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This paper is devoted to proposing a mathematical model in order to explore the dynamics of HTLV-Ⅰ (human T-cell leukemia virus type-Ⅰ) infection, in which the closely related target cell-virus-immune system interaction and the time-delay cytotoxic T lymphocyte (CTL) immune response are taken into consideration. Firstly, we give the relevant lemma for the existence of feasible equilibrium points of the model, and then further certify the global asymptotic stabilities of the infection-free equilibrium (IFFE) $ E_1 $ and the immune-free equilibrium (IMFE) $ E_2 $. Furthermore, we research the existence of Hopf bifurcation (HB) occurring at the immune equilibrium (IE) $ E^* $ due to the influence of the delay bifurcation parameter. Also, the numerical simulations confirm this fact. In addition, we obtain the explicit expressions which determine the direction and stability of HB. Finally, a succinct discussion shows that the delay in CTL response can destabilize $ E^* $ and generate HB, but not affect stabilities of $ E_1 $ and $ E_2 $. [ABSTRACT FROM AUTHOR]

Mathematical modeling of human immunodeficiency virus (HIV) and human T-lymphotropic virus type Ⅰ (HTLV-I) mono-infections has received considerable attention during the last decades. These two viruses share the same way of transmission between individuals; through direct contact with certain contaminated body fluids. Therefore, a person can be co-infected with both viruses. In the present paper, we construct and analyze 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 CD 4 + 4 + T cells, silent HIV-infected cells, active HIV-infected cells, silent HTLV-infected cells, Tax-expressing (active) 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 (VTC) and cell-to-cell (CTC). Both active and silent HIV-infected cells can infect the susceptible CD 4 + 4 + T cells by CTC mechanism. On the other side, HTLV-I has only one mode of transmission via direct cell-to-cell contact. The well-posedness of the model is established by showing that the solutions of the model are nonnegative and bounded. We calculate all possible equilibria and define the key 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 discussed the influence of CTL immune response on the co-infection dynamics. 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. [ABSTRACT FROM AUTHOR]

The relationship between cancer and the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection is controversial. While SARS-CoV-2 can worsen the status of a cancer patient, many remission cases after SARS-CoV-2 infection have been recorded. It has been suggested that SARS-CoV-2 could have oncolytic properties, which needs further investigations. Mathematical modeling is a powerful tool that can significantly enhance experimental and medical studies. Our objective was to propose and analyze a mathematical model for oncolytic SARS-CoV-2 with immunity. The basic properties of this model, including existence, uniqueness, nonnegativity, and boundedness of the solutions, were confirmed. The equilibrium points were computed, and their existence conditions were determined. The global stability of the equilibria was proven using the Lyapunov theory. Numerical simulations were implemented to validate the theoretical results. It was found that the model has thirteen equilibrium points that reflect different infection states. Based on the model's results, the infection of cancer cells by SARS-CoV-2 can lead to a reduction in the concentration of cancer cells. Additionally, the induction of cytotoxic T lymphocytes (CTLs) decreases the number of cancer cells, potentially resulting in cancer remission or an improvement in the overall health of cancer patients. This theoretical result aligns with numerous studies highlighting the oncolytic role of SARS-CoV-2. In addition, given the limited availability of real data, further studies are essential to better comprehend the role of immune responses and their impact on the oncolytic role of SARS-CoV-2. [ABSTRACT FROM AUTHOR]

This paper deals with an optimal control problem for a viral infection model with cytotoxic T-lymphocytes (CTL) immune response. The model under consideration describes the interaction between the uninfected cells, the infected cells, the free viruses and the CTL cells. The two treatments represent the efficiency of drug treatment in inhibiting viral production and preventing new infections. Existence of the optimal control pair is established and the Pontryagin's maximum principle is used to characterize these two optimal controls. The optimality system is derived and solved numerically using the forward and backward difference approximation. Finally, numerical simulations are performed in order to show the role of optimal therapy in controlling the infection severity. [ABSTRACT FROM AUTHOR]