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Human T-lymphotropic virus type 2 (HTLV-2) and human immunodeficiency virus type 1 (HIV-1) are two infectious retroviruses that infect immune cells, CD8+ T cells and CD4+ T cells, respectively. Multiple studies have revealed co-infected patients with HTLV-2 and HIV-1. In this paper, we formulated a new mathematical model for the co-infection of HTLV-2 and HIV-1 in vivo. The HIV-1-specific B-cell response is included. Six ordinary differential equations made up the model, which depicted the interactions between uninfected CD4+ T cells, HIV-1-infected CD4+ T cells, HIV-1 particles, uninfected CD8+ T cells, HTLV-2-infected CD8+ T cells, and HIV-1-specific B cells. We carried out a thorough study of the model, demonstrating the boundedness and nonnegativity of the solutions. Additionally, we determined the equilibrium points and demonstrated, under specific conditions, their global stability. The global asymptotic stability of all equilibria was established by constructing appropriate Lyapunov functions and applying the Lyapunov-LaSalle asymptotic stability theorem. We provide numerical simulations to corroborate the theoretical findings. We investigated how the B-cell response affects the dynamics of HIV-1 and HTLV-2 co-infection. The results suggested that the B-cell response regulates and inhibits the spread of HIV-1. We present a comparison between HTLV-2 or HIV-1 mono-infections and co-infections with HTLV-2 and HIV-1. Our findings support earlier research, suggesting that co-infection with HTLV-2 may be able to maintain the behavior dynamics of the CD4+ T cells, inhibit HIV-1 replication, and postpone the onset of AIDS. However, co-infected patients with HTLV-2 and HIV-1 may experience a greater occurrence of HTLV-2-related T-cell malignant diseases. [ABSTRACT FROM AUTHOR]

Severe acute respiratory syndrome coronavirus 2 (SARS‐CoV‐2) and influenza A virus (IAV) are two respiratory viruses and are similar concerning seasonal occurrence, transmission routes, clinical manifestations, and related immune responses. Recent studies showed that a substantial number of patients infected by SARS‐CoV‐2 were also coinfected with IAV. In this paper, we study the global properties of SARS‐CoV‐2 and IAV coinfection model in vivo. The role of humoral (antibody) immunity in controlling the coinfection is modeled. The model tracks uninfected epithelial cells, latent SARS‐CoV‐2‐infected epithelial cells, latent IAV‐infected epithelial cells, active SARS‐CoV‐2‐infected epithelial cells, active IAV‐infected epithelial cells, free SARS‐CoV‐2 particles, free IAV particles, SARS‐CoV‐2‐specific antibodies and IAV‐specific antibodies. The model includes six distributed‐time delays, two delays for the formation of latent SARS‐CoV‐2‐infected and latent IAV‐infected cells; two delays for the reactivation of latent SARS‐CoV‐2‐infected cells and latent IAV‐infected cells; and two delays for the maturation of new released SARS‐CoV‐2 and IAV virions. The regeneration and death of the uninfected epithelial cells are considered. We first examine the basic qualitative properties of the model, then we calculate all equilibria and prove their global stability. The global stability of equilibria is established using the Lyapunov method. The theoretical findings are demonstrated via numerical simulations. The importance of considering humoral immunity in the coinfection dynamics model is discussed. It is found that without modeling the humoral immunity, the case of IAV and SARS‐CoV‐2 coexistence will not occur. We discuss the effect of time delays on the dynamics of SARS‐CoV‐2 and IAV coinfection. It is noted that increasing the time delay length has similar impact as antiviral therapies. [ABSTRACT FROM AUTHOR]

