Discretization and Analysis of HIV-1 and HTLV-I Coinfection Model with Latent Reservoirs

This article formulates and analyzes a discrete-time Human immunodeficiency virus type 1 (HIV-1) and human T-lymphotropic virus type I (HTLV-I) coinfection model with latent reservoirs. We consider that the HTLV-I infect the CD4(+)T cells, while HIV-1 has two classes of target cells-CD4(+)T cells and macrophages. The discrete-time model is obtained by discretizing the original continuous-time by the non-standard finite difference (NSFD) approach. We establish that NSFD maintains the positivity and boundedness of the model's solutions. We derived four threshold parameters that determine 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 impact of latent reservoirs on the HIV-1 and HTLV-I co-dynamics is discussed. We show that incorporating the latent reservoirs into the HIV-1 and HTLV-I coinfection model will reduce the basic HIV-1 single-infection and HTLV-I single-infection reproductive numbers. We establish that neglecting the latent reservoirs will lead to overestimation of the required HIV-1 antiviral drugs. Moreover, we show that lengthening of the latent phase can suppress the progression of viral coinfection. This may draw the attention of scientists and pharmaceutical companies to create new treatments that prolong the latency period.

Stability of a delayed SARS-CoV-2 reactivation model with logistic growth and adaptive immune response

This paper develops and analyzes a SARS-CoV-2 dynamics model with logistic growth of healthy epithelial cells, CTL immune and humoral (antibody) immune responses. The model is incorporated with four mixed (distributed/discrete) time delays, delay in the formation of latent infected epithelial cells, delay in the formation of active infected epithelial cells, delay in the activation of latent infected epithelial cells, and maturation delay of new SARS-CoV-2 particles. We establish that the model's solutions are non-negative and ultimately bounded. We deduce that the model has five steady states and their existence and stability are perfectly determined by four threshold parameters. We study the global stability of the model's steady states using Lyapunov method. The analytical results are enhanced by numerical simulations. The impact of intracellular time delays on the dynamical behavior of the SARS-CoV-2 is addressed. We noted that increasing the time delay period can suppress the viral replication and control the infection. This could be helpful to create new drugs that extend the delay time period.

Stability of a delayed SARS-CoV-2 reactivation model with logistic growth and adaptive immune response.

This paper develops and analyzes a SARS-CoV-2 dynamics model with logistic growth of healthy epithelial cells, CTL immune and humoral (antibody) immune responses. The model is incorporated with four mixed (distributed/discrete) time delays, delay in the formation of latent infected epithelial cells, delay in the formation of active infected epithelial cells, delay in the activation of latent infected epithelial cells, and maturation delay of new SARS-CoV-2 particles. We establish that the model's solutions are non-negative and ultimately bounded. We deduce that the model has five steady states and their existence and stability are perfectly determined by four threshold parameters. We study the global stability of the model's steady states using Lyapunov method. The analytical results are enhanced by numerical simulations. The impact of intracellular time delays on the dynamical behavior of the SARS-CoV-2 is addressed. We noted that increasing the time delay period can suppress the viral replication and control the infection. This could be helpful to create new drugs that extend the delay time period.

Global stability of a general HTLV-I infection model with Cytotoxic T-Lymphocyte immune response and mitotic transmission

