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The coronavirus disease 2019 (COVID-19) is a respiratory disease that appeared in 2019 caused by a virus called severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). COVID-19 is still spreading and causing deaths around the world. There is a real concern of SARS-CoV-2 coinfection with other infectious diseases. Tuberculosis (TB) is a bacterial disease caused by Mycobacterium tuberculosis (Mtb). SARS-CoV-2 coinfection with TB has been recorded in many countries. It has been suggested that the coinfection is associated with severe disease and death. Mathematical modeling is an effective tool that can help understand the dynamics of coinfection between new diseases and well-known diseases. In this paper, we develop an in-host TB and SARS-CoV-2 coinfection model with cytotoxic T lymphocytes (CTLs). The model investigates the interactions between healthy epithelial cells (ECs), latent Mtb-infected ECs, active Mtb-infected ECs, SARS-CoV-2-infected ECs, free Mtb, free SARS-CoV-2, and CTLs. The model's solutions are proved to be nonnegative and bounded. All equilibria with their existence conditions are calculated. Proper Lyapunov functions are selected to examine the global stability of equilibria. Numerical simulations are implemented to verify the theoretical results. It is found that the model has six equilibrium points. These points reflect two states: the mono-infection state where SARS-CoV-2 or TB occurs as a single infection, and the coinfection state where the two infections occur simultaneously. The parameters that control the movement between these states should be tested in order to develop better treatments for TB and COVID-19 coinfected patients. Lymphopenia increases the concentration of SARS-CoV-2 particles and thus can worsen the health status of the coinfected patient. [ABSTRACT FROM AUTHOR]

In this paper, we propose and study a Middle East respiratory syndrome coronavirus (MERS-CoV) infection model with cytotoxic T lymphocyte (CTL) immune response and intracellular delay. This model includes five compartments: uninfected cells, infected cells, viruses, dipeptidyl peptidase 4 (DPP4), and CTL immune cells. We obtained an immunity-inactivated reproduction number R 0 and an immunity-activated reproduction number R 1 . By analyzing the distributions of roots of the corresponding characteristic equations, the local stability results of the infection-free equilibrium, the immunity-inactivated equilibrium, and the immunity-activated equilibrium were obtained. Moreover, by constructing suitable Lyapunov functionals and combining LaSalle's invariance principle and Barbalat's lemma, some sufficient conditions for the global stability of the three types of equilibria were obtained. It was found that the infection-free equilibrium is globally asymptotically stable if R 0 ≤ 1 and unstable if R 0 > 1 ; the immunity-inactivated equilibrium is locally asymptotically stable if R 0 > 1 > R 1 and globally asymptotically stable if R 0 > 1 > R 1 and condition (H1) holds, but unstable if R 1 > 1 ; and the immunity-activated equilibrium is locally asymptotically stable if R 1 > 1 and is globally asymptotically stable if R 1 > 1 and condition (H1) holds. [ABSTRACT FROM AUTHOR]

In this paper, a deterministic model characterizing the within-host infection of Hepatitis C virus (HCV) in intrahepatic and extrahepatic tissues is presented. In addition, the model also includes the effect of the cytotoxic T lymphocyte (CTL) immunity described by a linear activation rate by infected cells. Firstly, the non-negativity and boundedness of solutions of the model are established. Secondly, the basic reproduction number R 01 and immune reproduction number R 02 are calculated, respectively. Three equilibria, namely, infection-free, CTL immune response-free and infected equilibrium with CTL immune response are discussed in terms of these two thresholds. Thirdly, the stability of these three equilibria is investigated theoretically as well as numerically. The results show that when R 01 < 1 , the virus will be cleared out eventually and the CTL immune response will also disappear; when R 02 < 1 < R 01 , the virus persists within the host, but the CTL immune response disappears eventually; when R 02 > 1 , both of the virus and the CTL immune response persist within the host. Finally, a brief discussion will be given. [ABSTRACT FROM AUTHOR]

This paper studies the global dynamics of a general diffusive hepatitis B virus (HBV) infection model. The model includes both enveloped viruses and DNA containing capsids. Two immune responses are recruited to attack the virus and infected hepatocytes. These are the cytotoxic T-lymphocytes (CTL) which kill the infected liver cells, and B cells which send antibodies to attack the virus. The non-negativity and boundedness of the solutions are discussed. The existence of spatially homogeneous equilibrium points is examined. The global stability of all possible equilibrium points is proved by choosing suitable Lyapunov functionals. Some numerical simulations are performed to enhance the theoretical results and present the behavior of solutions in space and time. [ABSTRACT FROM AUTHOR]