Human immunodeficiency virus type 1 (HIV-1) gradually destroys the CD4+ T cells leading to immune system dysfunction. HIV-1 can result in acquired immunodeficiency syndrome (AIDS) if antiretroviral drugs are not used. HIV/AIDS patients are more vulnerable to opportunistic infections or cancers. Human herpesvirus 8 (HHV-8) targets B cells and causes an AIDS-related cancer known as kaposi sarcoma (KS). Numerous investigations have demonstrated co-infection instances between HIV-1 and HHV-8. In this research, we investigated the co-dynamics of HIV-1 and HHV-8 in vivo using a system of delay differential equations (DDEs). The model explained the interactions between uninfected CD4+ T cells, latently/actively HIV-1-infected CD4+ T cells, free HIV1 particles, uninfected B cells, latently/actively HHV-8-infected B cells, and free HHV-8 particles. Eight distributed-time delays were incorporated into the model to account for the delays that arose during the generation of both actively and latently infected cells, the activation of latent reservoirs, and the maturation of freshly discharged virions. By examining the nonnegativity and boundedness of the solutions, we demonstrated that the model was both mathematically and biologically well-posed. We calculated the model’s equilibria and threshold numbers. We studied the global asymptotic stability of the model’s equilibria by building appropriate Lyapunov functionals and applying the Lyapunov-LaSalle asymptotic stability theorem. Numerical simulations were used to display the results. For the basic reproduction numbers of HHV-8 single-infection (R1) and HIV-1 single-infection (R2), sensitivity analysis was carried out. Comparing HIV-1 or HHV-8 single infections with co-infections of HHV-8 and HIV-1 was shown. It’s interesting to note that we detected larger amounts of HHV-8 and HIV-1 when they co-infect than when they are infected alone. This outcome aligned with several findings seen in the literature. The effect of antiviral drugs and time delays on the co-dynamics of HIV-1 and HHV-8 was investigated. We found that the delay parameter and drug effectiveness both contributed to a decrease in the basic reproduction numbers, R1 and R2. Less treatment efficacies will be needed to keep the system at the infection-free equilibrium and remove HIV-1 and HHV-8 from the body if a model with time delays is employed. [ABSTRACT FROM AUTHOR]

Several mathematical models of two competing viruses (or viral strains) that have been published in the literature assume that the infection rate is determined by bilinear incidence. These models do not show co-existence equilibrium; moreover, they might not be applicable in situations where the virus concentration is high. In this paper, we developed a mathematical model for the co-dynamics of two competing viruses with saturated incidence. The model included the latently infected cells and three types of time delays: discrete (or distributed): (i) The formation time of latently infected cells; (ii) The activation time of latently infected cells; (iii) The maturation time of newly released virions. We established the mathematical well-posedness and biological acceptability of the model by examining the boundedness and nonnegativity of the solutions. Four equilibrium points were identified, and their stability was examined. Through the application of Lyapunov's approach and LaSalle's invariance principle, we demonstrated the global stability of equilibria. The impact of saturation incidence, latently infected cells, and time delay on the viral co-dynamics was examined. We demonstrated that the saturation could result in persistent viral coinfections. We established conditions under which these types of viruses could coexist. The coexistence conditions were formulated in terms of saturation constants. These findings offered new perspectives on the circumstances under which coexisting viruses (or strains) could live in stable viral populations. It was shown that adding the class of latently infected cells and time delay to the coinfection model reduced the basic reproduction number for each virus type. Therefore, fewer treatment efficacies would be needed to keep the system at the infection-free equilibrium and remove the viral coinfection from the body when utilizing a model with latently infected cells and time delay. To demonstrate the associated mathematical outcomes, numerical simulations were conducted for the model with discrete delays. [ABSTRACT FROM AUTHOR]

In this paper we construct a class of virus dynamics models with impairment of B-cell functions. Two forms of the incidence rate have been considered, saturated and general. The well-posedness of the models is justified. The models admit two equilibria which are determined by the basic reproduction number R0. 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.

