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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]

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.

The coronavirus disease 2019 (COVID-19) is caused by a new coronavirus known as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). SARS-CoV-2 infects the epithelial (target) cells by binding its spike protein, S, to the angiotensin-converting enzyme 2 (ACE2) receptor on the surface of epithelial cells. During the process of SARS-CoV-2 infection, ACE2 plays an important mediating role. In this work, we develop two models which describe the within-host dynamics of SARS-CoV-2 under the effect of humoral immunity, and considering the role of the ACE2 receptor. We consider two discrete (or distributed) delays: (i) Delay in the SARS-CoV-2 infection of epithelial cells, and (ii) delay in the maturation of recently released SARS-CoV-2 virions. Five populations are considered in the models: Uninfected epithelial cells, infected cells, SARS-CoV-2 particles, ACE2 receptors and antibodies. We first address the fundamental characteristics of the delayed systems, then find all possible equilibria. On the basis of two threshold parameters, namely the basic reproduction number, R0, and humoral immunity activation number, R1, we prove the existence and stability of the equilibria. We establish the global asymptotic stability for all equilibria by constructing suitable Lyapunov functions and using LaSalle's invariance principle. To illustrate the theoretical results, we perform numerical simulations. We perform sensitivity analysis and identify the most sensitive parameters. The respective influences of humoral immunity, time delays and ACE2 receptors on the SARS-CoV-2 dynamics are discussed. It is shown that strong stimulation of humoral immunity may prevent the progression of COVID-19. It is also found that increasing time delays can effectively decrease R0 and then inhibit the SARS-CoV-2 replication. Moreover, it is shown that R0 is affected by the proliferation and degradation rates of ACE2 receptors, and this may provide worthy input for the development of possible receptor-targeted vaccines and drugs. Our findings may thus be helpful for developing new drugs, as well as for comprehending the dynamics of SARS-CoV-2 infection inside the host. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the free vibration problem of a thermoelastic hollow cylinder in the context of the Lord and Shulman theory with one relaxation time. The eigenvalue approach is used to get the analytical solutions. The dispersion relations for the existence of various types of possible modes of vibrations are obtained. The validation of the roots for the dispersion relation is presented. The numerical results of frequency shift, natural frequency, and thermoelastic damping of vibrations have been presented graphically. PACS No.: 62.20.Dc. Nous etudions ici les vibrations libres d'un cylindre creux fait d'un materiau thermoelastique, en utilisant la theorie de Lord et Shulman avec un seul temps de relaxation. Nous utilisons une approche aux valeurs propres afin de trouver des solutions analytiques et obtenons les relations de dispersion pour les differents modes possibles de vibration. Nous validons les racines de ces relations de dispersion. Nous presentons graphiquement le deplacement en frequence, la frequence naturelle et l'amortissement thermoelastique des vibrations. [Traduit par la Redaction], 1. Introduction The linear theory of elasticity is of paramount importance in the stress analysis of steel, which is the most common engineering structural material. To a lesser extent, linear [...]

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]

A severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection can lead to morbidity and mortality. SARS-CoV-2 infects the epithelial cells of the respiratory tract and causes coronavirus disease 2019 (COVID-19). The immune system's response plays a significant role in viral progression. This article develops and analyzes a system of partial differential equations (PDEs), which describe the in-host dynamics of SARS-CoV-2 under the effect of cytotoxic T-lymphocyte (CTL) and antibody immune responses. The model characterizes the interplay between six compartments, healthy epithelial cells (ECs), latent infected ECs, active infected ECs, free SARS-CoV-2 particles, CTLs, and antibodies. We consider the logistic growth of healthy ECs. We first investigate the properties of the model's solutions, then, we calculate all steady states and determine the conditions of their existence and global stability. The global asymptotic stability is examined by constructing Lyapunov functions. The analytical findings are supported via numerical simulations. [ABSTRACT FROM AUTHOR]

This paper provides a method to study the effect of porosity and the thermal relaxation time in a poro-thermo-elastic medium using finite element method. One-dimensional application for a poro-elastic half-space is considered. Due to the complex basic equation, the finite element method has been adopted to solve this problem. The Laplace transformation technique is applied to the domain of time and the resulting equations are discretized by the finite element technique. The inversion of the Laplace transforms is obtained numerically. Numerical computations for displacements, temperatures and stresses are presented graphically for the fluid and the solid. [ABSTRACT FROM AUTHOR]