 infection in HIV patients. This result agrees with many studies that discussed the high risk of severe infection and death in HIV patients when they get SARS-CoV-2 infection. On the other hand, increasing the death rate of infected epithelial cells during the latency period can reduce the severity of SARS-CoV-2 infection in HIV patients. More studies are needed to understand the dynamics of SARS-CoV-2/HIV coinfection and find better ways to treat this vulnerable group of patients.

Stability analysis of general delayed HTLV-I dynamics model with mitosis and CTL immunity.

This paper formulates and analyzes a general delayed mathematical model which describe the within-host dynamics of Human T-cell lymphotropic virus class I (HTLV-I) under the effect Cytotoxic T Lymphocyte (CTL) immunity. The models consist of four components: uninfected CD$ 4^{+} $T cells, latently infected cells, actively infected cells and CTLs. The mitotic division of actively infected cells are modeled. We consider general nonlinear functions for the generation, proliferation and clearance rates for all types of cells. The incidence rate of infection is also modeled by a general nonlinear function. These general functions are assumed to be satisfy some suitable conditions. To account for series of events in the infection process and activation of latently infected cells, we introduce two intracellular distributed-time delays into the models: (ⅰ) delay in the formation of latently infected cells, (ⅱ) delay in the activation of latently infected cells. We determine a bounded domain for the system's solutions. We calculate two threshold numbers, the basic reproductive number $ R_{0} $ and the CTL immunity stimulation number $ R_{1} $. We determine the conditions for the existence and global stability of the equilibrium points. We study the global stability of all equilibrium points using Lyapunov method. We prove the following: (a) if $ R_{0}\leq 1 $, then the infection-free equilibrium point is globally asymptotically stable (GAS), (b) if $ R_{1}\leq 1 < R_{0} $, then the infected equilibrium point without CTL immunity is GAS, (c) if $ R_{1} > 1 $, then the infected equilibrium point with CTL immunity is GAS. We present numerical simulations for the system by choosing special shapes of the general functions. The effects of proliferation of CTLs and time delay on the HTLV-I progression is investigated. We noted that the CTL immunity does not play the role in clearing the HTLV-I from the body, but it has an important role in controlling and suppressing the viral infection. On the other hand, we observed that, increasing the time delay intervals can have similar influences as drug therapies in removing viruses from the body. This gives some impression to develop two types of treatments, the first type aims to extend the intracellular delay periods, while the second type aims to activate and stimulate the CTL immune response.

Analysis of an HTLV/HIV dual infection model with diffusion.

In the literature, several HTLV-I and HIV single infections models with spatial dependence have been developed and analyzed. However, modeling HTLV/HIV dual infection with diffusion has not been studied. In this work we derive and investigate a PDE model that describes the dynamics of HTLV/HIV dual infection taking into account the mobility of viruses and cells. The model includes the effect of Cytotoxic T lymphocytes (CTLs) immunity. Although HTLV-I and HIV primarily target the same host, CD4+T cells, via infected-to-cell (ITC) contact, however the HIV can also be transmitted through free-to-cell (FTC) contact. Moreover, HTLV-I has a vertical transmission through mitosis of active HTLV-infected cells. The well-posedness of solutions, including the existence of global solutions and the boundedness, is justified. We derive eight threshold parameters which govern the existence and stability of the eight steady states of the model. We study the global stability of all steady states based on the construction of suitable Lyapunov functions and usage of Lyapunov-LaSalle asymptotic stability theorem. Lastly, numerical simulations are carried out in order to verify the validity of our theoretical results.

Global dynamics of SARS-CoV-2/cancer model with immune responses.

The world is going through a critical period due to a new respiratory disease called coronavirus disease 2019 (COVID-19). This disease is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Mathematical modeling is one of the most important tools that can speed up finding a drug or vaccine for COVID-19. COVID-19 can lead to death especially for patients having chronic diseases such as cancer, AIDS, etc. We construct a new within-host SARS-CoV-2/cancer model. The model describes the interactions between six compartments: nutrient, healthy epithelial cells, cancer cells, SARS-CoV-2 virus particles, cancer-specific CTLs, and SARS-CoV-2-specific antibodies. We verify the nonnegativity and boundedness of its solutions. We outline all possible equilibrium points of the proposed model. We prove the global stability of equilibria by constructing proper Lyapunov functions. We do some numerical simulations to visualize the obtained results. According to our model, lymphopenia in COVID-19 cancer patients may worsen the outcomes of the infection and lead to death. Understanding dysfunctions in immune responses during COVID-19 infection in cancer patients could have implications for the development of treatments for this high-risk group.