Although some patients with coronavirus disease 2019 (COVID-19) develop only mild symptoms, fatal complications have been observed among those with underlying diseases. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the causative of COVID-19. Human T-cell lymphotropic virus type-I (HTLV-I) infection can weaken the immune system even in asymptomatic carriers. The objective of the present study is to formulate a new mathematical model to describe the co-dynamics of SARS-CoV-2 and HTLV-I in a host. We first investigate the properties of the model's solutions, and then we calculate all equilibria and study their global stability. The global asymptotic stability is examined by constructing Lyapunov functions. The analytical findings are supported via numerical simulation. Comparison between the solutions of the SARS-CoV-2 mono-infection model and SARS-CoV-2/HTLV-I coinfection model is given. Our proposed model suggest that the presence of HTLV-I suppresses the immune response, enhances the SARS-CoV-2 infection and, consequently, may increase the risk of COVID-19. Our developed coinfection model can contribute to understanding the SARS-CoV-2 and HTLV-I co-dynamics and help to select suitable treatment strategies for COVID-19 patients who are infected with HTLV-I. [ABSTRACT FROM AUTHOR]

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a novel respiratory virus that causes coronavirus disease 2019 (COVID-19). Symptoms of COVID-19 range from mild to severe illness. It was observed that disease progression in COVID-19 patients depends on their immune response, especially in elderly patients whose immune system suppression may put them at increased risk of infection. Human T-cell lymphotropic virus type-I (HTLV-I) attacks the CD4+ T cells (T cells) of the immune system and leads to immune dysfunction. Co-infection with HTLV-I and SARS-CoV-2 has been reported in recent studies. Modeling HTLV-I and SARS-CoV-2 co-infection can be a helpful tool to understand the in-host co-dynamics of these viruses. The aim of this study was to construct a model that characterizes the in-host dynamics of HTLV-I and SARS-CoV-2 co-infection. By considering the mobility of the viruses and cells, the model is represented by a system of partial differential equations (PDEs). The system contains two independent variables, time t and position x, and seven dependent variables for representing the densities of healthy epithelial cells (ECs), latent SARS-CoV-2-infected ECs, active SARS-CoV-2-infected ECs, SARS-CoV-2, healthy T cells, latent HTLV-I-infected T cells and active HTLV-I-infected T cells. We first studied the fundamental properties of the solutions of the system, then deduced all steady states and proved their global properties. We examined the global stability of the steady states by constructing appropriate Lyapunov functions. The analytical results were illustrated by performing numerical simulations. We discussed the effect of HTLV-I infection on COVID-19 progression. The results suggest that patients with HTLV-I have a weakened immune response; consequently, their risk of COVID-19 infection may be increased. [ABSTRACT FROM AUTHOR]

Infection with human immunodeficiency virus type 1 (HIV-1) or human T-lymphotropic virus type I (HTLV-I) or both can lead to mortality. CD4+T cells are the target for both HTLV-I and HIV-1. In addition, HIV-1 can infect macrophages. CD4+T cells and macrophages play important roles in the immune system response. This article develops and analyzes a discrete-time HTLV-I and HIV-1 co-infection model. The model depicts the within-host interaction of six compartments: uninfected CD4+T cells, HIV-1-infected CD4+T cells, uninfected macrophages, HIV-1-infected macrophages, free HIV-1 particles and HTLV-I-infected CD4+T cells. The discrete-time model is obtained by discretizing the continuous-time model via the nonstandard finite difference (NSFD) approach. We show that NSFD preserves the positivity and boundedness of the model's solutions. We deduce four threshold parameters that control the existence and stability of the four equilibria of the model. The Lyapunov method is used to examine the global stability of all equilibria. The analytical findings are supported via numerical simulation. The model can be useful when one seeks to design optimal treatment schedules using optimal control theory. [ABSTRACT FROM AUTHOR]