A modified mathematical model describing the human immunodeficiency virus (HIV) pathogenesis with cytotoxic T-lymphocytes (CTL) and infected cells in eclipse phase is presented and studied in this paper. The model under consideration also includes a saturated rate describing viral infection. First, the positivity and boundedness of solutions for nonnegative initial data are proved. Next, the global stability of the disease free steady state and the endemic steady states are established depending on the basic reproduction number R0 and the CTL immune response reproduction number RCTL. Moreover, numerical simulations are performed in order to show the numerical stability for each steady state and to support our theoretical findings. Our model based findings suggest that system immunity represented by CTL may control viral replication and reduce the infection. [ABSTRACT FROM AUTHOR]

Human T-lymphotropic virus type I (HTLV-I) and human immunodeficiency virus (HIV) are two famous retroviruses that share similarities in their genomic organization, and differ in their life cycle as well. It is known that HTLV-I and HIV have in common a way of transmission via direct contact with certain body fluids related to infected patients. Thus, it is not surprising that a single-infected person with one of these viruses can be dually infected with the other virus. In the literature, many researchers have devoted significant efforts for modeling and analysis of HTLV or HIV single infection. However, the dynamics of HTLV/HIV dual infection has not been formulated. In the present paper, we formulate an HTLV/HIV dual infection model. The model includes the impact of the Cytotoxic T lymphocyte (CTLs) immune response, which is important to control the dual infection. The model describes the interaction between uninfected CD 4 + T cells, HIV-infected cells, HTLV-infected cells, free HIV particles, HIV-specific CTLs, and HTLV-specific CTLs. We establish that the solutions of the model are non-negative and bounded. We calculate all steady states of the model and deduce the threshold parameters which determine the existence and stability of the steady states. We prove the global asymptotic stability of all steady states by utilizing the Lyapunov function and Lyapunov–LaSalle asymptotic stability theorem. We solve the system numerically to illustrate the our main results. In addition, we compared between the dynamics of single and dual infections. [ABSTRACT FROM AUTHOR]

In this paper, we study a diffusive and delayed virus dynamics model with Beddington–DeAngelis incidence and CTL immune response. By constructing Lyapunov functionals, we show that if the basic reproductive number is less than or equal to one, then the infection-free equilibrium is globally asymptotically stable; if the immune reproductive number is less than or equal to one and the basic reproductive number is greater than one, then the immune-free equilibrium is globally asymptotically stable; if the immune reproductive number is greater than one, then the interior equilibrium is globally asymptotically stable. [ABSTRACT FROM AUTHOR]

In this paper, we propose and investigate a diffusive viral infection model with distributed delays and cytotoxic T lymphocyte (CTL) immune response. Also, both routes of infection that are virus-to-cell infection and cell-to-cell transmission are modeled by two general nonlinear incidence functions. The well-posedness of the proposed model is also proved by establishing the global existence, uniqueness, nonnegativity and boundedness of solutions. Moreover, the threshold parameters and the global asymptotic stability of equilibria are obtained. Furthermore, diffusive and delayed virus dynamics models presented in many previous studies are improved and generalized. [ABSTRACT FROM AUTHOR]

In this paper, we consider the combined effects of cytotoxic T lymphocyte (CTL) responses on the competition dynamics of two Simian immunodeficiency virus (SIV) strains model. One of strains concerns a relatively slowly replicating and mildly cytopathic virus in the early infection (SIVMneCL8), the other is faster replicating and more cytopathic virus at later stages of the infection (SIVMne170). It is shown that the global dynamics of the ordinary differential equations can be determined by several threshold parameters, and we prove the global stability of the equilibria by rigorous mathematical analysis. To account for a series of infection mechanism leading to viral production, we incorporate time delays in the infection term. Using the methods of constructing suitable Lyapunov functionals and LaSalle’s invariance principle, we obtain the sufficient conditions for the global attractiveness of infection-free equilibrium with both virus strains going extinct, single-infection equilibrium with one of two virus strains out-competing the other one and the two strains coexisting infection equilibrium. We establish that the intracellular delays can destabilize the single-infection equilibrium leading to Hopf bifurcation and periodic oscillations. We show that introduction of immune responses is responsible for the coexistence of two virus strains and the intracellular delays may alter the two-strain competition results. Numerical simulations are presented to illustrate the theoretical conclusions. [ABSTRACT FROM AUTHOR]