Modeling and analysis of a within-host HIV/HTLV-I co-infection.

Human immunodeficiency virus (HIV) and human T-lymphotropic virus type I (HTLV-I) are two retroviruses that attack the CD4 + T cells and impair their functions. Both HIV and HTLV-I can be transmitted between individuals through direct contact with certain body fluids from infected individuals. Therefore, a person can be co-infected with both viruses. HIV causes acquired immunodeficiency syndrome (AIDS), while HTLV-I is the causative agent for adult T-cell leukemia (ATL) and HTLV-I-associated myelopathy/tropical spastic paraparesis (HAM/TSP). Several mathematical models have been developed in the literature to describe the within-host dynamics of HIV and HTLV-I mono-infections. However, modeling a within-host dynamics of HIV/HTLV-I co-infection has not been involved. The present paper is concerned with the formulation and investigation of 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 HTLV-infected cells, free HIV particles, HIV-specific CTLs and HTLV-specific CTLs. The HIV can spread by virus-to-cell transmission. On the other side, HTLV-I has two modes of transmission, (i) horizontal transmission via direct cell-to-cell contact through the virological synapse, and (ii) vertical transmission through the mitotic division of Tax-expressing HTLV-infected cells. The well-posedness of the model is established by showing that the solutions of the model are nonnegative and bounded. We define a set of 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 Lyapunov-LaSalle asymptotic stability theorem. 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.

Stability of HTLV/HIV dual infection model with mitosis and latency.

In this paper, we formulate and analyze an HTLV/HIV dual infection model taking into consideration the response of Cytotoxic T lymphocytes (CTLs). The model includes eight compartments, uninfected CD4+T cells, latent HIV-infected cells, active HIV-infected cells, free HIV particles, HIV-specific CTLs, latent HTLV-infected cells, active HTLV-infected cells and HTLV-specific CTLs. The HIV can enter and infect an uninfected CD4+T cell by two ways, free-to-cell and infected-to-cell. Infected-to-cell spread of HIV occurs when uninfected CD4+T cells are touched with active or latent HIV-infected cells. In contrast, there are two modes for HTLV-I transmission, (ⅰ) horizontal, via direct infected-to-cell touch, and (ⅱ) vertical, by mitotic division of active HTLV-infected cells. We analyze the model by proving the nonnegativity and boundedness of the solutions, calculating all possible steady states, deriving a set of key threshold parameters, and proving the global stability of all steady states. The global asymptotic stability of all steady states is proven by using Lyapunov-LaSalle asymptotic stability theorem. We performed numerical simulations to support and illustrate the theoretical results. In addition, we compared between the dynamics of single and dual infections.

Analysis of a within-host HIV/HTLV-I co-infection model with immunity.

Human immunodeficiency virus (HIV) and human T-lymphotropic virus type I (HTLV-I) are two retroviruses that attack the immune cells and impair their functions. Both HIV and HTLV-I can be transmitted between individuals through direct contact with certain body fluids from infected individuals. Therefore, a person can be co-infected with both viruses. HIV causes acquired immunodeficiency syndrome, while HTLV-I is the causative agent for adult T-cell leukemia and HTLV-I-associated myelopathy/tropical spastic paraparesis. Several mathematical models have been developed in the literature to describe the within-host dynamics of HIV and HTLV-I mono-infections. However, modeling a within-host dynamics of HIV/HTLV-I co-infection has not been involved. In the present paper, we are concerned to formulate and analyze a new HIV/HTLV 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 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 and cell-to-cell. On the other side, HTLV-I has two modes of transmission, (i) horizontal transmission via direct cell-to-cell contact, and (ii) vertical transmission through mitotic division of Tax-expressing HTLV-infected cells. The well-posedness of the model is established by showing that the solutions of the model are nonnegative and bounded. We define a set of 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 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.

Stability of an adaptive immunity delayed HIV infection model with active and silent cell-to-cell spread.