Co-infections with respiratory viruses were reported in hospitalized patients in several cases. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and influenza A virus (IAV) are two respiratory viruses and are similar in terms of their seasonal occurrence, clinical manifestations, transmission routes, and related immune responses. SARS-CoV-2 is the cause of coronavirus disease 2019 (COVID-19). In this paper, we study the dynamic behaviors of an influenza and COVID-19 co-infection model in vivo. The role of humoral (antibody) immunity in controlling the co-infection is modeled. The model considers the interactions among uninfected epithelial cells (ECs), SARS-CoV-2-infected ECs, IAV-infected ECs, SARS-CoV-2 particles, IAV particles, SARS-CoV-2 antibodies, and IAV antibodies. The model is given by a system of delayed ordinary differential equations (DODEs), which include four time delays: (i) a delay in the SARS-CoV-2 infection of ECs, (ii) a delay in the IAV infection of ECs, (iii) a maturation delay of newly released SARS-CoV-2 virions, and (iv) a maturation delay of newly released IAV virions. We establish the non-negativity and boundedness of the solutions. We examine the existence and stability of all equilibria. The Lyapunov method is used to prove the global stability of all equilibria. The theoretical results are supported by performing numerical simulations. We discuss the effects of antiviral drugs and time delays on the dynamics of influenza and COVID-19 co-infection. It is noted that increasing the delay length has a similar influence to that of antiviral therapies in eradicating co-infection from the body. [ABSTRACT FROM AUTHOR]

Studies have reported several cases with respiratory viruses coinfection in hospitalized patients. Influenza A virus (IAV) mimics the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) with respect to seasonal occurrence, transmission routes, clinical manifestations and related immune responses. The present paper aimed to develop and investigate a mathematical model to study the dynamics of IAV/SARS-CoV-2 coinfection within the host. The influence of SARS-CoV-2-specific and IAV-specific antibody immunities is incorporated. The model simulates the interaction between seven compartments, uninfected epithelial cells, SARS-CoV-2-infected cells, 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 investigate the global stability of all equilibria. The global stability of equilibria is established using the Lyapunov method. We perform numerical simulations and demonstrate that they are in good agreement with the theoretical results. The importance of including the antibody immunity into the coinfection dynamics model is discussed. We have found that without modeling the antibody immunity, the case of IAV and SARS-CoV-2 coexistence is not observed. Finally, we discuss the influence of IAV infection on the dynamics of SARS-CoV-2 single-infection and vice versa. [ABSTRACT FROM AUTHOR]

The mathematical modeling and analysis of within-host or between-host coronavirus disease 2019 (COVID-19) dynamics are considered robust tools to support scientific research. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the cause of COVID-19. This paper proposes and investigates a within-host COVID-19 dynamics model with latent infection, the logistic growth of healthy epithelial cells and the humoral (antibody) immune response. Time delays can affect the dynamics of SARS-CoV-2 infection predicted by mathematical models. Therefore, we incorporate four time delays into the model: (i) delay in the formation of latent infected epithelial cells, (ii) delay in the formation of active infected epithelial cells, (iii) delay in the activation of latent infected epithelial cells, and (iv) maturation delay of new SARS-CoV-2 particles. We establish that the model's solutions are non-negative and ultimately bounded. This confirms that the concentrations of the virus and cells should not become negative or unbounded. We deduce that the model has three steady states and their existence and stability are perfectly determined by two threshold parameters. We use Lyapunov functionals to confirm the global stability of the model's steady states. The analytical results are enhanced by numerical simulations. The effect of time delays on the SARS-CoV-2 dynamics is investigated. We observe that increasing time delay values can have the same impact as drug therapies in suppressing viral progression. This offers some insight useful to develop a new class of treatment that causes an increase in the delay periods and then may control SARS-CoV-2 replication. [ABSTRACT FROM AUTHOR]

In this work we present two mathematical models for the infection dynamics of scabies. The dynamics is described by four-dimensional system of ordinary differential equations that expresses the transmissions between susceptible and infectious/infective individuals. In the second model, we include the importance of adult scabiei mite in the real interaction with hosts. Nonnegativity and boundedness of solutions of the models are conducted. A threshold parameter is calculated for each model which ensures the existence of all corresponding equilibria. Using candidate Lyapunov functions, it is shown that whenever the threshold parameter is less than or equal unity, the models have an associated disease-free equilibrium that is globally asymptotically stable. In addition, when the threshold exceeds unity the models have a globally asymptotically stable endemic equilibrium. Finally, using some parameter values related to the scabies infection dynamics, numerical simulation results are demonstrated to clarify the main theoretical results. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]