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Sensitive and specific detection of DNA is of great significance for clinical diagnosis. In this paper, an effective cascade signal amplification strategy was introduced into photoelectrochemical (PEC) biosensor for ultrasensitive detection of human T-cell lymphotropic virus type I (HTLV-I) DNA. This proposed signal amplification strategy integrates λ-exonuclease (λ-Exo) aided target recycling with hybridization chain reaction (HCR) and enzyme catalysis. In the presence of target DNA (tDNA) of HTLV-I, the designed hairpin DNA (h 1 DNA) hybridized with tDNA, subsequently recognized and cleaved by λ-Exo to set free tDNA. With the λ-Exo aided tDNA recycling, an increasing number of DNA fragments (output DNA, oDNA) were released from the digestion of h 1 DNA. Then, triggered by the hybridization of oDNA with capture DNA (cDNA), numerous biotin-labeled hairpin DNAs (h 2 DNA and h 3 DNA) could be loaded onto the photoelectrode via the HCR. Finally, avidin-labeled alkaline phosphatase (avidin-ALP) could be introduced onto the electrode by specific interaction between biotin and avidin. The ALP could catalyze dephosphorylation of phospho-L-ascorbic acid trisodium salt (AAP) to generate an efficient electron donor of ascorbic acid (AA), and thereby greatly increasing the photocurrent signal. By utilizing the proposed cascade signal amplification strategy, the fabricated PEC biosensor exhibited an ultrasensitive and specific detection of HTLV-I DNA down to 11.3 aM, and it also offered an effective strategy to detect other DNAs at ultralow levels. [ABSTRACT FROM AUTHOR]

• A model for HTLV-I infection that includes uninfected & infected CD4+T cells and HTLV-I-specific CD8+T cells. • To better understand the dynamics of HTLV-I infection, we incorporate a CTL immune response delay. • Applying Lyapunov functional procedures to determine global stability by the reproduction numbers R0 and R1. • The model with delay experiences a destabilization of the infected steady state leading to Hopf bifurcation and periodic solutions. • We estimate the length of delay to preserve the stability of bifurcating limit cycle using Nyquist criteria. This paper deals with a four dimensional mathematical model for Human T-cell leukemia virus type-I (HTLV-I) infection that includes delayed CD8+ cytotoxic T-cells (CTLs) immune response. The proposed system has three biologically feasible steady states, namely disease-free steady state, CTL-inactive steady state and an interior steady state. Our theoretical analysis demonstrates that local and global stability analysis are established by the two critical parameters R 0 and R 1 , basic reproduction numbers due to viral infection and due to CTLs immune response, respectively. The disease-free steady state E 0 is globally stable if R 0 ≤ 1 , and the HTLV-I infections are eliminated. The asymptotic-carrier steady state E 1 is globally stable if R 1 ≤ 1 < R 0 , which indicates HTLV-I infection is chronic without persistence of CTLs immune response. The interior steady state E 2 is globally asymptotic stable if R 1 > 1 , which implies that the HTLV-I infection is choric in persistence of CTLs immune response. Due to immune response delay, our proposed model undergoes a destabilization of the interior steady state leading to Hopf bifurcation and periodic oscillations. We estimate the length of time delay that preserve the stability of period-1 limit cycle. We also derived the direction and stability of Hopf bifurcation around the interior steady state by center manifold theory and normal form method. To determine the robustness of the model, we performed normalized forward sensitivity analysis with reference to R 0 and R 1. Our proposed model undergoes Hopf bifurcation with respect to the production rate of uninfected CD4+T cells h , removal rate of virus-specific CTLs d 4 , spontaneous infected CD4+T cell activation d 2 and transmissibility coefficient β. Implications of our numerical illustrations to the pathogenesis of HTLV-I infection and the development of HTLV-I related HAM/TSP are explored. [ABSTRACT FROM AUTHOR]

• A new HIV/HTLV-I co-infection model with latency and Cytotoxic T lymphocytes (CTLs) immune response is developed and rigorously analyzed. • Both silent and active infected cells have been considered. • Well-possedness of the model and existence of equilibria are established. • Global stability of the equilibria are established by means of Lyapunov functions. • We have presented numerical simulations to illustrate the effectiveness of our main results. 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. [ABSTRACT FROM AUTHOR]