This paper investigates an adaptive immunity HIV infection model with three types of distributed time delays. The model describes the interaction between healthy CD4+T cells, silent infected cells, active infected cells, free HIV particles, Cytotoxic T lymphocytes (CTLs) and antibodies. The healthy CD4+T cells can be infected when they contacted by free HIV particles or silent infected cells or 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 the virus and cells are represented by general functions. The model is an improvement of the existing HIV infection models which have neglected the infection due to the incidence between the silent infected cells and healthy CD4+T cells. We show that the model is well posed and it has five equilibria and their existence are governed by five threshold parameters. Under a set of conditions on the general functions and the threshold parameters, 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 and time delays on the dynamical behavior of the system. We have shown that the inclusion of time delay can significantly increase the concentration of the healthy CD4+ T cells and reduce the concentrations of the infected cells and free HIV particles. While the inclusion of CTC transmission decreases the concentration of the healthy CD4+ T cells and increases the concentrations of the infected cells and free HIV particles.

Global stability of discrete virus dynamics models with humoural immunity and latency.

This paper studies the global stability of discrete-time viral infection models with humoural immunity. We consider both latently and actively infected cells. We study also a model with general production and clearance rates of all compartments as well as general incidence rate of infection. We use nonstandard finite difference method to discretize the continuous-time models. The positivity and boundedness of solutions of the discrete models are established. We establish by using Lyapunov method, the global stability of equilibria in terms of the basic reproduction number [Formula: see text] and the humoural immune response activation number [Formula: see text]. The results signify that the infection dies out if [Formula: see text]. Moreover, the infection persists with inactive immune response if [Formula: see text] and with active immune response if [Formula: see text]. We illustrate our theoretical results by using numerical simulations.

Stability of an adaptive immunity viral infection model with multi-stages of infected cells and two routes of infection.

This paper studies an (n + 4)-dimensional nonlinear viral infection model that characterizes the interactions of the viruses, susceptible host cells, n-stages of infected cells, CTL cells and B cells. Both viral and cellular infections have been incorporated into the model. The well-posedness of the model is justified. The model admits five equilibria which are determined by five threshold parameters. 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.

Stability of latent pathogen infection model with adaptive immunity and delays.

In this paper we propose and analyze a pathogen dynamics model with antibody and Cytotoxic T Lymphocyte (CTL) immune responses. We incorporate latently infected cells and three distributed time delays into the model. We show that the solutions of the proposed model are nonnegative and ultimately bounded. We derive four threshold parameters which fully determine the existence and stability of the five steady states of the model. Using Lyapunov functionals, we established the global stability of the steady states of the model. The theoretical results are confirmed by numerical simulations.

Global stability analysis of humoral immunity virus dynamics model including latently infected cells.

In this paper, we propose and analyse a virus dynamics model with humoral immune response including latently infected cells. The incidence rate is given by Beddington-DeAngelis functional response. We have derived two threshold parameters, the basic infection reproduction number R0 and the humoral immune response activation number R1 which completely determined the basic and global properties of the virus dynamics model. By constructing suitable Lyapunov functions and applying LaSalle's invariance principle we have proven that if R0 ≤ 1, then the infection-free equilibrium is globally asymptotically stable (GAS), if R1 ≤ 1 < R0, then the chronic-infection equilibrium without humoral immune response is GAS, and if R1 > 1, then the chronic-infection equilibrium with humoral immune response is globally asymptotically stable. These results are further illustrated by numerical simulations.

Global stability of HIV infection of CD4+ T cells and macrophages with CTL immune response and distributed delays.

We study the global stability of a human immunodeficiency virus (HIV) infection model with Cytotoxic T Lymphocytes (CTL) immune response. The model describes the interaction of the HIV with two classes of target cells, CD4(+) T cells and macrophages. Two types of distributed time delays are incorporated into the model to describe the time needed for infection of target cell and virus replication. Using the method of Lyapunov functional, we have established that the global stability of the model is determined by two threshold numbers, the basic reproduction number R0 and the immune response reproduction number R0(∗). We have proven that, if R0 ≤ 1, then the uninfected steady state is globally asymptotically stable (GAS), if R0* ≤ 1 < R0, then the infected steady state without CTL immune response is GAS, and, if R0* > 1, then the infected steady state with CTL immune response is GAS.