Mathematical models have been considered as a robust tool to support biological and medical studies of human viral infections. The global stability of viral infection models remains an important and largely open research problem. Such results are necessary to evaluate treatment strategies for infections and to establish thresholds for treatment rates. Human T-lymphotropic virus class I (HTLV-I) is a retrovirus which infects the CD4+T cells and causes chronic and deadly diseases. In this article, we developed a general nonlinear system of ODEs which describes the within-host dynamics of HTLV-I under the effect Cytotoxic T-Lymphocytes (CTLs) immunity. The mitotic division of actively infected cells are modeled. We consider general nonlinear functions for the generation, proliferation and clearance rates for all types of cells. The incidence rate of infec-tion is also modeled by a general nonlinear function. These general functions are assumed to satisfy a set of suitable conditions and include several forms presented in the literature. We determine a bounded domain for the system's solutions. We prove the existence of the system's equilibrium points and determine two threshold numbers, the basic reproductive number R0 and the CTL immunity stimulation number R1. We establish the global stability of all equilibrium points by con-structing Lyapunov function and applying Lyapunov-LaSalle asymptotic stability theorem. Under certain conditions it is shown that if R0 <= 1, then the infection-free equilibrium point is globally asymptotically stable (GAS) and the HTLV-I infection is cleared. If R1 < 1 < R0, then the infected equilibrium point without CTL immunity is GAS and the HTLV-I infection becomes chronic with no sustained CTL immune response. If R1 > 1, then the infected equilibrium point with CTL immu-nity is GAS and the infection becomes chronic with persistent CTL immune response. We present numerical simulations for the system by choosing special shapes of the general functions. The effect of Crowley-Martin functional response and mitotic division of actively infected cells on the HTLV-I progression are studied. Our results cover and improve several ones presented in the literature.(c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 4.0/).

Stability analysis of SARS-CoV-2/HTLV-I coinfection dynamics model

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. © 2023 the Author(s), licensee AIMS Press.

Global dynamics of IAV/SARS-CoV-2 coinfection model with eclipse phase and antibody immunity.

Coronavirus disease 2019 (COVID-19) and influenza are two respiratory infectious diseases of high importance widely studied around the world. COVID-19 is caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), while influenza is caused by one of the influenza viruses, A, B, C, and D. Influenza A virus (IAV) can infect a wide range of species. Studies have reported several cases of respiratory virus coinfection in hospitalized patients. IAV mimics the SARS-CoV-2 with respect to the seasonal occurrence, transmission routes, clinical manifestations and related immune responses. The present paper aimed to develop and investigate a mathematical model to study the within-host dynamics of IAV/SARS-CoV-2 coinfection with the eclipse (or latent) phase. The eclipse phase is the period of time that elapses between the viral entry into the target cell and the release of virions produced by that newly infected cell. The role of the immune system in controlling and clearing the coinfection is modeled. The model simulates the interaction between nine compartments, uninfected epithelial cells, latent/active SARS-CoV-2-infected cells, latent/active 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 prove the global stability of all equilibria. The global stability of equilibria is established using the Lyapunov method. The theoretical findings are demonstrated via numerical simulations. The importance of considering the antibody immunity in the coinfection dynamics model is discussed. It is found that without modeling the antibody immunity, the case of IAV and SARS-CoV-2 coexistence will not occur. Further, we discuss the effect of IAV infection on the dynamics of SARS-CoV-2 single infection and vice versa.

Global stability of a delayed SARS-CoV-2 reactivation model with logistic growth, antibody immunity and general incidence rate

Mathematical models have been considered as a robust tool to support biological and medical studies of the coronavirus disease 2019 (COVID-19). This new disease is caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). This paper develop a within-host SARS-CoV-2 dynamics model with logistic growth for healthy epithelial cells, humoral (antibody) immune response and general SARS-CoV-2-target incidence rate. The model is incorporated with four mixed (distributed/discrete) time delays, delay in the formation of latent infected epithelial cells, delay in the formation of active infected epithelial cells, delay in the activation of latent infected epithelial cells, and maturation delay of new SARS-CoV-2 particles. The model is formulated as a system of delay differential equations (DDEs). We establish that the model’s solutions are non-negative and ultimately bounded. We deduce that the model has three equilibria and their existence and stability are perfectly determined by two threshold parameters. We prove the global stability of the model’s equilibria by utilizing the Lyapunov method and applying the LaSalle’s invariance principle. To support and illustrate our theoretical findings we present numerical simulations for the model with a special form of the general incidence rate function. The effect of time delays on the SARS-CoV-2 dynamics is addressed. We observe that increasing time delays values can have the same impact as drug therapies in suppressing viral progression.